A Crash-Course on Cooperative Wireless Networks
Transcript of A Crash-Course on Cooperative Wireless Networks
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A Crash-Course onCooperative Wireless Networks
Mischa Dohler
Senior Research Expert
CTTC, Barcelona, Spain
One-Day Short-Course, Melbourne, Australia 1
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– UMTS & WiMAX Capacity & Coverage Extension –
The Opportunity Driven Multiple Access (ODMA) protocol [1] in 3GPP (discontinued with R’99) as
well as the WiMAX standard facilitate relaying to enhance capacity and coverage. An extension to a
distributed deployment will be shown to further boost capacity.
Figure 1: Traditional and distributed relaying in UMTS and WiMAX.
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– WLAN Capacity & Coverage Extension –
Wireless Local Area Networks (WLANs) have sporadic hot-spot coverage in offices, cafes, train
stations, etc [2]. Traditional and distributed relaying increases capacity at WLAN cell edges and
closes coverage holes in sufficiently dense deployment areas (e.g. Orange’s UNIK service).
Figure 2: Coverage extension of high-capacity indoor WLAN towards outdoor users.
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– Sensor Networks –
Large scale sensor networks are only recently emerging with a vast gamut of applications [3].
Traditional and distributed relaying increases link reliability and - under some conditions - saves
energy and hence increases the network’s lifetime.
fire-detecting sensor
Figure 3: Distributed relaying sensor network for fire detection in forests.
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– Unmanned Aerial Vehicles –
Hybrid solutions are also foreseen, such as UAVs and sensor networks. In [4], it has been shown
that cooperative UAVs considerably increase the reliability of the transmission of sensor readings.
Transmit Sensor Cluster Receive Sensor Cluster
60 km
UAV Relay Cluster
10
00
m
Figure 4: Distributed and cooperative UAVs acting as relays, which can utilise beamforming, STCs,
multiplexing, etc., to relay sensor readings.
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– Design Dilemma –
• Above example systems have infinite design degrees of freedom, having triggered
endless white papers, conference and journal publications.
• Indeed, Google search results on ’cooperative wireless communications’ yielded:
– 1999: a handful (beginning of my personal research on this subject);
– 2008: almost one million in May 2008!
• All of these documents contain some related information; but, even if only 10% of them
are really useful to us, we would have to read and analyse 100,000 links. If we took 10
minutes for each, we would be occupied for 2 full years!
• Hence, my questions at the beginning of this tutorial:
– Is it really useful to start working in an area which seems to be so well explored?
And if so, what are the areas which still need to be explored?
– Will these systems yield decades of research but barely any commercial products?
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– Tutorial Emphasis –
• Due to the large amount of fundamental and advanced material, I had to cut down on
many important contributions and focused on novel material from 2005 − 2008.
• Also, you all have a very diverse background, making a coherent exposure difficult.
• The aim of this tutorial is thus to give you:
– a sufficient overview of the concept,
– some “feeling” for certain approaches,
– some detailed knowledge on some analysis,
– and some tools which allow extending the analysis.
• Ideally, this tutorial should inspire you and stipulate you to apply your knowledge and
enthusiasm to wireless distributed, cooperative relaying systems.
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– Tutorial Outline –
1. Preliminaries
2. Capacity Bounds
3. Hardware Realisation
4. Channel Characterisation
5. Transparent PHY Algorithms
6. Regenerative PHY Algorithms
7. MAC and Cross-Layer Design
8. System Considerations
9. The Road Ahead
10. References
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PART 1PRELIMINARIES
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– Preliminary Note –
• Due to your differing background and also due to the large degrees of freedom of
cooperative networks, a common understanding of the subject matter is pivotal.
• Such a common understanding is complicated by the fact that the same or similar
concepts are given entirely different names; or, entirely different concepts, the same
name.
• With the aim to harmonise at least some of the concepts, we will hence precede the
tutorial with some important preliminaries, i.e.:
1. useful definitions;
2. key milestones; and
3. design challenges.
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1.1 Useful Definitions
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– Structure of Definitions –
• We will give some useful definitions as per below structure:
System
Link
Node
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– System: Infrastructure –
• Infrastructure (physical or logical):
– infrastructure-based (ie available prior to deployment, eg cellular networks or WLAN),
– infrastructure-less (ie emerges after deployment or unavailable, eg ad hoc networks).
• Management of infrastructure:
– centralised (eg cellular network),
– decentralised (eg WLAN mesh network).
• Note that:
– you may have a decentralised infrastructure-based system (e.g. decentralised RRM)
– you may have a centralised infrastructure-less system (e.g. clustering)
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– System: Canonical Links –
• Four canonical information links between nodes are possible:
– point-to-point (traditional)
–
–
–
P2P P2MP MP2P MP2MP
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– System: Information Flow [1/5] –
• From these canonical links, we can build different flows through network:
– direct link
– serial relaying
–
–
– and composites thereof
• We differentiate further between flows:
– with/without interference between flows
– with/without direct link between nodes which use relays
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– System: Information Flow [2/5] –
• Serial Relaying:
Source
Relay#1
Destination
Relay#K
possible direct link
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– System: Information Flow [3/5] –
• Relaying:
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– System: Information Flow [4/5] –
• Relaying:
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– System: Information Flow [5/5] –
• Composites Thereof:
Source
Relay#2,1
Destinationpossible direct link
Space-
Time TRx
Relay#1 Relay#2,N2
Relay#(K-1),1
Relay#(K-1),NK-1
Space-
Time TRx
Relay#K,1
Relay#K,NK
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– System: Synch versus Asynch –
• The following synchronisms can occur at PHY layer:
– Synchronous Networks, i.e. all communications can be synchronised to the precision
of carrier and phase; facilitating e.g. distributed beamforming, space-time coding, etc.
– Asynchronous Networks, i.e. communication is not synchronised which requires
attention because synchronous designs break down.
• The following synchronisms can occur at MAC layer:
– Slotted Networks, i.e. access is allowed at predefined moments and phases only;
facilitating e.g. slotted ALOHA, etc.
– Unslotted Networks, i.e. access is allowed at any moment which usually deteriorates
throughput and delay.
• Note that achieving and maintaining synchronised networks is very complex if not in
most cases prohibitive.
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– Node: Node Behaviour –
• The nodes in the network can have the following behaviour:
– egoistic (no help)
– supportive (unidirectional help)
– cooperative (mutual help)
egoistic supportive cooperative
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– Node: Relaying Methods –
• Relaying: neither information nor waveform are modified, allowing for
simple power scaling and/or phase rotations; examples are:
– Amplify and Forward (AF), i.e. amplification of analogue signal;
– Linearly-Process and Forward (LF), i.e.
– Nonlinearly-Process and Forward (nLF), i.e. relay nonlinear soft information.
• Relaying: information (bits) or waveform (samples) are modified,
requiring more complex baseband operations; examples are:
– Estimate and Forward (EF), i.e. detect and forward estimated signal;
– Compress and Forward (CF), i.e.
– Decode and Forward (DF), i.e.
– Purge and Forward (PF), i.e. eliminate interference at relay;
– Aggregate/Gather and Forward (GF), i.e. perform source coding and compression.
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– Node: Relaying Access Protocols –
• Transmission and reception in relays leads to interference/competition, which needs to
be resolved by suitable access protocols.
• The following access protocols can be used:
– Time Division Relay Access (TDRA), i.e. reception and transmission happen in
different time moments/slots;
– Frequency Division Relay Access (FDRA), i.e. reception and transmission happen in
different frequency bands;
• Note that this is not to handle multiple access problems between relays, to which
CDMA, etc., are well applicable.
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– Link: Capacity over Gaussian Channel –
• Shannon proved that one can design codes facilitating a communication rate R
bits/symbol with arbitrarily small error.
• He also showed that these codes must be infinite (very long), so as to average out the
effect of noise.
• His theory was not concerned with code construction or code complexity, nor with
decoding delay.
• The maximum data rate at which reliable communication is possible is referred to as
capacity C of the channel and is independent of the signal processing used at either
end of the channel.
• The capacity (per dimension) of a AWGN channel with signal power constraint S and
noise power N is:
C =
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– Link: Ergodic Channel –
• A stochastic process is ergodic if the time averages may be used to replace ensemble
averages; or, no sample helps meaningfully to predict values that are very far away in
time from that sample (i.e. the stochastic process is not sensitive to initial conditions).
• An ergodic channel can support a maximum error-free transmission rate with 100%
reliability, which is referred to as capacity. Generally, the concept of average is
applicable, e.g. the capacity for a SISO channel is C = Eλ
{log2
(1 + λ S
N
)}.
λ
Codeword #n
Time t
Instantaneous
Channel Power
[dB]
codeword length T ∞→Codeword #n
Time t
Codeword #m
codeword length T ∞→
Figure 5: Fading behaviour of an ergodic channel.
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– Link: Non-Ergodic Channel –
• A stochastic process is non-ergodic if it is not ergodic; or, any sample helps
meaningfully to predict values that are very far away in time from that sample (i.e. the
stochastic process is sensitive to initial conditions).
• A non-ergodic channel cannot support a maximum error-free transmission rate with
100% reliability; however, it can support any given rate R with a certain probability
Pout(R) which is referred to as rate outage probability. Generally, the concept of
outage is applicable.
λ
Codeword #n
Time t
Instantaneous
Channel Power
[dB]
codeword length T ∞→Codeword #n
Time t
Codeword #m
codeword length T ∞→
Figure 6: Fading behaviour of a non-ergodic channel.26
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– Link: Diversity/Multiplexing Trade-Off [1/3] –
• Multiplexing Capability:
– achievable rate R is proportional to log SNR;
– proportionality factor is multiplexing gain r, i.e. r = R/ log SNR.
• Diversity Gain:
– error or outage probability Pe/out(R) is proportional to SNR−d;
– exponent d is called the diversity gain.
• Diversity d - Multiplexing r Trade-Off [5]:
– d and r are related by: d = − limSNR→∞ . . .
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– Link: Diversity/Multiplexing Trade-Off [2/3] –
• Example PAM modulation over Rayleigh Channel:
– constellation minimum distance Dmin ≈ √SNR/2R;
– error probability at high SNR isa Pe(R) ≈ 12
(1 −
√D2
min
4+D2min
)≈ . . .
– from which the diversity-multiplexing tradeoff follows as dPAM = . . .
• Example QAM modulation over Rayleigh Channel:
– constellation minimum distance Dmin ≈ √SNR/2R/2;
– error probability at high SNR is the same as above;
– from which the diversity-multiplexing tradeoff follows as dQAM = . . .
aNote that 1√1+x
≈ 1 − 12x
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– Link: Diversity/Multiplexing Trade-Off [3/3] –
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Spatial Multiplexing Gain r
Div
ersi
ty G
ain
d
PAM ModulationQAM Modulation
Figure 7: Diversity gain shows how fast outage / error exponent decreases with SNR; multiplexing
gain shows how fast the rate can be increased with SNR.
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– Link: Diversity/Coding/Rate Gains –
0 1 2 3 4 5 6 7 8 9 10
10−2
10−1
100
Signal−to−Noise Ratio SNR [dB]
Asy
mp
toti
c O
uta
ge
Pro
bab
ility
/ E
rro
r R
ate
Diversity Gain = 1, Rate = 1Diversity Gain = 2, Rate = 1Diversity Gain = 2, Rate = 2Diversity Gain = 2, Coding Gain = 2
increase in diversity order
increase in rate
increase in coding strength
Figure 8: Diversity (inclination), rate (right-shift) and coding (left-shift) gains can be inferred for outage
or error rates from above figure.
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1.2 Key Milestones
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– First Key Milestones –
• Early innovative contributions on supportive relaying as well as MIMO inspired the
concept of cooperative relaying and distributed MIMO.
• Surprisingly, relaying systems had already been studied for almost four decades! Early
key milestones are summarised on subsequent slides.
Supportive
Relaying
Cooperative
Relaying
1968
Meulen
1979
Cover & Gamal
2000
Dohler2002
Laneman,
Hunter
2003
Gupta,
Stefanov
2000
Laneman
1998
Sendonaris
et al
Distributed
MIMO
1996
3GPP ODMA
1998
Nix et al
MIMO1996
Foshini, Telatar
1998
Alamouti, Tarokh
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– My Pre-PhD Presentation Winter 1999/2000 –
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– Relaying Systems [1/4] –
• The method of relaying has been introduced in 1971 by van der Meulen in [6] and has also
been studied by Sato [7]. A first rigorous information theoretical analysis of the relay channel,
however, has been exposed by Cover and Gamal in [8], a more detailed description to which
can be found in his book [9].
• In these contributions, a source MT communicates with a target MT directly and via a relaying
MT. In [8] the maximum achievable communication rate has been derived in dependency of
various communication scenarios, which include the cases with and without feedback to either
source MT or relaying MT, or both. The capacity of such a relaying configuration was shown to
exceed the capacity of a simple direct link.
• It should be noted that the analysis was performed for Gaussian communication channels only;
therefore, neither the wireless fading channel has been considered, nor have the power gains
due to shorter relaying communication distances been explicitly incorporated into the analysis.
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– Relaying Systems [2/4] –
• Only in the middle of the 90s, research in and around the Concept Group Epsilon revived the
idea of utilising relaying to boost the capacity of wireless networks, thereby leading to the
concept of ODMA [1]. The power gains due to the shorter relaying links have been the main
incentive to investigate such systems to reach MTs out of BS coverage. The emphasis of the
study was its applicability to cellular systems, as well as a suitable protocol design; no
theoretical investigations into capacity bounds, etc., have been performed.
• Interesting milestones into the above-mentioned theoretical studies have been the contributions
by Sendonaris, Erkip and Aazhang, which date back to 1998 [10]. In their study, a very simple
but effective user cooperation protocol has been suggested to boost the uplink capacity and
lower the uplink outage probability for a given rate. The designed protocol stipulates a MT to
broadcast its data frame to the BS and to a spatially adjacent MT, which then re-transmits the
frame to the BS. Such a protocol certainly yields a higher degree of diversity because the
channels from both MTs to the BS can be considered uncorrelated.
• The simple cooperative protocol has been extended by the same authors to
more sophisticated schemes, which can be found in the excellent contributions [11] and [12].
Note that in its original formulation [10], no distributed space-time coding has been considered.
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– Relaying Systems [3/4] –
• The contributions by Laneman in 2000 [13] are a conceptual and mathematical extension to [10],
where energy-efficient multiple access protocols are suggested based on decode-and-forward
and amplify-and-forward relaying technologies. It has been shown that significant diversity and
outage gains are achieved by deploying the relaying protocols when compared to the direct link.
Note again, that no distributed space-time coding has been considered.
• The case of distributed space-time coding has been analysed by Laneman in his PhD
dissertation [14]. In his thesis, information theoretical results for distributed SISO channels with
possible feedback have been utilised to design simple communication protocols taking into
account systems with and without temporal diversity, as well as various forms of cooperation. He
has demonstrated that cooperation yields full spatial diversity, which allows drastic transmit
power savings at the same level of outage probability for a given communication rate.
• A vital asset of his thesis is also a discussion on the applicability of the suggested protocols to
cellular and ad-hoc networks. However, [14] does not incorporate an analysis of distributed
cooperative MIMO multi-stage communication systems.
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– Relaying Systems [4/4] –
• Gupta and Kumar were the first to statistically analyse the information theoretically offered
throughput for large scale relaying networks [15]. They showed that under somewhat ideal
situations of no interference, hop-by-hop transmission and pre-defined terminal locations,
capacity per MT decreases by 1/√
M with an increasing number of MTs M in a fixed
geographic area. They also showed that if the terminal and traffic distributions are random, then
the capacity per terminal decreases even in the order of 1/√
M log M .
• The analysis in [15] has been extended by the same authors to more general communication
topologies, where the interested reader is referred to the landmark paper [16].
• Furthermore, Grossglauser and Tse have shown that mobility counteracts the decrease in
throughput for an increasing number of users in a fixed area [17]. The protocols suggested
therein benefit from the decreased power for a hop-per-hop transmission for decreasing
transmission distances. It also benefits from the location variability due to mobility, i.e. a packet
is picked up from the source MT by any passing by r-MT and only re-transmitted (and hence
delivered) when passing by the target MT.
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– MIMO Systems –
• Contributions on MIMO systems have flourished ever since the publication of the landmark
papers by Telatar [18] and Foschini & Gans [19] on capacity and Foschini [20], Alamouti [21]
and Tarokh [22, 23] on the construction of suitable space-time transceivers.
• The BLAST system introduced by Foschini in 1996 [20], a transmitter spatially multiplexes signal
streams onto different transmit antennas which are then iteratively extracted at the receiving side
using the fact that the fades from any transmit to any receive antenna are uncorrelated and of
different strength. The BLAST concept has ever since been extended to more sophisticated
systems, a good summary of which can be found in [24].
• Alamouti introduced a very appealing transmit diversity scheme by orthogonally encoding two
complex signal streams from two transmit antennas, thereby achieving a rate one space-time
block code [21].
• His work was then mathematically enhanced by the landmark paper of Tarokh [23], who
essentially exposed various important properties of space-time block codes. In [22], he also
showed how to construct suitable space-time trellis codes which were shown to yield diversity
and coding gain.
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– Distributed MIMO Systems [1/2] –
• A system utilising the advantages of both MIMO and relaying has been suggested by M. Dohler
in the winter 1999/2000 and has hence become one of the main research topics within the
Mobile Virtual Centre of Excellence (M-VCE).
• Numerous studies [25] have led to a set of patents [26], which are backed by about 20 industrial
members, such as Vodafone, Nokia, Philips, Nortel Networks, Samsung, etc.
• The studies encompassed the following (in timely order):
– downlink distributed receive diversity in cellular systems
– downlink distributed MIMO in cellular systems
– uplink distributed MIMO in cellular systems
– introduction of distributed relaying to cellular systems
– extension of the above to WLAN and hot-spot systems
– generalisation to arbitrary distributed relaying topologies
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– Distributed MIMO Systems [2/2] –
• A landmark contribution on relaying systems deploying multiple antennas at transmitting and
receiving side has been made by Gupta and Kumar [16]. The network topology exposed therein
is the most generic flat topology, i.e. any MT may communicate with any other MT.
• In [16], an information theoretic scheme for obtaining an achievable communication rate region
in a network of arbitrary size and topology has been derived. The analysis showed that
sophisticated multi-user coding schemes are required to provide the derived capacity gains.
Exposed theory is fairly intricate making the design of realistic protocols a difficult task.
• Specific distributed space-time coding schemes have also been suggested recently, e.g. by A.
Stefanov and E. Erkip [27]. In this publication, two spatially adjacent MTs cooperate to achieve
a lower frame error rate to one or more destination(s), where a quasi-static fading channel has
been assumed. Distributed space-time trellis codes have been designed which maximise the
performance for the direct link from either of the MTs to the destination and the relaying link.
• In [28], A. Ozgur et al. have shown for the first time that linear transport capacity scaling is
possible in a large network by means of cooperative hierarchies and distributed MIMO.
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1.3 Design Challenges
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– System Design –
The design of any system is a very complex interplay between business and technology.
Business CaseServices, CAPEX, OPEX, etc.
RequirmentsScenario, Channel Model, Tx Powers, etc.
Performance AnalysisCapacity, Link & System Level, Formal Verfication, etc.
Algorithmic DesignPHY, MAC, NTW, Applications, etc.
Hardware Designµ-Controller, Memory, Amplifiers, etc.
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– Example Challenges for Business Case –
Services
• identification of commercially viable services using relaying topology
• seamless integration into existing services
• facilitation of simple billing mechanisms and incentive schemes
CAPEX & OPEX
• correct estimation of short- and mid-term CAPEX
• correct estimation of mid- and long-term OPEX
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– Example Challenges for Requirements –
Channel Modelling
• measurements of channel in distributed scenarios (low Tx & Rx)
• deterministic modelling using e.g. ray tracing tools (specific environments)
• stochastic-empirical modelling, reflecting
– temporal, spectral and spatial dependency of
– pathloss (pathloss coefficient, breakpoint behaviour, etc)
– shadowing (statistics, variance)
– fading (Doppler, PDP; statistics, variance)
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– Example Challenges for Performance Analysis –
Link Capacity
• closed form Shannon capacity expressions for systems with the following properties:
– cooperative, multi-user, MIMO
– broadcast, multiple access or general relaying channel
– Rayleigh fading channel
• extension of the above to generalised fading (statistics, correlation, temporal behaviour)
• extension of the above to the case of imperfect channel state information
• max mutual information for other constraints (non-Gaussian codebooks, delay limits)
• synthesis of topology from the above insights and design guidelines
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– Example Challenges for Hardware Design –
Radio Front-End
• distributed synchronisation for cooperative communication
• saturation of amplifiers (near-far effect during cooperation)
• filter to minimise power spill-over during relaying
• low noise transparent relaying mechanisms
• efficiency and power consumption
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– Example Challenges for Algorithmic Design [1/2] –
Physical Layer
• choice of relaying, ie transperant/regenerative/hybrid [very well explored]
• degree of cooperation, ie number and choice of nodes [well explored]
• determination of suitable performance metrics (total power, complexity, etc.)
• tangible cross-layer design (coding, modulation, power control, etc.)
• codes which are robust to synchronisation, channel estimation errors, etc.
• codes which can easily trade diversity gains, coding gains, throughput and complexity
• novel interference cancellation techniques (use of temporal characteristics)
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– Example Challenges for Algorithmic Design [2/2] –
MAC Layer
• determination of suitable performance metrics (protocol overhead, etc.)
• unifying framework for distributed MACs
• tangible cross-layer design (ACM, power control, persistency factor, packet length,
routing)
• optimum access strategies (CSMA/reservation/hybrids)
• interference mitigation and avoidance protocols
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Open Issues
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– Open Issues –
There is one important thing which really deserves some attention:
• A complete and consistent set of
– terms,
– notation,
– concepts, and
– protocols,
used in the context of cooperative systems.
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PART 2CAPACITY BOUNDS
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– A Little Glimpse [16] –
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– Preliminary Note –
• Obtaining the capacity of a wireless system is vital in understanding the achievable
rates and their reliability.
• There are more than 100 highly complex contributions available today, which requires us
to concentrate on a very few of them.
• For this reason, we will concentrate on the following topics:
1. achievable rate region in the case of cooperation;
2. rate outage probabilities in the case of cooperation;
3. rate & outage for distributed space-time (block) coding;
4. throughput for multi-hop distributed space-time block coding;
5. capacity scaling in hierarchical MIMO cooperation structure.
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2.1 Achievable Rate Region
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– System Model –
Following [11], we would like to know what is the maximum achievable network rate for
below simple system assuming ergodic channels. From this, more general topologies can
be analysed as well as the rate outage probability obtained.
s-MT#1
s-MT#2
t-MT#0
Encoder s-MT#1
Encoder
s-MT#2
W1
Y1
Y2
W2
X1
K10
K20
K12
K21
X2
Z2
Z1
Z0 Y0
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– Mathematical Formulation –The mathematical formulation of the cooperative communication model is [11]:
Y0 = (1)
Y1 = K21 · X2 + Z1 (2)
Y2 = (3)
where
• Y0, Y1, Y2 are the received signal at the target mobile terminal (t-MT), first source MT
(s-MT#1) and second source MT (s-MT#2), respectively;
• X(1,2) is the signal transmitted by s-MT (1,2);
• Kij are the respective Rayleigh fading coefficients with variance ξ2ij and are assumed
to be frequency-flat and ergodic;
• Z0, Z1, Z2 are the respective AWGN components with total spectral density N0.
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– Transmitters & Receivers [1/2] –
• Three cases concerning channel knowledge at the Tx are considered in [11]:
– user i knows nothing about Ki0,
– user i knows knows only the phase of Ki0,
– user i knows knows amplitude and phase of Ki0.
• The user’s transmitters use the classical superposition coding (super-imposed
codebooks of large block length).
• The receivers utilise suitable decoders, such as:
– successive decoder,
– sliding-window decoder,
– backward decoder.
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– Transmitters & Receivers [2/2] –
• Without violating causality, s-MT#1 structures its information W1 such that:
– information W10 is sent at rate R10 directly to BS with fractional power P10,
– information W12 to be sent at rate R12 to the BS via #2 with fractional power P12,
– cooperative information U1 is sent directly to BS with fractional power PU1.
• The encoder then constructs signal X1 = X10 + X12 + U1 to be sent with power
P1 = P10 + P12 + PU1.
• s-MT#2 proceeds similarly as s-MT#1.
• It is imperative that power and rate allocations are such that all codebooks can be
perfectly decoded.
• For a given power constraint, it is hence the aim to determine the maximum feasible rate
in such a network.
58
�
�
�
�
– Achievable Rates [1/4] –
Theorem [11]: An achievable rate region for the system given in (1)−(3) is the closure of the convex
hull of all rate pairs (R1, R2) such that R1 = R10 + R12 and R2 = R20 + R21, with
R12 < (4)
R21 < (5)
R10 < (6)
R20 < E
{C
(K2
20P20
N0
)}(7)
R10 + R20 < E
{C
(K2
10P10 + K220P20
N0
)}(8)
R10 + R20 + R12 + R21 < E
{C
(K2
10P10 + K220P20 + 2K10K20
√PU1PU2
N0
)}(9)
where C(x) = 12 log2(1 + x) is the capacity of an AWGN channel and E{·} denotes the
expectation with respect to the fading realisations Kij .
59
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�
�
– Achievable Rates [2/4] –
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Rate R2
Rat
e R
1
no cooperation
cooperation
ideal
Figure 9: Symmetric rate region for no cooperation, ideal cooperation with error-free inter-user
channel, and realistic cooperation with good inter-user channel (E{K12} = .95); N0 = 1,
P1 = P2 = 2, E{K10} = E{K20} = .63 [11].
60
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�
�
– Achievable Rates [3/4] –
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Rate R2
Rat
e R
1 ideal cooperation
cooperation
no cooperation
Figure 10: Asymmetric rate region for no cooperation, ideal cooperation with error-free inter-user
channel, and realistic cooperation with medium inter-user channel (E{K12} = .71); N0 = 1,
P1 = P2 = 2, E{K10} = .95 and E{K20} = .30 [11].
61
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�
– Achievable Rates [4/4] –
• Ideal cooperation is for a noiseless inter-user channel and serves as an upper bound of
cooperation. No cooperation (ignoring Y1 and Y2) yields the typical multiple access
channel. In the cooperative case, as the inter-user channel degrades, performance
approaches that of no cooperation.
• Points of interest are the
– equal rate point (R1 = R2),
– maximum rate sum point (max(R1 + R2)),
– degraded relay rate points (R1 = 0, R2 �= 0 and R1 �= 0, R2 = 0).
• [11] showed that in the design region of interest “increase in sum capacity ≈ increase in
coverage area”.
• [11] also demonstrated that repetition-based coding using CDMA spreading sequences
performs well within the rate regions.
62
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�
2.2 Rate Outage Probabilities
63
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�
– System Model [1/2] –
The characteristics of below coded cooperative scheme are [94, 95]:
• each user tries to transmit (punctured) incremental redundancy to its partner;
• overall code might be block or convolutional code or hybrid;
• no feedback is required, because decisions are based on CRC.
s-MT#1
s-MT#2
t-MT#0
own bitsCRC
Decoder
RCPC
N1 user 1 bits N2 user 2 bits
N1 user 2 bits N2 user 1 bits
Frame 1 Frame 2
Frame 1 Frame 2
punctured N1 bitsto Tx
partner'sbits
RCPC
N2 bits
N2 bits
no
yes
CRC
check
64
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�
– System Model [2/2] –The system operates as follows:
• Rate R code of each user has length N1 + N2; we define α = N1/(N1 + N2).
• N1 valid punctured code bits are transmitted to t-MT & partner.
• If partner decodes N1 successfully (CRC check), then remaining N2 parity bits are sent
by partner to t-MT; otherwise the partner’s own N2 parity bits are sent.
• 4 cases are possible, which the t-MT is either informed of or decides blindly (CRC):
#1
#2
#2's parity
#1's parity
x x
#1's parity
#2's parity
x
#1's parity
#1's parity
x
#2's parity
#2's parity
65
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�
�
– Outage Probability [1/4] –
• For an instantaneous SNR γ, the ’capacity’ of the link is given as C(γ) = log2(1 + γ)bits/s/Hz.
• The channel is in outage, if the ’capacity’ falls below a threshold R; the corresponding
outage event is C(γ) < R or γ < . . ..
• The outage probability is hence
Pout = Pr(γ < . . .) =∫ ...
...pγ(γ)d γ, (10)
where pγ(γ) denotes the pdf of the SNR.
• For a Rayleigh fading process with mean power Γ, γ is negative-exponentially
distributed as 1Γe−γ/Γ and the outage probability is hence
Pout = . . . (11)
66
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�
– Outage Probability [2/4] –Case 1 (Θ = 1) :
• Both partners decode correctly, which for the inter-user channel means that the capacity
offered by the channel is greater than the rate, i.e.
C12(γ12) = α log2(1 + γ12) > R
C21(γ21) = α log2(1 + γ21) > R
• The outage event for both users given the cooperative information can be written as
C10(γ10, γ20|Θ = 1) = α log2(1 + γ10) + . . . R
C20(γ10, γ20|Θ = 1) = + . . . R
Cases 2,3 & 4 (Θ = 2,3,4) :
• These cases are obtained in a similar fashion as above.67
�
�
�
�
– Outage Probability [3/5] –
• We can calculate the outage probability for the first user and the first outage case as:
Pout,1(Θ = 1) = Pr(link12 is not in outage) AND
Pr(link21 is not in outage) AND
Pr(link10 is in outage) AND
Pr(link20 is in outage)
= . . .
68
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�
�
– Outage Probability [4/5] –
• Combining the 4 possible cases, the total outage probability for user 1 can hence be
calculated as [95]
Pout,1 = Pr(γ12 > 2R/α − 1) · Pr(γ21 > 2R/α − 1)
·Pr((1 + γ10)α(1 + γ20)1−α < 2R) +
Pr(γ12 < 2R/α − 1) · Pr(γ21 < 2R/α − 1)
·Pr(γ10 < 2R − 1) +
Pr(γ12 > 2R/α − 1) · Pr(γ21 < 2R/α − 1)
·Pr((1 + γ10)α(1 + γ10 + γ20)1−α < 2R) +
Pr(γ12 < 2R/α − 1) · Pr(γ21 > 2R/α − 1)
·Pr(γ10 < 2R − 1).
• Closed form expressions for the Rayleigh fading case can be found in [95].
69
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�
– Outage Probability [5/5] –
−10 −5 0 5 10 15 20 25 3010
−4
10−3
10−2
10−1
100
Mean (Uplink) SNR Γ [dB]
Out
age
Pro
babi
lity
C<
R no cooperation
coded cooperation
Figure 11: Outage versus mean uplink SNR, where inter-user channel is 10dB weaker; α = 0.7,
R = 0.5bits/s/Hz.
70
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2.3 Distributed ST(B)C
71
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�
– System Model –
• Transmitter:
– number of distributed transmit antennas: t
– transmitted space-time codeword: x ∈ Ct×1
– transmit power constraint: tr(E{xxH
}) ≤ S
• Channel:
– channel from transmitter i ∈ (1, t) to receiver j ∈ (1, r): hi,j
– fading realisations of hi,j : frequency-flat & uncorrelated
– grouping of sub-channel gains hi,j : H
• Receiver:
– received signal: y = Hx + n
– r−dimensional noise vector n has variance N per entry
• Cooperative Link:
– assumed to be error-free (!)
72
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�
– Exact MIMO Capacity [1/5] –
H =
⎛⎜⎜⎜⎜⎜⎝
h11 h12 · · · h1,t
h21 h22 · · · h2,t
......
. . ....
hr,1 hr,2 · · · hr,t
⎞⎟⎟⎟⎟⎟⎠
We assume first that each sub-channel realisation
hi,j is Rayleigh distributed with unit power, i.e.
E{|hi,j |2
}= 1, which will be relaxed later on.
InformationSource
Space-TimeEncoder
Space-TimeDecoder
InformationSink
s s
t
Transmit
Antennas
r
Receive
Antennas
h11
hr,t
H
MIMO
Channel
Figure 12: Multiple-Input-Multiple-Output (MIMO) transceiver model.
73
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�
– Exact MIMO Capacity [2/5] –Telatar proved in his landmark theorem that the MIMO capacity can be expressed as [18]
C =∫ ∞
0
log2
(1 +
λ
t
S
N
)·
m−1∑k=0
k!(k + n − m)!
[Ln−m
k (λ)]2
λn−me−λdλ (12)
where m � min{t, r}, n � max{t, r}. Furthermore, Ln−mk (λ) is the associated Laguerre
polynomial of order k and λ is an unordered eigenvalue of the Wishart matrix
W �
⎧⎨⎩HHH r < t
HHH r ≥ t(13)
The capacity in (12) can also be expressed as
C = Eλ
{m log2
(1 +
λ
t
S
N
)}(14)
with
pdfλ(λ) =1m
m−1∑k=0
k!(k + n − m)!
[Ln−m
k (λ)]2
λn−me−λ. (15)
74
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�
– Exact MIMO Capacity [3/5] –
The intricate integral expression can be solved in explicit form as [100]
C =m−1∑k=0
k!(k + d)!
[k∑
l=0
A2l (k, d) C2l+d(a) + (16)
k∑l1=0
k∑l2=0,l2 �=l1
(−1)l1+l2Al1(k, d) Al2(k, d) Cl1+l2+d(a)
]
where d � n − m, Al(k, d) � [(k + d)!]/[(k − l)! (d + l)! l!] and
Cζ(a) =1
log(2)
ζ∑μ=0
ζ!(ζ − μ)!
[(−1)ζ−μ−1(1/a)ζ−μe1/aEi(−1/a) (17)
+ζ−μ∑k=1
(k − 1)!(−1/a)ζ−μ−k
]
Here, Ei(ζ) is the exponential integral function.
75
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�
– Exact MIMO Capacity [4/5] –
Asymptotic capacity increases linearly with SNR and m = min{t, r}:
0 10 20 30 40 50 60 70 80 90 1000
50
100
150
200
250
300
SNR [dB]
Cap
acity
[bits
/s/H
z]
8 × 8
4 × 12
12 × 4
1 × 16
16 × 1
Monte−CarloExact − IterativeExact − Explicit
Figure 13: Capacity versus SNR for various configurations of t × r.
76
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�
– Exact MIMO Capacity [5/5] –
To obtain an exact expression for the case of unequal channel gains, i.e. distributed MIMO with
channel matrix Hd, has evaded a closed solution until today; we will hence invoke an upper capacity
bound.
To this end, we remember that (12) was derived from
C = EH
{log2 det
(Ir +
HHH
t
S
N
)}. (18)
Invoking Jensen’s inequality, it is easy to show that
det(Ir +
HHH
t
S
N
)≥ det
(Ir +
HdHHd
t
S
N
), (19)
for ‖H‖2 = ‖Hd‖2, where ‖H‖ denotes the Frobenius norm of H.
This means that the distributed MIMO capacity with unequal sub-channel gains can be
upperbounded by the capacity of an equivalent MIMO system with equal sub-channel gains and a
total channel power equal to the distributed system.
77
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– Exact O-MIMO Capacity [1/9] –
Orthogonal space-time block codes (STBCs) is a signal processing scheme which orthogonalises
the MIMO channel, henceforth referred to as O-MIMO. For simplicity, we will refer to the maximum
mutual information achievable with such signal processing as O-MIMO Capacity.
We will consider distributed orthogonal STBCs of arbitrary rate R. Furthermore, the sub-channel
realisation hi,j obey Nakagami fading with fading parameter f . The sub-channels may have
different gains, thereby reflecting a possibly distributed deployment.
Distributed
Space-Time Block Encoder
Distributed
Space-Time Block Decoder
Channel
Encoder
FractionalSTBC
Space-Time
Block Decoder
Channel
Decoder
s
s
h11
hr,t
O-MIMO
Channel
FractionalSTBC
FractionalSTBC
Receiver
Receiver
Receiver
Information
Sink
Information
Source
H
Figure 14: Distributed Space-Time Block Code transceiver model.
78
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– Exact O-MIMO Capacity [2/9] –
The capacity (maximum mutual information) for O-MIMO channels with fixed channel coefficients can
generally be expressed as [96]
C = R log2
(1 +
1R
‖H‖2
t
S
N
)(20)
‖H‖ denotes the Frobenius norm of H, the square of which is given as
‖H‖2 =t∑
i=1
r∑j=1
|hij |2 = tr(HHH
)(21)
where tr(·) denotes the trace operation. From (21), it is clear that
‖Ht×r‖ = ‖h1×t·r‖ (22)
where h � vectorized(H).
79
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�
– Exact O-MIMO Capacity [3/9] –To simplify subsequent notation, we define
u � t · r (23a)
λi � hih∗i (23b)
λ � ‖h‖2 =u∑
i=1
hih∗i =
u∑i=1
λi (23c)
γi � E {hih∗i } (23d)
With reference to definitions (23), the capacity over an ergodic flat Rayleigh fading O-MIMO channel
can be expressed as
C = Eλ
{R log2
(1 +
1R
λ
t
S
N
)}(24)
=∫ ∞
0
R log2
(1 +
1R
λ
t
S
N
)pdfλ(λ)dλ (25)
where the pdfλ(λ) of λ =∑
λi solely depends on the statistics of each sub-channel.
80
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�
�
– Exact O-MIMO Capacity [4/9] –From (23c) it is clear that the pdfλ(λ) can be obtained via a u-fold convolution in the respective pdfs
of λi, i.e.
pdfλ(λ) = pdfλ1(λ1) ∗ pdfλ2(λ2) ∗ . . . ∗ pdfλu(λu) (26)
where ∗ denotes the operation of convolution. Although analytically feasible, it has been proven
easier to use the moment generating function (MGF) to solve (26). The MGF φλ(s) of λ is defined
as
φλ(s) �∫ ∞
0
pdfλ(λ)esλ dλ (27)
the application of which is known to transform (26) into
φλ(s) =u∏
i=1
φλi(s) (28)
The pdf of λ is now obtained by performing the inverse transformation, obtained as
pdfλ(λ) =1
2πj
∫ σ+j∞
σ−j∞φλ(s)e−sλ ds (29)
Operations (27) and (29) are rarely performed since tabled, see e.g. [87].
81
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�
– Exact O-MIMO Capacity [5/9] –The MGF of the instantaneous power λi can be calculated from the respective statistics. For
instance, for Rayleigh with pdfλ(λ) = 1γ e−λ/γ , and Nakagami as
φλ(s) =
⎧⎨⎩ Rayleigh
(1 − γs)−f Nakagami(30)
which allow one to find closed form expressions for the capacity of channels with the above-given
statistics and possibly different channel gains γi, as shown below.
If all sub-channel gains are equal then γ1 = . . . = γu, henceforth simply denoted as γ. From (30)
and (28), the MGF of the instantaneously experienced power λ can then be expressed as
φλ(s) =1
(1 − γs)u (31)
the inverse of which yields the desired pdf [90]
pdfλ(λ) =1
Γ(u)λu−1
γue−λ/γ (32)
82
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�
– Exact O-MIMO Capacity [6/9] –
With reference to (25) and some changes in variables, the capacity of the orthogonalised MIMO
channel can be expressed in closed form as
C =R
Γ(u)
∫ ∞
0
log2
(1 + λ
1R
γ
t
S
N
)λu−1 e−λ dλ (33)
=R
Γ(u)· Cu−1
(1R
γ
t
S
N
)(34)
where Cζ(a) is the Capacity Integral given in closed form in (35).
The procedure to find the O-MIMO capacity is hence always the same:
1. determine the MGF from the PDF of each link i;
2. multiply all MGFs of all u links;
3. determine the PDF from this resultant MGF;
4. calculate the capacity using this PDF.
83
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�
– Exact O-MIMO Capacity [7/9] –
The capacity (maximum mutual information) for O-MIMO channels over Nakagami fading channels
with unequal sub-channel gains γi∈(1,u) and fading parameters fi∈(1,u) can be expressed as [97]
C = Ru∑
i=1
fi∑j=1
Ki,j
Γ(j)Cj−1
(1R
γi
jt
S
N
)(35)
Ki,j =
(− 1
Rγi
fitSN
)j−fi
(fi − j)!∂fi−j
∂sfi−j
⎡⎢⎢⎣
u∏i′=1,i′ �=i
1(1 − 1
Rγi′fi′ t
SN · s
)fi′
⎤⎥⎥⎦
s=
�
1R
γifit
SN
�−1
(36)
Cζ(a) =1
log(2)
ζ∑μ=0
ζ!(ζ − μ)!
[(−1)ζ−μ−1(1/a)ζ−μe1/aEi(−1/a) (37)
+ζ−μ∑k=1
(k − 1)!(−1/a)ζ−μ−k
]
where Γ(·) is the complete Gamma function and Ei(ζ) is the exponential integral function.
84
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�
– Exact O-MIMO Capacity [8/9] –
Capacity saturates fast with f and it never exceeds the Gaussian channel:
2 4 6 8 10 12 14 16 18 202
2.5
3
3.5
Nakagami−f Fading Factor
Cap
acity
[bits
/s/H
z]
1 Tx2 Tx Alamouti3 Tx − 3/4−Rate4 Tx − 3/4−Rate3 Tx − 1/2−Rate4 Tx − 1/2−RateGaussian Channel
Figure 15: Capacity versus the Nakagami f fading factor; SNR=10dB, r = 1.
85
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– Exact O-MIMO Capacity [9/9] –
Capacity of distributed STBC scheme exhibits a high stability:
γ1Fractional
STBC
FractionalSTBC
γ2
ChannelEncoder
InformationSource
Space-Time
Block Decoder
Channel
Decoder
InformationSink
(a) Distributed Alamouti scheme with unequal
sub-channel gains due to different pathloss &
shadowing.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.5
1
1.5
2
2.5
3
3.5
4
4.5
γ1
Cap
acity
[bits
/s/H
z]
1 Tx − SISO (γ1)
1 Tx − SISO (γ2=2−γ
1)
2 Tx − Alamouti (γ1 & γ
2=2−γ
1)
(b) Capacity versus the normalised power γ1
in the first link over a Nakagami fading channel;
SNR=10dB, f = 10 and γ2 = 2 − γ1.
Figure 16: Topology and performance of distributed Alamouti scheme.
86
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�
– Approximate MIMO Capacity [1/2] –To simplify analysis for the subsequent multi-stage topology, we use log2(1 + x) ≈ √
x and define
Λ(t, r) � Eλ
{m√
λ/t}
; this approximates the MIMO capacity as
C ≈√
γS
N· Λ(t, r) (38)
For the Rayleigh fading MIMO channel, we can obtain Λ(t, r) in explicit form as
Λ(t, r) =1√t
m−1∑k=0
k!(k + d)!
Γ3(d + k + 1)Γ(d + 32 )Γ(k − 1
2 )(k!)2Γ(d + 1)Γ(− 1
2 )× (39)
3F2(−k, d +32,32; d + 1,
32− k; 1)
where 3F2(·) is the generalised hypergeometric function with three parameters of type 1 and two
parameters of type 2. For the generic Nakagami fading MIMO channel, we have
Λ(t, r) =
√R
t
√S
N
u∑i=1
fi∑j=1
Ki,jΓ(j + 0.5)
Γ(j)
√γi
j(40)
87
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�
�
– Approximate MIMO Capacity [2/2] –
The error between exact and approximate capacity expressions does not exceed 10%:
0 1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
SNR [dB]
Cap
acity
[bits
/s/H
z]
1 Tx, 1 Rx (exact)1 Tx, 1 Rx (approx)8 Tx, 2 Rx (exact)8 Tx, 2 Rx (approx)2 Tx, 8 Rx (exact)2 Tx, 8 Rx (approx)8 Tx, 8 Rx (exact)8 Tx, 8 Rx (approx)
Figure 17: Exact and approximate capacities versus SNR for various array configurations.
88
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�
– Approximate O-MIMO Capacities –
The same approach can be taken to calculate the approximate capacity for various O-MIMO
channels, some of which are summarised below as
Λ(t, r) =
⎧⎪⎪⎨⎪⎪⎩
√R√t
Γ(u+1/2)Γ(u) O-MIMO Rayleigh - Equal Channel Gains
√R√ft
Γ(fu+1/2)Γ(fu) O-MIMO Nakgami - Equal Channel Gains
√Rπ√t
∑ui=1 Ki
√γi O-MIMO Rayleigh - Unequal Channel Gains,
(41)
where Γ(x) is the Gamma function, R the rate of the STBC, t the number of transmit antennas, r
the number of receive antennas, f the Nakagami fading parameter, u = t · r, and the constants K i
are obtained as [100]
Ki =u∏
i′=1,i′ �=i
γi
γi − γi′. (42)
89
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�
2.4 Multi-Stage Distributed STBC
90
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�
�
– Choice of (practical) Topology [1/4] –
• The theoretical findings of Cover, Kumar, Gupta, Tse, Laneman, etc. are very interesting,
however, very difficult to deploy and optimise in a practical manner. Already the multiple access,
broadcast and single-hop relaying schemes over Gaussian channels, as analysed by Cover, are
fairly intricate to optimise.
• Cover [9, chapter 14.3] has established the capacity bounds for the multiple access channel
where, using sophisticated multi-user (MU) transceivers, the achievable rates for 2 users are
R1 ≤ 12
log2
(1 +
P1
N
), R2 ≤ 1
2log2
(1 +
P2
N
), R1+R2 ≤ 1
2log2
(1 +
P1 + P2
N
)
• Using orthogonal FDMA, for example, the achievable rates for 2 users are [9]
R1 =W1
2log2
(1 +
P1
NW1
), R2 =
W2
2log2
(1 +
P2
NW2
)
• The MU case (dotted line) and FDMA case (solid line) are depicted in Figure 18. Similar curves
are obtained for the broadcast channel as well as relaying channel.
91
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�
– Choice of (practical) Topology [2/4] –
Loss in rate due to sub-optimum channel access scheme is small:
0 0.1 0.2 0.3 0.4 0.5 0.60
0.1
0.2
0.3
0.4
0.5
Rate of User #1
Rat
e of
Use
r #2
FDMA/TDMA CapacityCDMA/MU Capacity
C=0.5⋅ log2(1+P
2/N)
C=0.5⋅ log2(1+P
2/(P
1+N))
C=0.5⋅ log2(1+P
1/(P
2+N))
C=0.5⋅ log2(1+P
1/N)
Area, where FDMA.TDMA is inferior toCDMA/Multi−User Detection
Optimum resource sharing, where bandwidth is proportinal to
signal power.
Figure 18: Achievable rates for a multiple access channel with two users.
92
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�
– Choice of (practical) Topology [3/4] –
• It can first be observed that maximum (MU) and practical (FDMA) sum rate, i.e. R1 + R2, is the
same in the point where the users in the FDMA scheme are allocated an optimum bandwidth
equal to their power, i.e. W1 = P1 and W2 = P2.
• If FDMA (or TDMA) is used, then the resource allocation scheme which maximises capacity
hence also ensures that the achieved sum-capacity is equal (or close) to the maximum
achievable capacity.
• Since only FDMA and TDMA schemes are analytically tractable for large relaying networks,
these will be the main subject of the tutorial.
• Besides the basic multiple access schemes, i.e. FDMA and TDMA, we assume a path
reservation protocol where communication from source to sink is not interfered by other links
due to a prior reserved routing path. This routing path is reserved only during the transmission
of a single packet or several packets.
• The main aim of the analysis is hence to design resource allocation rules which maximise the
throughput along a reserved path through the given topology.
93
�
�
�
�
– Choice of (practical) Topology [4/4] –
We will investigate the end-to-end throughput of a communication link from a source towards a sink
operating over generic ergodic and non-ergodic fading channels, where relaying and cooperation is
allowed, and each terminal is in possession of multiple antenna elements.
2nd Interference Zone Z-th Interference Zone1st Interference Zone
6th
VAA
5th
VAA
4th
VAA
(V-2)nd
VAA
(V-1)st
VAA
V-th
VAA
targ
et te
rmin
al
3rd
VAA
2nd
VAA
1st
VAA
so
urc
e t
erm
inal
1st
RelayingStage
2nd
RelayingStage
co
op
era
tion
rela
yin
g t
erm
ina
l
Figure 19: Distributed-MIMO multi-stage relaying topology with interference zones.
94
�
�
�
�
– Related Definitions –Source, Sink and Relaying Terminals:
Wireless terminals with intention to transmit information from a source towards a sink with
the possible aid of relays.
Virtual Antenna Array (VAA):
Grouping of terminals in spatial proximity which wirelessly cooperate to enhance signal
reception (diversity) and transmission (diversity, space-time coding & multiplexing).
Cooperation:
Procedure which utilises the wireless interface between terminals belonging to the same
Virtual Antenna Array to enhance signal reception.
Relaying Stage:
The wireless interface between two consecutive Virtual Antenna Arrays.
Interference Zone:
Within an interference zone, resources in terms of frame duration, frequency band and
spreading code must not be re-used.95
�
�
�
�
– General Deployment [1/3] –
Source Terminal:
• it broadcasts its data to the remaining terminals in the first VAA,
• it uses given cooperative resources in terms of power, etc.
First Relaying VAA:
• it is formed by q1 spatially adjacent terminals (including the source!),
• each terminal possesses n1,i antenna elements (first subscript relates to first VAA and 1 ≤ i ≤ q1),
• after cooperation, the data is space-time encoded (codebook has t1 =
�q1i=1 n1,i spatial dimensions),
• each terminal transmits only n1,i∈(1,q1) spatial dimensions (so that no codeword is duplicated),
• it uses relaying resources in terms of power, bandwidth, frame duration.
96
�
�
�
�
– General Deployment [2/3] –
Second Relaying VAA:
• it is formed by q2 spatially adjacent terminals with n2,i antenna elements each,
• some may cooperate, hence forming Q2 clusters (everybody coop.: Q2 = 1, nobody coop.: Q2 = q2),
• j−th cluster contains r2,j receive antennas (1 ≤ j ≤ Q2 ,
�q2i=1 n2,i =
�Q2j=1 r2,j ),
• there are hence Q2 MIMO channels in the first stage (each with t1 Tx antennas and r2,j Rx antennas),
• cooperation uses given cooperative resources,
• after cooperation, the data is space-time encoded (codebook has t2 =
�q2i=1 n2,i spatial dimensions),
• each terminal transmits only n2,i∈(2,q2) spatial dimensions (so that no codeword is duplicated),
• it uses relaying resources in terms of power, bandwidth, frame duration.
97
�
�
�
�
– General Deployment [3/3] –
v−th Relaying VAA:
• it is formed by qv spatially adjacent terminals with nv,i antenna elements each,
• cooperation, space-time encoding and resource utilisation is congruent to above.
V −th Relaying VAA:
• it is formed by qV adjacent terminals with nV,i antenna elements each (including the target!),
• all terminals cooperate (non-cooperative terminals have no influence on data flow),
• there is hence one MIMO channel (with tV −1 Tx antennas and
�qVi=1 nV,i Rx antennas),
Target Terminal:
• after cooperation, data is space-time decoded and passed to information sink .
98
�
�
�
�
– Aim of Capacity Analysis –Find optimum fractional resources to be assigned to each node/mobile
terminal so as to maximise the end-to-end data throughput for a specifiedcommunication scenario, where the resource considered are
frame duration, frequency band and power.
Frame Duration:
• In time-division multiple access (TDMA), each relaying stage is assigned a given frame
duration which may or may not overlap with other stage’s frames.
Frequency Band:
• In frequency-division multiple access (FDMA), each relaying stage is assigned a given
frequency band which may or may not overlap with other stage’s frequency bands.
Power/Energy:
• Each terminal in the relaying stage is assigned a given power (energy). The energy
required to deliver a packet from source to sink ought to be independent of the topology.
99
�
�
�
�
– FMDA-Based Relaying –
• α(f)v is the fractional bandwidth allocated to the v−th relaying stage operating in FDMA,
• for fairness of comparison, we have∑V −1
v=1 α(f)v = 1.
1st VAA
Orthogonal
FDMA-based
Relaying
1st Stage
t
f
t t
f
t
f
W
W#1
W#2
W#3
W#4
T
Non-Orthogonal
FDMA-based
Relaying
t
f
t t
f
t
f
W
W#1
W#2
T
Interference
2nd VAA 3rd VAA 4th VAA 5th VAA
2nd Stage 3rd Stage 4th Stage
Figure 20: Orthogonal (no interference) and non-orthogonal (interference) relaying methods.
100
�
�
�
�
– TMDA-Based Relaying –
• α(t)v is the fractional frame duration allocated to the v−th stage operating in TDMA,
• for fairness of comparison, we have∑V −1
v=1 α(t)v = 1.
Orthogonal
TDMA-based
Relaying
t
f
t t
f
t
f
W
T#
1
T#
2
T#
3
T#
4
T
Non-Orthogonal
TDMA-based
Relaying
t
f
t t
f
t
f
W
T#
1
T#2
T
1st VAA
1st Stage
2nd VAA 3rd VAA 4th VAA 5th VAA
2nd Stage 3rd Stage 4th Stage
Interference
Figure 21: Orthogonal (no interference) and non-orthogonal (interference) relaying methods.
101
�
�
�
�
– Power & Energy Allocation –
FDMA-based Relaying TDMA-based Relaying
Ev = β(Ef )v E, Tv = T, Wv = α
(f)v W Ev = β
(Et)v E, Tv = α
(t)v T, Wv = W∑V −1
v=1 β(Ef )v ≡ 1,
∑V −1v=1 α
(f)v ≡ 1
∑V −1v=1 β
(Et)v ≡ 1,
∑V −1v=1 α
(t)v ≡ 1
Sv = β(Sf )v S, Sv = Ev/Tv Sv = β
(St)v S, Sv = Ev/Tv
→ β(Sf )v = β
(Ef )v → β
(St)v = β
(Et)v /α
(Et)v∑V −1
v=1 β(Sf )v ≡ 1,
∑V −1v=1 α
(f)v ≡ 1
∑V −1v=1 α
(t)v β
(St)v ≡ 1,
∑V −1v=1 α
(t)v ≡ 1
Time T
Power S1st Stage 2nd Stage 3rd Stage
E1
E2
E3
S1, S
3
S2
T1
T2
T3
Figure 22: Relationship between power, energy and time.
102
�
�
�
�
– Equivalence between TDMA & FDMA –
FDMA-based Relaying TDMA-based Relaying
C = α(f)v · W · log2
(1 + β
(Sf )v ·S
α(f)v ·W ·N0
)C = α
(t)v · W · log2
(1 + β(St)
v ·SW ·N0
)= α
(f)v · W · log2
(1 + β
(Ef )v
α(f)v
· SN
)= α
(t)v · W · log2
(1 + β(Et)
v
α(t)v
· SN
)
C is the Shannon capacity, W is the total bandwidth, N is the total noise power captured over W ,
N0 is the noise power spectral density, αv is the fractional bandwidth/frame duration and βv is the
fractional energy allocated to the v−th stage.
Since both access schemes are equivalent, we will henceforth use:
C = αv · W · log2
(1 +
βv
αv· SN
)(43)
V−1∑v=1
βv ≡ 1 &V−1∑v=1
αv ≡ 1 (44)
103
�
�
�
�
– Ergodic: End-to-End Throughput [1/3] –
• The aim is to maximise the end-to-end data throughput for the topology shown in Figure 19
assuming an ergodic fading channel.
• Throughput is defined as the information delivered from source towards sink, which requires a
certain duration of communication T and frequency band W .
• Subsequent analysis will refer to the normalised (spectral) throughput Θ in [bits/s/Hz].
• An ergodic channel offers a normalised capacity C in [bits/s/Hz] with 100% reliability, which
allows relating capacity and throughput via Θ = C .
• Maximising the throughput Θ is hence equivalent to maximising the capacity C .
• If a certain capacity was to be provided from source to sink, all channels involved must
guarantee error-free transmission.
The end-to-end capacity C is hence dictatedby the capacity of the weakest link.
104
�
�
�
�
– Ergodic: End-to-End Throughput [2/3] –
• Each topology has K = V − 1 distributed relaying stages.
• The v−th stage has Qv+1 MIMO channels with tv transmit antennas and rv+1,j∈(1,Qv+1)
receive antennas (for the example below: Qv+1 = 2, tv = 5, rv+1,1 = 3 and rv+1,2 = 3).
(v+1)-st Tier VAAv-th Tier VAA
nv,1
nv,2
nv,3
nv+1,1
nv+1,2
nv+1,3
MIMO #1: (nv,1
+nv,2
+nv,3
) x (nv+1,1
+nv+1,2
)
MIMO #2: (nv,1
+nv,2
+nv,3
) x (nv+1,3
)
Figure 23: Established MIMO channels from the vth to the (v + 1)st relaying VAA.
105
�
�
�
�
– Ergodic: End-to-End Throughput [3/3] –
• At each stage, we cluster such that the capacity of all clusters (MIMO channels) is as equal as
possible.
• For the analysis, we discard all but the weakest MIMO channel because the stronger MIMO
channels will then definitely be error-free.
• (If all sub-channel gains are equal, then the weakest MIMO channel is dictated by the cluster
with the smallest number of antennas.)
• For the analysis, the v−th relaying stage is hence represented by one MIMO channel with tv
transmit and rv � minj∈(1,Qv+1){rv+1,j} receive antennas.
• The aim of the analysis is to maximise the minimum capacity C , i.e.
C = supα,β
{min
{C1(α1, β1, λ1, γ1), . . . , CK(αK , βK , λK , γK)
}}(45)
over the fractional sets α � (α1, . . . , αK) and β � (β1, . . . , βK) in dependency of the
channel statistics λ � (λ1, . . . , λK) and average channel gains γ � (γ1, . . . , γK).
106
�
�
�
�
– Ergodic: MIMO Relaying [1/4] –
• With the parameter constraints given by (44), increasing one capacity inevitably requires
decreasing the other capacities.
• The minimum is maximised if all capacities are equated and then maximised.
• The capacity of the v−th stage is given as Cv = αv · Eλv
{mv log2
(1 + λv
γv
tv
βv
αv
SN
)}.
• Using (38), the end-to-end throughput-maximising optimised fractional power and optimised
fractional bandwidth (frame duration) can be obtained as [97]
αv =
∏w �=v Eλw
{mv log2
(1 + λwρw
γw
tw
SN
)}∑K
k=1
∏w �=k Eλw
{mv log2
(1 + λwρw
γw
tw
SN
)} (46)
βv = ρv · αv (47)
with
ρv ≈ K ·∏
w �=v3√
γw · Λ2(tw, rw)∑Kk=1
∏w �=k
3√
γw · Λ2(tw, rw)(48)
107
�
�
�
�
– Ergodic: MIMO Relaying [2/4] –
• Similarly, the end-to-end throughput-maximising optimised fractional power with equal fractional
bandwidth (frame duration) can be obtained as [97]
αv =1K
(49)
βv =
∏w �=v γw · Λ2(tw, rw)∑K
k=1
∏w �=k γw · Λ2(tw, rw)
(50)
• For the purpose of comparison, the case of no optimisation is also considered, for which the
resource allocation strategies are
αv =1K
(51)
βv =1K
(52)
108
�
�
�
�
Inp
ut
Ch
ann
el G
ain
s
fro
m e
ach
Re
layin
g S
tag
eγ 1
, ..
., γ
Κ
Inp
ut
Num
be
r o
f A
nte
nn
a
Ele
men
ts a
t e
ach S
tage
t 1, r
1, …
, t K
, r K
Ca
lcu
late
MIM
O G
ain
s a
t ea
ch
Sta
ge
Λ1,
...,
ΛΚ
Ca
lcu
late
Au
xili
ary
Co
eff
icie
nts
ρ1,
...,
ρΚ
Ca
lcu
late
Fra
ction
al B
and
wid
ths
α1,
...,
αΚ
So
rtF
ractio
na
l R
esou
rce
s
α1<
...
< α
Κ,
β1<
...
< β
Κ
Ca
lcu
late
Fra
ction
al P
ow
ers
β1,
...,
βΚ
Ou
tpu
tF
ractio
nal B
an
dw
idth
Alloca
tio
ns
Ou
tpu
tF
ractio
na
l P
ow
er
Allo
ca
tio
ns
α1,.
..,
αΚ
−1,
αΚ
=1
− α
1−
...−
αΚ
−1
β1,.
..,
βΚ
−1,
βΚ
=1
− β
1−
...−
βΚ
−1
109
�
�
�
�
– Ergodic: MIMO Relaying [4/4] –
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
1.4
SNR at First Relaying Stage [dB]
End
−to
−E
nd C
apac
ity C
[bits
/s/H
z]
Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerEqual Bandwidth and Optimised PowerEqual Bandwidth and Equal Power
t1 = 1, r
1 = 1
t2 = 1, r
2 = 1
t3 = 1, r
3 = 1
p = [0, 5, 10]
p = [0, 0, 0]
p = [0, −5, −10]
(a) Achieved end-to-end capacity of various
fractional resource allocation strategies for a 3-
stage network.
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
2.5
SNR at First Relaying Stage [dB]
End
−to
−E
nd C
apac
ity C
[bits
/s/H
z]
Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerEqual Bandwidth and Optimised PowerEqual Bandwidth and Equal Power
t1 = 1, r
1 = 2
t2 = 2, r
2 = 3
t3 = 3, r
3 = 2
p = [0, 5, 10]
p = [0, 0, 0]
p = [0, −5, −10]
(b) Achieved end-to-end capacity of various
fractional resource allocation strategies for a 3-
stage network.
Figure 24: Performance of fractional resource allocation algorithms for different 3-stage topologies;
here p � [10 log10(γ1/γ1), 10 log10(γ2/γ1), 10 log10(γ3/γ1)]
110
�
�
�
�
– Ergodic: O-MIMO with Unequal Gains [1/5] –
• If the channel attenuations within the v−th stage are different, then the fractional power βv
allocated to that stage can be distributed among the transmitting elements in an optimum
manner.
• Assuming a Rayleigh fading channel, the capacity of a space-time block encoded MIMO system
with unequal average sub-channel gains can be expressed in closed form as [99]
C = R ·t∑
i=1
r∑j=1
K(i−1)r+j · C0
(εi · γ(i−1)r+j
R
S
N
)(53)
with
K(i−1)r+j =t∏
i′=1
r∏j′=1
εi · γ(i−1)r+j
εi · γ(i−1)r+j − εi′ · γ(i′−1)r+j′
∣∣∣∣∣(i′−1)r+j′ �=(i−1)r+j
(54)
Here, εi∈(1,t) is the fractional power allocated to the i-th transmit antenna for which the
normalisation∑t
i=1 εi ≡ 1 holds.
111
�
�
�
�
– Ergodic: O-MIMO with Unequal Gains [2/5] –
• An optimum transmit power strategy allocates little or no power to the antenna(s) from which the
weakest subchannels depart; the antenna from which the strongest subchannels depart is
allocated most power.
• With this in mind, the approximate fractional power allocation εi to the i−th transmit antenna is
(possibly non-linearly) proportional to the total strength of the departing subchannels, i.e.
εi ∝
��
r�
j=1
γ(i−1)r+j
��
q
(55)
where the non-linearity coefficient q is determined numerically so as to minimise the mean-error
between optimum allocation εi and near-optimum allocation εi in a given SNR range.
• Normalising εi so that∑t
i=1 εi = 1, the power allocation can be approximated as
εi ≈(∑r
j=1 γ(i−1)r+j
)q
∑tk=1
(∑rj=1 γ(k−1)r+j
)q (56)
where q = 3 has shown to yield the smallest error for a large variety of conducted case studies.
112
�
�
�
�
– Ergodic: O-MIMO with Unequal Gains [3/5] –
Proposed allocation yields near-optimum performance for 2Tx & 1Rx:
γ1Fractional
STBC
FractionalSTBC
γ2
ChannelEncoder
InformationSource
Space-Time
Block Decoder
Channel
Decoder
InformationSink
(a) Distributed Alamouti scheme with unequal
sub-channel gains due to different pathloss &
shadowing.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Relative Gain γ1 in First Sub−Channel
Cap
acity
[bits
/s/H
z]
Optimum Transmit Power DistributionNear−Optimum Transmit Power DistributionEqual Transmit Power Distribution
t = 2, r = 1γ2 = 2 − γ
1
SNR = 10dB
(b) Capacity for various power distribution al-
gorithms with deployed Alamouti scheme and
one receive antenna; SNR=10dB.
Figure 25: Topology and performance of distributed Alamouti scheme.
113
�
�
�
�
– Ergodic: O-MIMO with Unequal Gains [4/5] –
Proposed allocation yields near-optimum performance for 2Tx & 2Rx:
FractionalSTBC Space-Time
Block Decoder
FractionalSTBC
Receiver
Receiverγ
1
γ2
γ3
γ4
γ3
γ4
(a) (Distributed) Alamouti scheme with unequal
sub-channel gains due to different pathloss &
shadowing.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.5
3
3.5
4
4.5
5
5.5
6
6.5
7
Relative Gain γ1 in First Sub−Channel
Cap
acity
[bits
/s/H
z]
Optimum Transmit Power DistributionNear−Optimum Transmit Power DistributionEqual Transmit Power Distribution
t = 2, r = 2γ2 = 1.8
γ3 = 2 − γ
1, γ
4 = 0.2
SNR = 15dB
SNR = 10dB
SNR = 5dB
(b) Capacity for various power distribution al-
gorithms with deployed Alamouti scheme and
two receive antennas; SNR=5, 10, 15dB.
Figure 26: Topology and performance of distributed Alamouti scheme.
114
�
�
�
�
– Ergodic: O-MIMO with Unequal Gains [5/5] –
Proposed allocation yields near-optimum end-to-end throughput:
3rd TierVAA2nd Tier
VAA
1st Tier
VAA
So
urc
e M
T
4th Tier
VAA
Targ
et M
T
1.6
1.6
1.6
0.4
0.4
0.4
1.0 1.0
(a) 3-Stage distributed O-MIMO communica-
tion scenario.
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
SNR at First Relaying Stage [dB]
End
−to
−E
nd C
apac
ity C
[bits
/s/H
z]
Optimum End−to−End CapacityOptimised Bandwidth, Power & Transmit Power Distribution at each transmitting VAAOptimised Bandwidth & Power, Equal Transmit Power at each transmitting VAAEqual Bandwidth, Power & Transmit Power at each transmitting VAA
t1 = 1, r
1 =2
t2 = 2, r
2 =2
t3 = 2, r
3 = 1
p = [0, 5, 10]
p = [0, 0, 0]
p = [0, −5, −10]
(b) Capacity of various fractional resource allo-
cation strategies over O-MIMO Rayleigh chan-
nels.
Figure 27: Topology and performance of distributed Alamouti 3-stage relaying scheme.
115
�
�
�
�
– Ergodic: Frequency-Selectivity [1/2] –
• A channel appears frequency-selective if the channel delay spread exceeds the symbol duration.
• A frequency selective channel is characterised by the frequency dependent channel transfer
function H(f) over a given bandwidth W .
• In [102], it has been shown that the capacity of a frequency selective channel assuming perfect
channel state information at the receiver is given as
C = maxS(f)
∫W
EH(f)
{log2 det
(Ir +
H(f)S(f)HH(f)N
)}df (57)
where capacity maximising codewords x(f) have to be determined with a given covariance
matrix S(f) = E{x(f)xH(f)} which satisfies the power constraint∫
Wtr(S(f)
)df ≤ S.
• In [102], it is shown that the statistics of H(f) do not depend on the frequency f (Theorem 6:
“frequency selectivity does not affect the ergodic capacity of wideband MIMO channels”), which
reduces the wideband ergodic capacity (57) to the narrowband ergodic capacity given by (18).
• Therefore, developed algorithms for ergodic channels can also be applied to the wideband
system per frequency component; non-ergodic behaviour, such as outage probabilities, change.
116
�
�
�
�
– Ergodic: Frequency-Selectivity [2/2] –
6 6.5 7 7.5 8 8.5 9 9.5 101.4
1.6
1.8
2
2.2
2.4
2.6
2.8
SNR at First Relaying Stage [dB]
End
−to
−E
nd C
apac
ity C
[bits
/s/H
z]
Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerQuantised Bandwidth and Optimised PowerEqual Bandwidth and Equal Power
4 sub−carriers 16 sub−carriers
32 sub−carriers
t1 = 1, r
1 = 2
t2 = 2, r
2 = 4
(a) Achieved end-to-end capacity with quan-
tised fractional bandwidth for a 2-stage relaying
network over O-MIMO Rayleigh channels.
6 6.5 7 7.5 8 8.5 9 9.5 101.4
1.6
1.8
2
2.2
2.4
2.6
2.8
SNR at First Relaying Stage [dB]
End
−to
−E
nd C
apac
ity C
[bits
/s/H
z]
Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerQuantised Bandwidth (power of 2) and Optimised PowerEqual Bandwidth and Equal Power
4 sub−carriers (2 + 2)
16 sub−carriers (8 + 8)
32 sub−carriers (16 + 16)
t1 = 1, r
1 = 2
t2 = 2, r
2 = 4
(b) Achieved end-to-end capacity with quan-
tised fractional bandwidth of power of two for
a 2-stage O-MIMO relaying network.
Figure 28: Example: OFDM system with 64 sub-carriers.
117
�
�
�
�
– Non-Ergodic: Throughput [1/4] –
• The aim is to maximise the end-to-end data throughput for the topology depicted in Figure 19
assuming a non-ergodic fading channel.
• The normalised (spectral) throughput Θ measured in [bits/s/Hz] is given as [100]
Θ = Φ · (1 − Pout(Φ))
(58)
• For each dependency Pout on Φ, there exists an optimum rate Φ which maximises the
throughput Θ according to (58).
• Such rate Φ is found by differentiating (58) to arrive at
1 − Pout(Φ) = Φ · ∂
∂ΦPout(Φ) (59)
which, with respect to the closed form expressions of the outage probabilities, has proven to be
impossible to obtain in explicit form.
• To this end, the approximation of the outage probability allows the problem for non-ergodic
fading channels to be transformed into a similar problem as for ergodic channels.
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– Non-Ergodic: Throughput [2/4] –
• The outage capacity of a SIMO channel can be expressed as [100]
Pout(Φ) ≈ a ·(
2Φ − 1S/N
)b
(60)
where a = a(r) and b = b(r) and are tabled in [100]. It is easily resolved in favour of Φ as
Φ (Pout) ≈ log2
(1 + b
√Pout
a
S
N
)(61)
• Taking into account log2(1 + x) ≈ √x, the throughput in (58) can be approximated as
Θ ≈ (1 − Pout) · 2b
√Pout
a
√SN (62)
• The throughput-maximising outage probability is obtained by differentiating (62) w.r.t. Pout,
leading to
Pout ≈ 11 + 2b
. (63)
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– Non-Ergodic: Throughput [3/4] –
The outage probability is indeed approximately independent from the SNR, and hence from fractional
power and bandwidth allocation:
1 2 3 40
10
20
30
40
50
60
70
80
90
100
Number of Receive Antennas
Thr
ough
put−
Max
imis
ing
Out
age
Pro
babi
lity
[%]
Approximate Throughput−Maximising Outage Probability (independent of SNR)Exact Throughput−Maximising Outage Probability (SNR=3dB)Exact Throughput−Maximising Outage Probability (SNR=6dB)Exact Throughput−Maximising Outage Probability (SNR=9dB)
(a) Differing number of receive elements,
i.e. SIMO channel.
1 2 3 40
10
20
30
40
50
60
70
80
90
100
Number of Transmit AntennasT
hrou
ghpu
t−M
axim
isin
g O
utag
e P
roba
bilit
y [%
]
Approximate Throughput−Maximising Outage Probability (independent of SNR)Exact Throughput−Maximising Outage Probability (SNR=3dB)Exact Throughput−Maximising Outage Probability (SNR=6dB)Exact Throughput−Maximising Outage Probability (SNR=9dB)
(b) Differing number of transmit elements,
i.e. MISO channel.
Figure 29: Comparison between exact and approximate throughput-maximising outage probability.
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– Non-Ergodic: Throughput [4/4] –
• [SIMO:] Combining (63), (61) and (58), and allocating a fractional bandwidth αv and a fractional
power βv to the v−th relaying stage, the throughput of that stage can be expressed as
Θv ≈ αv ·(
2b
1 + 2b
)· log2
(1 +
γv
b√
a(1 + 2b)βv
αv
S
N
)(64)
• [MISO:] Similarly, the maximum throughput for the MISO channel can be approximated as
Θv ≈ αv ·(
2b
1 + 2b
)· log2
(1 +
γv
t · b√
a(1 + 2b)βv
αv
S
N
)(65)
• [O-MIMO:] STBCs over a Rayleigh fading channel with unequal channel coefficients and an
optimum fractional transmit power εi∈(1,t) yields the following throughput
Θv ≈ αvR
(2b
1 + 2b
)log2
⎛⎝1 +
1tR
γv
b√
a(1 + 2b)1
b
√∑ti=1
∑rj=1
K(i−1)r+j
(εi·γ(i−1)r+j)b
βv
αv
S
N
⎞⎠
with K(i−1)r+j given by (54).
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– In Summary –
We developed near-optimum and sub-optimum fractional resource allocation strategies for
various multi-stage cooperative relaying networks, i.e. for
• ergodic channels
– equal sub-channel general MIMO without resource re-use
– unequal sub-channel O-MIMO without resource re-use
• non-ergodic channels
– equal sub-channel general MIMO without resource re-use
– unequal sub-channel O-MIMO without resource re-use
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2.5 Hierarchical Cooperative MIMO
123
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– Capacity of Large-Scale Networks [1/3] –
• After having investigated the capacity of a distributed point-to-point and distributed
multi-stage system, we now move on to large-scale systems with multiple users.
• What is the (transport) capacity Θ of below unit-area network where N randomly
placed source and destination pairs wish to randomly communicate with each other?
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– Capacity of Large-Scale Networks [2/3] –
• This question had been posed before, where
– Gupta & Kumar proved in [16] that with a flat topology, network capacity scales with
Θ =√
N/ log N ;
– Franceschetti et al. proved in [109] that, using percolation theory, one can do better
by building a virtual infrastructure (’highways’), leading to Θ =√
N ;
– Aeron et al. proved in [110] that, using a specific 3-phase protocol with distributed
MIMO, yields a total network throughput of Θ(N2/3);
– Ozgur et al. improved the latter specific 3-phase protocol and showed in [28] that
one can achieve Θ(N), i.e. a linear scaling!
• There is, however, no proof on the optimality of any architecture and topology doing
better than Θ =√
N/ log N .
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– Capacity of Large-Scale Networks [3/3] –
• According to the different protocols, the per-node-throughput hence scales as follows:
101
102
103
104
10−3
10−2
10−1
100
Number of Nodes [logarithmic]
Per
−No
de−
Th
rou
gh
pu
t [l
og
arit
hm
ic]
KumarFranceschettiAeronOzgur
126
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– Multi-Scale Hierarchical Cooperation [1/2] –
• Divide the area into C clusters with each containing in average M = N/C nodes.
• Initiate a three-phase communication protocol as follows:
– Phase 1 − Transmit Cooperation:
Within each cluster with source nodes, exchange required information between M
nodes; do this for all clusters in parallel in the network.
– Phase 2 − MIMO Transmission:
Set up long range M×M long-range MIMO link between each cluster containing
sources and sinks; do this sequentially in the network.
– Phase 3 − Cooperative Decoding: Within each cluster, decode information after
passing quantised observations between nodes; do this for all clusters in parallel.
• Repeat above steps by dividing each cluster C into C′ sub-clusters, given that this
iterative splitting increases capacity.
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– Multi-Scale Hierarchical Cooperation [2/2] –
• The key ideas hence are:
– use local, thus globally non-interfering, short-range communications to exchange
distributed MIMO information at source and destination;
– use global, thus potentially globally interfering and hence necessarily sequential,
long-range communications to achieve spatial multiplexing over large distances.
• The principle is depicted in below figure (taken from [28]):
PHASE 1 PHASE 2 PHASE 3
PHASE 1 PHASE 2 PHASE 3 PHASE 1 PHASE 2 PHASE 3
PHASE 1PHASE 2
PHASE 3
PHASE 1 PHASE 3PHASE 2
PHASE 3PHASE 1PHASE 2
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Open Issues
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– Open Issues –
In the field of capacity, there are endless unsolved problems. However, I believe that these
are some interesting open issues:
• Analysis of rate & outage behaviour of
– synchronisation-robust cooperative systems,
– cooperative systems with imperfections (channel, feedback, correlation, etc.),
– cooperative systems in shadowing channels.
• Using capacitive insights to
– optimise the choice (and placement) of cooperative nodes,
– optimise the cooperative communication protocol.
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PART 3HARDWARE REALISATION
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– Preliminary Note –
• In the end, it is the hardware which will facilitate as well as limit any implementation of
cooperative relaying schemes.
• These limitations in hardware render the implementation of some of the recently
proposed cooperative protocols infeasible.
• To understand what is really feasible, we will henceforth deal with the following topics:
1. hardware architectures for transparent relaying transceivers;
2. hardware architectures for regenerative relaying transceivers;
3. comparison between these architectures;
4. cost estimates of architectures.
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3.1 Transparent Transceivers
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– Amplify & Forward Architecture –
• Important building blocks for the AF architecture:
– frequency translator facilitating shift of df and variable gain power amplifier;
– excellent duplex filters to avoid spillage (surface/bulk acoustic wave - SAW/BAW);
– no storage of received signal, hence only (!) FDRA/FDMA protocols feasible.
f-Translator
df
Antenna
BP
F1
LNA BPFPA
Variable Gain
BP
F2
PLL VCO
Programmable Synthesizer
Rx ChainDuplex Filter
Tx Chain
f(RSSI)
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– Linearly-Process & Forward Architecture –
• Important building blocks for the LF architecture:
– frequency translator df , good duplex filters, and variable gain power amplifier;
– linear processing, such as phase rotation, etc;
– no storage of received signal, hence only (!) FDRA/FDMA protocols feasible.
f-Translator
df
Antenna
BP
F1
LNA BPFPA
Variable Gain
BP
F2
PLL VCO
Programmable Synthesizer
Rx ChainDuplex Filter
Tx Chain
f(RSSI)
Linear
Operations
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– Nonlinearly-Process & Forward Architecture –
• Important building blocks for the nLF architecture:
– processing is performed at baseband because function is designed without carrier;
– realisation with I/Q is possible, as well as sampled version;
– generally no storage of received signal, hence only FDRA/FDMA protocols feasible.
BPF
fc � BB
df
Antenna
BP
F1
LNA BPFPA
Variable Gain
BP
F2
PLL VCO
Programmable Synthesizer
Rx ChainDuplex Filter
Tx Chain
f(RSSI)
Non-Linear
Operations
df
PLL VCO
Programmable Synthesizer
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– TDMA Realisation of Transparent Architectures –
• TDRA/TDMA protocols can be implemented by using below architecture; however, it is
very unlikely that such architecture would be used;
• important building blocks for the TDRA/TDMA architecture are mainly large memory and
fast data buses to store (over-)sampled signals.
IF
f
BPF
I
Q
ADC
ADC
Dig
ital
Sto
rag
e DAC
DAC
I
Q
+
f
Antenna
BP
F1
LNA BPFPA
Variable Gain
BP
F2
Rx ChainDuplex Filter
Tx Chain
f(RSSI)
137
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3.2 Regenerative Transceivers
138
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– Sample Processing Architectures –
• Important building blocks for the EF and CF architectures:
– f-translators to baseband, synchronisation and ADC/DAC;
– fast but not complex baseband, including memory, data buses, etc;
– processing of received signal, hence any type of protocol is feasible.
IF
f
BPF
I
Q
ADC
ADC
DAC
DAC
I
Q
+
f
Sa
mp
le-B
ase
d
Pro
ce
ssin
g
Antenna
BP
F1
LNA BPFPA
(Variable Gain )
BP
F2
Rx ChainDuplex Filter
Tx Chain
f(RSSI)
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– Information-Bit Processing Architectures –
• Important building blocks for the DF and PF architectures:
– f-translators to baseband, synchronisation and ADC/DAC;
– powerful baseband, including μ−controller, memory, data buses, etc;
– processing of received signal, hence any type of protocol is feasible.
IF
f
BPF
I
Q
ADC
ADC
DAC
DAC
I
Q
+
f
Info
rma
tion
-Bit
Pro
ce
ssin
g
Antenna
BP
F1
LNA BPFPA
(Variable Gain )
BP
F2
Rx ChainDuplex Filter
Tx Chain
f(RSSI)
140
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3.3 Architectural Comparisons
141
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– Multiple Access Schemes –
• transparent relaying schemes can only use FDRA/FDMA;
• regenerative relaying schemes can use any of these.
AF LF nLF EF CF DF PF GF
TDRA × × × � � � � �FDRA � � � � � � � �
TDMA × × × � � � � �FDMA � � � � � � � �CDMA × × × (�) (�) � � �
OFDMA × × × (�) (�) � � �MC-CDMA × × × (�) (�) � � �
142
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– Transceiver Complexity –
• using FMDA-like access requires very good filters to minimise spurious power spillage;
• information processing schemes are likely to be used with more sophisticated
multi-carrier wideband access schemes, which require highly linear amplifiers;
• the complexity of non-transparent schemes is generally higher, where DF, PF and GF
have highest complexity.
AF LF nLF EF CF DF PF GF
clock accuracy +++ +++ +++ +++ +++
filter design ++ ++ ++ ++ ++
power amplifier +/+++ +/+++ +++ +++ +++
complexity ++ ++ +++ +++ +++
memory ++ ++ ++ ++ ++
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3.4 Cost Estimates
144
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– Typical Cost of Transparent Architecture –
• The cost of the transparent architecture for the production of 1000 items at 900 MHz
can be approximately estimated as per below table.
List of Items Approximate Cost in Euros
Bandpass Filter 2
Duplex Filter 6
Low Noise Amplifier 1
Programmable Synthesizer 8
Variable Gain Amplifier 5
Printed Circuit Board 5
Other Items 2
Total 27
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– Typical Cost of Regenerative Architecture –
• The cost of the regenerative architecture for the production of 1000 items at 900 MHz
can be approximately estimated as per below table.
List of Items Approximate Cost in Euros
Transparent Architecture (minus Synthesizer) 19
Programmable Synthesizer 2 × 8
I&Q Brancher 2×5
ADCs/DACs 2×5
Signal Processing 15
Total 80
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– Cost Trends [1/2] –
• Regenerative architecture is about 3 times more expensive than the transparent one.
• Every decade in produced items diminishes the cost by approximately 10 %.
• Going from 900 MHz to 2 GHz increases the price by approximately 5 %.
• Going from 900 MHz to 5 GHz increases the price by approximately 20 %.
• All estimates usually have a 10 % error margin.
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– Cost Trends [2/2] –
100
101
102
103
104
105
106
107
108
0
20
40
60
80
100
120
140
Production Volume [logarithmic]
Ap
pro
xim
ate
Co
st [
Eu
ro]
Transparent Architecture, fc = 900MHz
Regenerative Architecture, fc = 900MHz
Regenerative Architecture, fc = 2GHz
Regenerative Architecture, fc = 5GHz
Figure 30: Transparent transceiver is significantly cheaper, whereas change in frequency has no
major impact on costs.
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Open Issues
149
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– Open Issues –
Since there are no relay-specific components in the transceiver, there are the usual open
problems with hardware design.
However, to improve cooperative relaying performance, the following issues are important:
• Facilitator of FDRA over closely space frequency bands, i.e. excellent duplex filters.
• Guarantor of reliable synchronisation, i.e. precise clocks.
150
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PART 4CHANNEL CHARACTERISATION
151
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– Preliminary Note –
• In addition to physical channel, cooperative network becomes part of the channel [30].
• The cooperative relaying channel can be decomposed into the following cases:
1. (general channel characteristics as a baseline;)
2. channel for regenerative relaying (BS-to-MT & MT-to-MT channel);
3. channel for transparent relaying (cascaded channel);
4. distributed MIMO channel behaviour.
NLOS, from BS:
same pathloss
same shadowing
different fading
NLOS, distributed:
different pathloss
different shadowing
different fading
LOS, distributed:
different pathloss
same shadowing
different fading
BS
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4.1 General Characteristics
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– General Characteristics [1/5] –
Base Station : BSMobile Station : MS
Line-of-Sight: LOSnon-LOS: nLOS
MS#1
(LOS)
BS
MS#1
(nLOS)
3. Scattering
1. Free-SpacePropagation
2. Reflection
4. Diffraction
MS#2
(LOS)
MS#2
(nLOS)
Figure 31: Channel scenario for LOS/nLOS traditional and cooperative links.
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– General Characteristics [2/5] –
Re
ceiv
ed
Po
we
r [d
B]
Distance [m]
-20dB/dec (Free-Space)
-n*10dB/dec (Clutter )
Shadowing Mean
Shadowing
Fading (measured)
Figure 32: Received power versus distance due to pathloss, shadowing and fading.
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– General Characteristics [3/5] –
Pathloss:
• Characteristics: deterministic due to free-space propagation, n = 2,
measurable > 1000 · λ
• Disadvantage: power loss which requires more Tx power with increasing distance
• Advantage: spatially limits generated interference
Shadowing:
• Characteristics: random due to obstacles, lognormal, mean absorbed in pathloss
(hence n = 2, . . . , 6), variance 2dB-18dB, measurable > 40 · λ
• Disadvantage: random power loss which requires link-budget margin
• Advantage: further limits spatially generated interference; capture effect at MAC
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– General Characteristics [4/5] –
(Small-Scale) Fading:
• Characteristics: random due to phasor additions, central/non-central complex Gaussian
or other, measurable at ≈ λ/2
• Disadvantage: random power loss which requires link-budget margin; often, rapid
changes in channel which needs to be catered for
• Advantage: creates temporal, spectral and spatial signatures (picked up by proper code)
Fourier Transform → useful tool for visualising fading
• channel time variation → doppler spectrum
• multipath component (MPC) delays → frequency spectrum
• spatial fading → angular spectrum
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– General Characteristics [5/5] –
Fading Cases:
• time domain: slow/fast fading (large/small coherence time)
• frequency domain: non-selective/selective fading (large/small coherence bandwidth)
• spatial domain: non-selective/selective fading (large/small coherence distance)
8 possible fading cases: (4 in time & frequency, spatial domain treated later)
• slow & frequency-flat
• fast & frequency-flat
• slow & frequency-selective
• fast & frequency-selective
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– Slow & Frequency-Flat Fading –
• Characteristics: no inter-pulse overlap, no amplitude change from pulse to pulse
• Disadvantage: no power gains possible, possible long fades
• Advantage: no ISI, coherent communication facilitated
s(t) Tx s(t) Tx s(t) Tx
r(t)/h(t) Rx Rx Rx
t0
1 1 1
r(t)/h(t) r(t)/h(t)
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– Fast & Frequency-Flat Fading –
• Characteristics: no inter-pulse overlap, amplitude change from pulse to pulse
• Disadvantage:
• Advantage:
Tx Tx Tx
Rx Rx Rx
t0
s(t) s(t) s(t)
r(t)/h(t)
1 1 1
r(t)/h(t) r(t)/h(t)
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– Slow & Frequency-Selective Fading –
• Characteristics: inter-pulse overlap, no amplitude change from pulse to pulse
• Disadvantage:
• Advantage:
s(t) Tx s(t) Tx s(t) Tx
r(t)/h(t) Rx Rx Rx
t0
1 1 1
r(t)/h(t) r(t)/h(t)
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– Fast & Frequency-Selective Fading –
• Characteristics: inter-pulse overlap, amplitude change from pulse to pulse
• Disadvantage:
• Advantage:
Tx Tx Tx
Rx Rx Rx
t0
s(t) s(t) s(t)
r(t)/h(t)
1 1 1
r(t)/h(t) r(t)/h(t)
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– Spatial Fading –
• Please, see subsequent section on “Distributed MIMO Behaviour”.
163
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– Important Channel Parameters –
• pathloss coefficient
• shadowing variance and shadowing correlation distance
• fading statistics for each multipath component (MPC) and correlation properties
• power delay profile (PDP) with RMS delay spread
Power
P
Delay τ
Instantaneous contributions
of MPCs to PDP
Instantaneous
PDP
Mean
Delay
RMS Delay
Spread
Averaged
PDP
P1
P2
P3
Tap#1
Tap#2
Tap#3
164
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4.2 Regenerative Relaying Channel
165
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– Regenerative Relaying Scenario –
• The regenerative relaying channel exhibits the following properties:
– class of distribution remains unchanged;
– mean and variance are changed;
– correlation functions also change.
BS
(fixed)
direct link
traditional
linkcooperative
link
Regenerative
Relay (mobile)
Destination
(mobile)
Figure 33: Regenerative relaying link and - as benchmark - the direct link.
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– Regenerative Relaying Channel Trends –
-20dB/dec (Free-Space)
-n*10dB/dec (Clutter )
Shadowing Mean
Shadowing
Fading (measured)
Narrowband & Non-Cooperative Wideband & Non-Cooperative
reduced Fading
Narrowband & Cooperative
reduced Shadowing Mean
and less Aggregate Pathloss
reduced
Shadowing Variance
Wideband & Cooperative
further reduced Fading
reduced Shadowing Mean
and less Aggregate Pathloss
reduced
Shadowing Variance
reduced but more
frequent Fading
Figure 34: Regenerative cooperative communication reduces pathloss, shadowing and fading.
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– General Channel Parametersa[1/2] –
Pathloss
• traditional links (high BS/AP, low MTs): n = 2 (LOS), n = 2, . . . , 4 (nLOS)
• cooperative links (low cooperating MTs): n = 2 (LOS), n = 4, . . . , 6 (nLOS)
Shadowing Variance
• traditional links (high BS/AP, low MTs): 2, . . . , 6dB (LOS), 6, . . . , 18dB (nLOS)
• cooperative links (low cooperating MTs): 0, . . . , 2dB (LOS), 2, . . . , 6dB (nLOS)
Shadowing Coherence Distance
• traditional links (high BS/AP, low MTs): >100m (LOS), tens of meters (nLOS)
• cooperative links (low cooperating MTs): 40-80m (LOS), 20-40m (nLOS)
aAll trends are (slightly) frequency dependent; these values are only indications based on [31]−[43]and [60]−[68].
168
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– General Channel Parameters [2/2] –
First MPC Fading Statistics (other MPCs are Rayleigh distributed)
• traditional links (high BS/AP, low MTs): Ricean K = 2, . . . , 10 (LOS), Rayleigh (nLOS)
• cooperative links (low cooperating MTs): Ricean K > 10 (LOS), Rayleigh (nLOS)
Power Delay Profile
• traditional links (high BS/AP, low MTs): negative-exponential, clustered
• cooperative links (low cooperating MTs): negative-exponential
RMS Delay Spread
• traditional links (high BS/AP, low MTs): depends on cell size, τRMS = 50ns, . . . , 4μs
• cooperative links (low cooperating MTs): τRMS = 10ns, . . . , 40ns
169
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– Specific Channel Models –
Cellular & Fixed Broadband (traditional link)
• Pathloss: Okumura-Hata, Walfish-Ikegami, COST231, Dual-Slope Model
• Channel Model: COST207, 3GPP A&B, Stanford University Interim Channels SUI1-6
Indoors & WLAN (traditional & cooperative link)
• Pathloss: COST231, COST259-Multiwall Model
• Channel Model: ETSI-BRAN, IEEE
(Bluetooth,) Zigbee & UWB (cooperative link)
• Pathloss: IEEE 802.15.3a CH1-CH4, IEEE 802.15.4a
• Channel Model: IEEE 802.15.3a CH1-CH4, IEEE 802.15.4a, (UWB book)
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– IEEE 802.15.3a HDR UWB Model –
• Due to unresolved disputes, this IEEE WG is discontinued!
• HDR PANs deployed in residential and office environments
• based on measurements by S. Ghassemzadeh, et al., M. Pendergrass, J. Foerster, et
al., J. Kunisch, et al., A.F. Molisch, et al., G. Shor, et al. [41]
• model distinguishes four radio environments
– LOS with a distance between TX and RX of up to 4 m (CM1)
– NLOS for a distance of up to 4 m (CM2)
– NLOS for a distance of 4−10 m (CM3)
– “heavy multipath” environments (CM4)
• pathloss model adopted from Ghassemzadeh et. al. [43]
• channel model matched to Saleh-Valenzuela model
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– IEEE 802.15.4a LDR UWB Model [1/3] –
• communication with extremely low power consumptions [36]
• development of channel models for different environments at low (100−960 MHz) and
high (3−10 GHz) frequency bands
• distance & frequency dependency has been formulised as
L(d, f) = L(d) ·L(f) =12·K0 · ηTx(f) · ηRx(f) · c2
(4πd0f0)2· (f/f0)
−2(κ+1)
(d/d0)n
• shadowing has been formulised as
PL(d) =[L(d0) − 10n log10
(d
d0
)]+ S
where the variables are subsequently described and parameterised in Table 1.
172
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– IEEE 802.15.4a LDR UWB Model [2/3] –
• the factor of 1/2 has been included to account for average attenuations caused by people close
to the antennas;
• K0 is a constant which has to be chosen so that at reference distance, d0, and reference
frequency, f0, the value L(d, f) is equal to the tabled parameter L(d0);
• ηTx(f) and ηRx(f) are the frequency dependent transmit and receive antenna efficiencies
and have to be provided by the system designer;
• d0 is the reference distance, which, in subsequent parameterisations, is equal to 1m;
• f0 is the reference frequency, which, in subsequent parameterisations, is equal to 5 GHz (no
frequency dependency in the lower bands has been reported so far);
• κ is the frequency decay factor;
• c ≈ 3 · 108 m/s is the speed of light;
• L(d0) is the pathloss measured at reference distance d0; and
• S is a Gaussian distributed random variable with zero mean and standard deviation σS .
173
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– IEEE 802.15.4a LDR UWB Model [3/3] –Table 1: IEEE 802.15.4a pathloss parameterisation for various scenarios [42].
L(d0) [dB] n κ σS [dB]
residential, LOS, high frequency −43.9 1.79 1.12 ± 0.12 2.22
residential, NLOS, high frequency −48.7 4.58 1.53 ± 0.32 3.51
office, LOS, high frequency −35.4 1.63 0.03 1.90
office, NLOS, high frequency −57.9 3.07 0.71 3.90
industrial, LOS, high frequency −56.7 1.20 -1.10 6.00
industrial, NLOS, high frequency −56.7 2.15 -1.43 6.00
outdoors, LOS, high frequency −45.6 1.76 0.12 0.83
outdoors, NLOS, high frequency −73.0 2.50 0.13 2.00
open outdoors, LOS, high frequency −49.0 1.58 0.00 3.96
indoors, NLOS, low frequency n.a. 2.40 0.00 5.90
174
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– Temporal Characteristics [1/4] –We assume a SISO narrowband 2D-isotropic scatterer mobile-to-mobile channel [45]−[48].
• The auto-correlation function is given as
Rhh(τ) = (66)
where f1 = v1/λ and f2 = v2/λ are Doppler shifts induced by the MTs, λ is the
wavelength, v1,2 are the velocities, τ is the time-lag, J0(x) is the zeroth-order Bessel
function of the first kind, and a = f2/f1.
• The Doppler spectrum is given as
S(f) =1
π2f1√
aK
⎡⎣1 + a
2√
a
√1 −
(f
(1 + a)f1
)2⎤⎦ , (67)
where K(x) is the complete elliptic integral of the first kind.
175
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– Temporal Characteristics [2/4] –
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.5
0
0.5
1
Time−Lag τ [s]
Au
to−C
orr
elat
ion
Fu
nct
ion
Rh
h(τ
)
BS−to−MT (MT @ 1 m/s)MT−to−MT (both MTs @ 1 m/s)
Figure 35: Observations: MT-to-MT channel decorrelates faster than BS-to-MT channel, which is
good for code design but bad for channel estimation purposes.
176
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– Temporal Characteristics [3/4] –
• The Level Crossing Rate (LCR) is the expected number of times per second the
channel envelope |h| crosses level γ in the positive direction, and is given as
LCR(γ) =√
2π√
1 + a2 · f1 · ρ · e−ρ2, (68)
where ρ = γ/E{|h|2}.
• The Average Fade Duration (AFD) is the average duration of time the envelope
spends below level γ, and is given as
AFD =1√
2π√
1 + a2 · f1 · ρ(eρ2 − 1
). (69)
177
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– Temporal Characteristics [4/4] –
−40 −30 −20 −10 0 10 200
2
4
6
8
10
12
Crossing−Level γ [dB]
Lev
el C
ross
ing
Rat
e L
CR
(γ)
[1/s
]
BS−to−MT (MT @ 1 m/s)MT−to−MT (both MTs @ 1 m/s)
Figure 36: Observations: MT-to-MT channel varies faster than BS-to-MT channel, which is good for
scheduling fairness but leads to large overhead due to frequent channel state updates.
178
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– Advanced Channel Modelling –Akki’s results have been extended to other cases, such as
• Non-Isotropic Scatterer: Akki’s model assumes isotropic scatterers, which has been
extended to non-isotropic 2D scatterers in [51].
• More General Fading Distributions: Akki’s model assumes Rayleigh fading, which
has been extended to Rician channels in [49, 50].
• 3D Scattering Environment: The 3D case has been treated in [52, 53].
• MIMO: The analysis has been extended to the MIMO case in [50] and [54]−[59].
• Correlation: The analysis has been extended in [50] to the correlated case.
• Wideband: The analysis has been extended in [53] to the wideband case.
• Measurements: Prior analysis has been corroborated and extended by means of
measurements, such as [60]−[68].
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– Non-Isotropic Relay Channel [2/3] –
−4 −3 −2 −1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
1.4
Angle of Arrival/Departure (AoA/AoD)
Pro
bab
ility
Den
sity
Fu
nct
ion
(p
df)
κ = 0κ = 5κ = 10
Figure 37: Increasing κ yields larger concentration around mean; μ = 0.
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– Non-Isotropic Relay Channel [3/3] –
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time−Lag τ [s]
Mo
du
le o
f A
uto
−Co
rrel
atio
n F
un
ctio
n R
hh(τ
)
κ1 = 1, κ
2 = 1, μ
1 = 0, μ
2 = 0
κ1 = 1, κ
2 = 5, μ
1 = 0, μ
2 = 0
κ1 = 5, κ
2 = 5, μ
1 = 0, μ
2 = 0
κ1 = 5, κ
2 = 5, μ
1 = −π/2, μ
2 = 0
Figure 38: Increasing concentration κ yields higher correlation; non-aligned means yield lower cor-
relation; v1 = v2 = 1m/s.
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– Ricean Relay Channel [1/3] –We assume a SISO narrowband 2D-isotropic scatterer mobile-to-mobile Ricean fading
channel [49].
• The auto-correlation function is given as
Rhh(τ) =1
1 + K[J0(2πf1τ) · J0(2πaf1τ) + Q(τ)] , (70)
where f1 = v1/λ and f2 = v2/λ are Doppler shifts induced by the MTs, λ is the
wavelength, v1,2 are the velocities, τ is the time-lag, J0(x) is the zeroth-order Bessel
function of the first kind, a = f2/f1, K the Ricean fading factor, and
Q(τ) = Kej2πf3τ cos θ′ , (71)
where f3 = v3/λ, v3 =√
(v1 · cos θd − v2)2 + (v1 · sin θd)2, θd = ang(v1, v2),
θ′ = θs + θ′′, θs = ang(v1, LOS), and θ′′ = cos−1(
v21+v2
3−v22
2v1v3
).
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– Ricean Relay Channel [2/3] –
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time−Lag τ [s]
Mo
du
le o
f A
uto
−Co
rrel
atio
n F
un
ctio
n R
hh(τ
)
K = −∞ dBK = 0 dBK = 10 dB
v1 = 1 m/s
v2 = 1 m/s
Figure 39: Increasing LOS component causes increases correlation; good for channel estimation
purposes but bad for interleaver design.
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– Ricean Relay Channel [3/3] –
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time−Lag τ [s]
Mo
du
le o
f A
uto
−Co
rrel
atio
n F
un
ctio
n R
hh(τ
)
v1 = 1 m/s, v
2 = 1 m/s
v1 = 1 m/s, v
2 = 2 m/s
v1 = 1 m/s, v
2 = 2 m/s
Figure 40: Increasing speed and/or angle between Tx/Rx yields lower coherence; good for interleaver
design but bad for channel estimation purposes; K = 0dB.
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– Non-Isotropic Relay Channel [1/3] –We assume a SISO narrowband non-isotropic scatterer mobile-to-mobile Rayleigh fading
channel [51].
• The non-isotropic behaviour is described by means of the von Mises distribution, which
describes the pdf of AoD & AoA with mean μ and concentration κ:
pdfα(α) = exp(κ cos(α − μ))/(2πJ0(κ)). (72)
• With this, the auto-correlation function is given as
Rhh(τ) =2∏
i=1
J0
(√κ2
i − 4π2f2i τ2 + j4πκifiτ cos μi
)/J0(κi) (73)
where f1 = v1/λ and f2 = v2/λ are Doppler shifts induced by the MTs, λ is the
wavelength, v1,2 are the velocities, τ is the time-lag, and J0(x) is the modified
zeroth-order Bessel function of the first kind.
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– MIMO Relay Channel [1/3] –We assume a 2×2 MIMO narrowband 2D-isotropic scatterer mobile-to-mobile Rayleigh
fading channel [55, 56].
• The space-time cross-correlation function is given as
Rhh(τ) =2∏
i=1
J0
(2π√
(δi/λ)2 + (fiτ)2 − 2gi(δi, τ))
(74)
where f1 = v1/λ and f2 = v2/λ are Doppler shifts induced by the MTs, λ is the
wavelength, v1,2 are the velocities, τ is the time-lag, J0(x) is the zeroth-order Bessel
function of the first kind, and
gi(δi, τ) = (δi/λ)(fiτ) cos(αi − βi), (75)
where δi is the antenna separation at Tx/Rx, αi is the angle of Tx/Rx movement, and βi
is the antenna tilt at Tx/Rx.
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– MIMO Relay Channel [2/3] –
00.05
0.10.15
0.20.25
0.30.35
0.40.45
0.5
0
0.1
0.2
0.3
0.4
0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time−Lag τ [s]Spatial Seperation δ [m]
Mo
du
le o
f C
orr
elat
ion
Fu
nct
ion
R
Figure 41: Spatial and temporal domains decorrelate similarly; v1 = v2 = 1m/s; λ = 30cm;
αi = 0, βi = π/2.
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– MIMO Relay Channel [3/3] –
00.05
0.10.15
0.20.25
0.30.35
0.40.45
0.5
0
0.1
0.2
0.3
0.4
0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time−Lag τ [s]Spatial Seperation δ [m]
Mo
du
le o
f C
orr
elat
ion
Fu
nct
ion
R
Figure 42: Fast terminal movements make the temporal domain to decorrelate faster; v1 = 1m/s,
v2 = 10m/s; λ = 30cm; αi = 0, βi = π/2.
188
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– Empirical Relay Channel Model [1/3] –
Measurements performed for low transmit and receive antenna heights have been
conducted in London and have lead to the following empirically fitted models [64].
• The pathloss is a function of LOS and nLOS and is given as
PLLOS = 4.62 + 20 log10(4π/λ) − 2.24ht − 4.9hr + 29.6 log10 d(76)
PLnLOS = 20 log10(4π/λ) − 2hr + 40 log10 d + C (77)
where λ is the wavelength, ht,r the transmit and receive antenna heights, d the
distance and C = 0 (buildings > 18m) and C = −4 (buildings < 12m).
• The shadowing is lognormally distributed with a std varying between 6 and 11dB.
• The auto-correlation function exhibited de-correlation between 20 and 80m, with a
mean distance of 40m.
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– Empirical Relay Channel Model [2/3] –The following insights have been given [64]:
• The pathloss slope changes significantly over the range of measured distances; the
slope alters to a much steeper angle as the distance from the transmitter increases.
• The pathloss increases as the transmitter height decreases and this is more evident at
short distances from the transmitter.
• The pathloss is also larger for lower receiver heights, which is again more apparent at
short distances from the transmitter.
• The pathloss does not depend on the transmitted height for nLOS scenarios.
• The ratio between LOS and nLOS decreases almost linearly in log scale from 1 to
1000m.
• The shadowing std does not depend on antenna heights nor distances between
transmitter and receiver.
190
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– Empirical Relay Channel Model [3/3] –
Figure 43: The model gives fairly good predictions with a mean error of 0.5dB [64].
191
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4.3 Transparent Relaying Channel
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– Transparent Relaying Scenario –
• The transparent relaying channel exhibits the following properties:
– class of distribution changes;
– mean and variance also change;
– correlation functions also change.
BS
(fixed)
direct link
traditional
linkcooperative
link
Transparent
Relay (mobile)
Destination
(mobile)
Figure 44: Transparent relaying link and - as benchmark - the direct link.
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– Transparent Relaying Channel Trends –
-20dB/dec (Free-Space)
-n*10dB/dec (Clutter )
Shadowing Mean
Shadowing
Fading (measured)
Narrowband & Non-Cooperative Wideband & Non-Cooperative
reduced Fading
Narrowband & Cooperative
reduced Shadowing Mean
and less Aggregate Pathloss
reduced
Shadowing Variance
Wideband & Cooperative
reduced Shadowing Mean
and less Aggregate Pathloss
reduced
Shadowing Variance
increased and more
frequent Fading
(wrt non-cooperative case)
increased Fading
(wrt non-cooperative case)
but reduced Fading
(wrt narrow-band case)
Figure 45: Transparent cooperative communication reduces pathloss & shadowing but not fading.
194
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– Two-Hop Transparent Relay Channel [1/2] –
• Exposed results related to the transparent relay channel have been compiled
from [47, 48].
• We assume AF transparent relaying from BS → relay MT (r-MT) → target MT (t-MT).
• The received signal at the t-MT, r2, can be expressed as (omitting the time index)
r2 = A · h2 · (h1 · s + n1) + n2 (78)
where
– A is amplification factor
– h1 is channel between BS & r-MT and h2 between r-MT & t-MT
– both channels are modelled as ZMCG with power σ21 and σ2
2 , respectively
– n1,2 are the respective AWGN noise terms with equal power N
– P1 and P2 is transmission power of BS and r-MT, respectively195
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– Two-Hop Transparent Relay Channel [2/2] –
• The fixed gain relay amplification factor A has been proposed by [69]
A =
√P2
P1 · σ21 + N
, (79)
which requires only statistical knowledge of the first-hop channel.
• The variable gain relay amplification factor A has been proposed by [70]
A =
√P2
P1 · |h1|2 + N, (80)
which requires instantaneous knowledge of the first-hop channel.
• Other application-dependent factors have been proposed, but are not considered here.
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– Statistical Characteristics [1/3] –
• The pdf of the double-Gaussian channel envelope α = |h| = |h1 · h2| with fixed gain
A � 1 can be derived as
fα(α) =4α
σ21 · σ2
2
K0
(2
√α2
σ21 · σ2
2
), (81)
where K0(x) is the zeroth order modified Bessel function of the second kind.
• Assuming a variable gain, the pdf of the double-Gaussian channel envelope α, where
α = P2|h1|2|h1|2/(P1|h1|2 + N), can be derived as
fα(α) =4αP1
P2σ22
e−P1α2
P2σ22
[√Nα2
P2σ21σ2
2
K1
(2
√Nα2
P2σ21σ
22
)+
N
P1σ21
K0
(2
√Nα2
P2σ21σ2
2
)],
(82)
where K1(x) is the first-order modified Bessel function of the second kind.
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– Statistical Characteristics [2/3] –
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3
3.5
Channel Envelope α
Pro
bab
ility
Den
sity
Fu
nct
ion
Single−Hop Rayleigh; σ2=1
Fixed−Gain 2−Hop Rayleigh; sigma12=0.5, sigma
12=0.5
Fixed−Gain 2−Hop Rayleigh; sigma12=0.9, sigma
12=0.1
Figure 46: Behaviour is symmetric; the weaker the product of both channels (σ21σ
22 ), the lower the
mean and hence the worse the error rate performance.
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– Statistical Characteristics [3/3] –
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3
3.5
4
Channel Envelope α
Pro
bab
ility
Den
sity
Fu
nct
ion
Single−Hop Rayleigh; σ2=1
Fixed−Gain 2−Hop Rayleigh; sigma12=0.5, sigma
12=0.5
Variable Gain 2−Hop Rayleigh; sigma12=0.5, sigma
12=0.5
Figure 47: Variable gain improves performance by shifting the mean towards higher values of the
envelope (and hence power).
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– Temporal Characteristics [1/2] –
• The temporal auto-correlation function of h(t) with fixed gain A � 1 is given as
Rhh(τ) = 1/2 · σ21 · σ2
2 · (83)
where f1 = v1/λ1, f2 = v1/λ2, f3 = v2/λ2 are Doppler shifts induced by MTs, λ
is the wavelength, v is the velocity, τ is the time-lag, and J0(x) is zeroth-order Bessel
function of the first kind.
• With variable gain, the temporal auto-correlation function of h(t) is approximately
Rhh(τ) ≈ ξP2πJ0(2πf1τ)(1 − J0(2πf1τ)2)4P1
2F1(1.5, 1.5, 2, J0(2πf1τ)2)r2, (84)
where r2 = σ22/2J0(2πf2τ)J0(2πf3τ), ξ = 0.4037 for unit channel variances,
noises and transmit powers, and 2F1 is the Gauss hypergeometric function.
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– Temporal Characteristics [2/2] –
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
Time−Lag τ [s]
Au
to−C
orr
elat
ion
Fu
nct
ion
Rh
h(τ
)
BS−to−MT (MT @ 1 m/s)Fixed Gain MT−to−MT (both MTs @ 1 m/s)Variable Gain MT−to−MT (both MTs @ 1 m/s)
Figure 48: The 2-hop relay channel decorrelates faster than single-hop channel, which is good for
code design but bad for channel estimation purposes; variable gain decorrelates even faster.
201
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4.4 Distributed MIMO Behaviour
202
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– Spatial Fading Representation –
• MIMO channel is described by H, where hk,l is channel from k−th Tx to l−th Rx antenna
H =
⎛⎜⎜⎜⎜⎜⎝
h11 h12 · · · h1,t
h21 h22 · · · h2,t
......
. . ....
hr,1 hr,2 · · · hr,t
⎞⎟⎟⎟⎟⎟⎠
• model is useful for analysis but difficult to visualise
Distributed
Space -Time Decoder
Distributed
Space -Time Encoder
Channel
Encoder
Fractional
STC Word
Space-Time Decoder
Channel
Decoder
s
s
h11
hr,t
Distributed MIMO Channel
Fractional
STC Word
Fractional STC Word
Receiver
Receiver
Receiver
Information Sink
Information
Source
H
Figure 49: Distributed MIMO transceiver and channel.
203
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– Angular Fading Representation [1/3] –
• According to [5], using transformation
HΩ = U∗r · H · Ut
with unitary matrix U{r,t} with entries
1√{r, t}e(−j2πkl/{r,t}), {k, l} = 0, . . . , {t − 1, r − 1}
gives information over spatial domain Ω, i.e.
HΩ =
⎛⎜⎜⎜⎜⎜⎝
hΩ11 hΩ
12 · · · hΩ1,t
hΩ21 hΩ
22 · · · hΩ2,t
......
. . ....
hΩr,1 hΩ
r,2 · · · hΩr,t
⎞⎟⎟⎟⎟⎟⎠ ,
where non-zero entries of this angular matrix correspond to resolved MPCs.
204
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– Angular Fading Representation [2/3] –
t
Distributed Tx Antennas
r
Distributed Rx Antennas
resolved clusters in angular domain
Figure 50: Distributed MIMO channel resolved in the angular domain.
205
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– Angular Fading Representation [3/3] –Degree-of-Freedom (Rank):
• minimum number of non-zero rows and non-zero columns in HΩ
• depends on amount of clutter in channel & antenna separation
• determines the data multiplexing capabilities of the channel
Diversity Gain:
• number of non-zero entries in HΩ
• depends on connectivity of channel & antenna separation
• determines the reliability of the channel
Power Gain:
• strongest eigenvalue of HΩ (w.r.t. weaker eigenvalues; condition number max λi/ min λi)
• determines the beamforming capabilities
206
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– Distributed MIMO Channel Trends –
Distributed topology is submerged into rich clutter environment, resulting in:
• full-rank channel → maximum degrees-of-freedom (high data throughput)
• fully connected channel → maximum diversity gain (high reliability)
• well conditioned channel → little beamforming gain (limited range)
NLOS, from BS:
same pathloss
same shadowing
different fading
NLOS, distributed:
different pathloss
different shadowing
different fading
LOS, distributed:
different pathloss
same shadowing
different fading
BS
Figure 51: Typical (distributed) relaying pathloss, shadowing and fading behaviour.
207
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Open Issues
208
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– Open Issues –
As far as we are aware of, these are still open or only partially solved problems:
• Real-time distributed channel measurements & modelling, which capture
– shadowing correlation length for more general cooperative scenarios,
– distributed temporal shadowing behaviour,
– distributed temporal fading behaviour,
– interference pollution in cooperative bands.
• Closed-form mathematical description of AF relaying channel
– in terms of statistics and temporal behaviour,
– for different choice of amplification,
– for more general channels (Nakagami, Lognormal, composite),
– for generic number of relaying stages.
209
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PART 5TRANSPARENT PHY LAYER
210
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– Preliminary Note –
• Analysing the PHY layer performance of a wireless system is vital in understanding,
optimising and synthesising system parameters.
• There are several hundred highly complex contributions on transparent PHY layer
analysis and design available today, which requires us to concentrate on a very few of
them.
• For this reason, we proceed with the following topics:
1. discussion on optimum relay function;
2. performance analysis of canonical topologies;
3. space-time trellis transceiver design.
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5.1 Optimal Relay Function
212
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– Optimal Relay Function [1/2] –
• [71] and [72] questioned the optimality of transparent and regenerative relaying functions.
• They have derived different optimum functions for different underlying assumptions;
e.g. assuming BPSK modulation and a memoryless relay channel, the SNR-optimum f(r) is:
f(x + n1) = f(r) =
√Pr
E{tanh2(
√Psr)
} · tanh(√
Psr), (85)
where Ps and Pr are the source and relay powers, respectively.
• These results are a starter only, as they do not include the wireless fading and shadowing
channel.
Source: x Relay: f(x+n1) Destination: f(x+n1)+n2
Figure 52: Finding the optimum relaying function f(r).
213
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– Optimal Relay Function [2/2] –
−4 −3 −2 −1 0 1 2 3 4−3
−2
−1
0
1
2
3
Relay Input r
Rel
ay O
utp
ut
f(r)
Amplify & ForwardHard−DecisionSNR−Optimal Function
Figure 53: Finding the optimum SNR-maximising relaying function f(r).
214
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5.2 Performance Analysis
215
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– Performance: Topology I [1/3] –
• We will follow [46] and assume the following:
– 2-hop relay;
– single relay;
– fixed gain relay
– Rayleigh fading channels;
– no source-destination link;
• Derived results for MGF are in closed-form; however, most error rates remain in integral form.
Source
Rayleigh
Relay Rayleigh
Destination
216
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– Performance: Topology I [2/3] –
• According to [46], the end-to-end SNR at the receiver with fixed gain A and partial CSI at the
relay can be written as
γ =γ1γ2
C + γ2, (86)
where γi = Pih2i /N , Pi is the transmission power, hi is the Rayleigh fading channel, N the
noise power, C = γ1
[e1/γ1E1(1/γ1)
]−1, E1(x) is the exponential integral function and
γi = PiE{h2i }/N .
• This facilitates the MGF to be calculated, from which the performance of many coherent and
differential modulation schemes can be derived in closed form:
M(s) =1
γ1s + 1+
Cγ1seC/γ2(γ1s+1)
γ2(γ1s + 1)2E1
(C
γ2(γ1s + 1)2
). (87)
• For instance, the BER of binary DPSK is
Pb(E) =12M(1). (88)
217
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– Performance: Topology I [3/3] –
• To derive (87), one would typically go via the outage probability where we also use∫∞0
exp(−a/(4x) − bx)dx =√
a/bK1(√
ab), i.e.
Pout = P [γ < γth] =∫ ∞
0
. . . (89)
= (90)
= (91)
• By taking the derivative w.r.t. γth and using ddxK1(x) = −K0(x) − K1(x)/x and replacing
γth by γ, we obtain the pdf of γ as
pγ(γ) = (92)
• The MGF is finally found by evaluating M(s) =∫∞0
pγ(γ)e−sγdγ.
218
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– Performance: Topology II [1/3] –
• We will follow [73] and assume the following:
– 2-hop relay with single relay;
– fixed & variable relaying gains;
– Rayleigh fading channels throughout;
– N > 1 receiver antennas at destination;
– M-PSK SER with MRC at destination.
• Closed-form results are asymptotic and only hold for high SNRs.
Source
Rayleigh
Relay
Destination
219
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– Performance: Topology II [2/3] –
• Assuming P1 = P2 and constant amplification using (79), we get for the M-PSK
Ps(E) =1π
∫ π(M−1)/M
0
(−ξ)N−1eξΓ(0, ξ) −∑N−1j=1 (j − 1)!(−ξ)N−1−j
Γ(N)(1 + 1/ξ)N1/ξdθ
≤ M − 1M
Γ(N − 1)Γ(N)
(P1
2N
)−(N+1)
, (93)
where Γ(x) is the Gamma function, Γ(·, ·) is the upper incomplete Gamma function, and
ξ = sin2 θ/(sin2(π/M)P1/N). Diversity order is hence ’only’ N + 1.
• Assuming P1 = P2 and variable amplification using (80), we get for the M-PSK
Ps(E) =1π
∫ π(M−1)/M
0
(1 +
sin2(π/M)sin2 θ
P1
N
)−2N
dθ
≤ M − 1M
(P1
2N
)−2N
, (94)
where above integral is actually solvable in closed form. Full diversity order of 2N is achieved.
220
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– Performance: Topology II [3/3] –
0 2 4 6 8 10 12 14 16 18 20
10−4
10−3
10−2
10−1
100
Source−Destination SNR [dB]
SE
R
N = 2, fixed gainN = 2, variable gainN = 3, fixed gainN = 3, variable gain
Figure 54: Upper bound to the SER of 4-PSK for different N and relay strategies.
221
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– Performance: Topology III [1/3] –
• We will follow [74] and assume the following:
– 2-hop relay;
– K relay stations;
– variable relaying gains;
– Rayleigh fading channels throughout;
– M-PSK SER with MRC at destination.
• Exact integral and loose closed-form upper and lower SER bounds neglect noise in relays.
Source
Rayleigh
Relay #1
Destination
Relay #K
222
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– Performance: Topology III [2/3] –
• According to [74], the end-to-end SNR with MRC at the destination using a modified variable
gain, Ak =√
Pr,k/(P0|h1,k|2), which neglects noise at the relay, can be written as
γ = γ0 +K∑
k=1
γk, where γk =γ1,kγ2,k
γ1,k + γ2,k. (95)
• Again, the MGF can be calculated via the derivative of the outage; however, this leads to an
intractable integral for the SER. [74], however, proposed a tight upper and lower bound:
PL =
[(1 + γ0g)
K∏k=1
(1 + gγp,k/γσ,k
)]−1
· W (K, M), (96)
PU = 2K/g(K+1)
[γ0
K∏k=1
γp,k/γσ,k
]−1
· W (K, M), (97)
where g = sin2(π/M), γp,k = γ1,kγ2,k , γσ,k = γ1,k + γ2,k and
W (K, M) = 1/π∫ π(M−1)/M
0sin2K+2 φdφ.
223
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– Performance: Topology III [3/3] –
0 5 10 15 20 25 30
10−4
10−3
10−2
10−1
100
Source−Destination SNR [dB]
SE
R
K = 1, Lower BoundK = 1, Upper BoundK = 3, Lower BoundK = 3, Upper Bound
Figure 55: Lower and upper bounds to the SER of BPSK for different number K of relays.
224
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– Performance: Topology IV [1/3] –
• We will follow [75] and assume the following:
– K-hop relay;
– fixed relaying gains;
– partial CSI is available;
– Rice & Nakagami fading channels;
• Derivation of optimum fixed relaying gains; derivation of fairly good upper bounds on the
end-to-end SNR.
Source
gene
ral
fadi
ng
Relay#1
Destination
Relay#(K-1)
225
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– Performance: Topology IV [2/3] –
• According to [75], the end-to-end SNR with MRC at the destination using a fixed gain,
Ak =√
1/(CkN) can be written as
1γ
=1γ1
+C1
γ1γ2+ . . . +
C1 . . . CK−1
γ1 . . . γK=
1K
H, (98)
where H is the harmonic mean, i.e. H =[1/K
∑Kk=0(
∏kj=1 γj/Cj−1)−1
]−1
.
• Above SNR is intractable; however, using the fact that the harmonic mean can be upper
bounded by the geometric mean, i.e. H ≤ G = K
√∏Kk=1(
∏kj=1 γj/Cj−1), allowing γ to be
upper bounded as
γ ≤ γU = Z ·[
K∏k=1
γ(K+1−k)/Kk
](99)
where Z =[
1N
∏Kk=1 C
−(K−k)/Kk
].
226
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– Performance: Topology IV [3/3] –
• The optimum gains Ak can now be derived for Nakagami-m channels as:
Ak =
√eλkλmk
k Γ(1 − mk, λk)Nk
, (100)
where λk = mk/γk.
• This allows the n−th statistical moment to be computet as:
E{γnU} = Zn
K∏k=1
⎡⎣( γk
mk
)n(K−k+1)/KK Γ
(mk + n(K−k+1)/K
K
)Γ(mk)
⎤⎦ . (101)
• Using these moments, error rates and outages can be calculated either in closed form or
approximated by a converging series of moments.
227
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– Performance: Topology V [1/2] –
• We will follow [76] and assume the following:
– general multi-stage, multi-branch relay topology with variable relaying gains;
– derivations are applicable to any fading channel;
– MRC combining at destination.
• Noise in relays has been neglected to facilitate closed-forms. Asymptotically tight SERs are
derived using a McLaurin expansion of the channel’s pdf around zero.
Source
Relay#1
Destination
Relay#(K-1)
general fading
Relay#1 Relay#(K-1)
228
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– Performance: Topology V [2/2] –
• According to [76], the end-to-end SNR with MRC at the destination using a variable gain and
neglecting noise can be written as
γ ≈ γ1γ2
γ1 + γ2+ γ0. (102)
• The SER can be calculated as Ps(E) =∫∞0
Q (kγ) pdfγ(γ)dγ, where k depends on the
modulation scheme, Q(x) is the Marcum Q-function and pdfγ(γ) is the channel’s pdf.
• [76] has observed that Q (kγ) drops rapidly to zero for increasing γ, hence giving little
contributions to the integral. The main contribution comes from the region close to zero, in which
a McLaurin series expansion is applicable, i.e. pγ(γ) = aγt + o(γ), leading to
Ps(E) → 2taΓ(t + 3/2)√π(t + 1)
(kγ)−(t+1). (103)
• a depends on the channel; for instance, for a Rician-K channel, the SER can be bounded as
Ps(E) → 3(K + 1)2
4k2
(1γ1
+1γ2
)1γ0
. (104)
229
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5.3 Space-Time Transceiver Design
230
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– Transceiver Design: General –
• There is no time to discuss the numerous contributions which have recently emerged dealing
with the transceiver design of transparent relaying schemes; however, some are listed below.
• [77] proposes a noise reduction scheme at the transparent relay, which is only applicable to
binary modulations.
• [78] proposes a unitary precoder for the cooperative system achieving full diversity. For 4-QAM,
they arrive at a closed-form optimum precoder, greatly improving performance.
• [79] proposes a lattice-coded cooperation scheme which generalises prior non-orthogonal
amplify and forward protocols, while keeping the decoding complexity relatively low.
• [80] proposes novel STBCs based on the nonvanishing determinant criterion and is shown to
achieve the optimal diversitymultiplexing trade-off of the channel.
• [81] propose equalization methods for cooperative STBC diversity schemes over
frequency-selective fading channels.
231
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– Transceiver Design: STTC [1/4] –
• [82] and later [83] have investigated the code design requirements for transparent space-time
trellis codes (STTCs).
• By using prior analysis from [23] and [84], we wanted to derive design criteria for STTCs over
below example topology.
• We assumed n transmit and m receive antennas and arbitrary channel fading statistics.
Source
Relay
Destination
Relay
RelayRelay
232
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– Transceiver Design: STTC [2/4] –
• Rank & Determinant Criterion (m × n ≤ 3): The average error probability of that sequence eis received if c had been sent is:
〈P (c → e)〉 ≤ E(β1,1,...,βn,m) {P (c → e|(β1,1, . . . , βn,m)} (105)
=∫
β∈Rn×m
dβ · p(β)m∏
j=1
n∏i=1
e−14
EsN0
·λi|βi,j |2 ,
where Es the symbol energy and N0 the noise spectral density; m, n the number of receive
and transmit antennas, respectively; and λi the ith eigenvalue of the distance matrix
A(c, e) = B(c, e)BH(c, e), where BH denotes the Hermitian of B. The difference matrix Bfor codewords of length l is given as [23]:
B(c, e) =
⎛⎜⎜⎜⎝
e11 − c1
1 · · · e1l − c1
l
.... . .
...
en1 − cn
1 · · · enl − cn
l
⎞⎟⎟⎟⎠ (106)
233
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– Transceiver Design: STTC [3/4] –
• Furthermore, in (105), p(β) is the probability distribution of the n × m dimensional random
vector β = (β1,1, . . . , βn,m). For arbitrary channel realisations, this can be upper-bounded by
〈P (c → e)〉 ≤m∏
j=1
n∏i=1
[∫βi,j
p(βi,j) · e−14
EsN0
·λi|βi,j |2dβi,j
].
• Defining g(βi,j , λi) = e−14
EsN0
·λi|βi,j |2 , x = βi,j and using Schwarz’ integral inequality, it can
be shown that
〈P (c → e)〉 ≤m∏
j=1
n∏i=1
⎡⎣( 1
2π
Es
N0
) 14
·(
1λi
) 14
⎤⎦ (107)
=
(r∏
i=1
λi
)−m4
·(
2π
Es
N0
)−mr4
.
• Therefore, the minimum determinant of all codeword difference matrices needs to be maximised.
The determinant criterion hence constitutes a sufficient upper bound for channels with any pdf.
234
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– Transceiver Design: STTC [4/4] –
0 2 4 6 8 10 12 14 16 18 2010
−2
10−1
100
SNR
FE
R
3TX, 1 t−MT, 0 r−MT, 4 States3TX, 1 t−MT, 0 r−MT, 8 States3TX, 1 t−MT, 0 r−MT, 16 States3TX, 1 t−MT, 1 r−MT, 4 States3TX, 1 t−MT, 1 r−MT, 8 States3TX, 1 t−MT, 1 r−MT, 16 States3TX, 1 t−MT, 2 r−MT, 4 States3TX, 1 t−MT, 2 r−MT, 8 States3TX, 1 t−MT, 2 r−MT, 16 States
Figure 56: FER versus SNR for STTCs over transparent relays: 3 TX, 1 t-MT, a varying number of
r-MTs and STTC states.
235
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Open Issues
236
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– Open Issues –
I believe that these are some interesting open issues:
• Analysis and optimisation of
– robust synchronisation schemes tailored to transparent architectures,
– space-time codes tailored to transparent fading channel.
• Advanced topics, such as
– utilisation of analytical insights to obtain optimum relay placements,
– capacity-approaching distributed channel and space-time code design.
237
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PART 6REGENERATIVE PHY LAYER
238
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– Preliminary Note –
• Analysing the PHY layer performance of a wireless system is vital in understanding,
optimising and synthesising system parameters.
• There are several hundred highly complex contributions on regenerative PHY layer
analysis and design available today, which requires us to concentrate on a very few of
them.
• For this reason, we proceed with the following topics:
1. Distributed Space-Time Block Codes;
2. Estimate and Forward Protocols;
3. Decode and Forward Protocols;
4. Asynchronous Protocols.
239
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6.1 Distributed STBCs
240
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– System Model –
• Transmitter:
– number of distributed transmit antennas: t
– transmitted space-time block codeword: x ∈ Ct×1
– transmit power constraint: tr(E{xxH
}) ≤ S
• Channel:
– channel from transmitter i ∈ (1, t) to receiver j ∈ (1, r): hi,j
– fading realisations of hi,j : frequency-flat & uncorrelated
– grouping of sub-channel gains hi,j : H
• Receiver:
– received signal: y = Hx + n
– r−dimensional noise vector n has variance N per entry
• Cooperative Link:
– assumed to be error-free (!)
241
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�
– Exact STBC Error Probabilities [1/4] –
• Following [86], we will consider distributed cooperative STBCs of arbitrary rate R.
• Furthermore, the sub-channel realisation hi,j obey Nakagami fading with fading parameter f ;
the sub-channels may have different gains, thereby reflecting a possibly distributed deployment.
• We define u � t · r, γi � E {hih∗i } and assume
∑ui=1 γi = u.
Distributed
Space-Time Block Encoder
Distributed
Space-Time Block Decoder
FractionalSTBC
Space-Time
Block DecoderError
Detector
s s
h11
hr,t
O-MIMO
Channel
FractionalSTBC
FractionalSTBC
Receiver
Receiver
Receiver
Information
Source
H
s
Figure 57: Distributed Space-Time Block Code transceiver system.
242
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�
– Exact STBC Error Probabilities [2/4] –
Let’s define
PPSK(α, u, M) � 1(1 + α)u
[1
2√
π
Γ(u + 1/2)Γ(u + 1) 2F1
(u, 1/2; u + 1; (1 + α)−1
)(108)
+√
1 − gPSK
πF1
(1/2, u, 1/2 − u; 3/2;
1 − gPSK
1 + α, 1 − gPSK
)]
PQAM(α, u, M) � 1(1 + α)u
2q√π
Γ(u + 1/2)Γ(u + 1) 2F1
(u, 1/2; u + 1; (1 + α)−1
)(109)
− 1(1 + 2α)u
2q2
π(2u + 1)F1
(1, u, 1; u + 3/2;
1 + α
1 + 2α, 1/2
)
where Γ(x) is the complete Gamma function, 2F1(a, b; c; x) is the Gauss hypergeometric function
with 2 parameters of type 1 and 1 parameter of type 2 [87] (§9.14.1)), and F1(a, b, b′; c; x, y) is the
Appell hypergeometric function of two variables [87] (§9.180.1). Furthermore, α is a parameter, M
is the modulation order, gPSK � sin2(π/M), gQAM � 3/2/(M − 1), q � 1 − 1/√
M .
243
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�
�
– Exact STBC Error Probabilities [3/4] –
• Based on the analysis of [88] & [86], the symbol error rate (SER) of M-QAM and M-PSK STBC
systems operating over a Nakagami fading channel with different sub-channel gains γ i∈(1,u)
and different fading factors fi∈(1,u) can be derived in closed form as
Ps(e) =u∑
i=1
fi∑j=1
Ki,j · PPSK/QAM
(1R
γi
fit
S
N, j, M
)(110)
where
Ki,j =1
(fi − j)!(− 1
Rγi
fitSN
)fi−j
∂fi−j
∂sfi−j
⎡⎢⎣ u∏
i′=1,
i′ �=i
1(1 − 1
Rγi′fi′ t
SN · s
)fi′
⎤⎥⎦
s=
�
1R
γifit
SN
�−1
.
• For memoryless fading channels, the bit error rate (BER) and frame error rate (FER) for frames
of D symbols are respectively well approximated by
Pb(e) ≈ Ps(e)log2(M)
and Pf (e) ≈ 1 − (1 − Ps(e)
)D(111)
244
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�
– Exact STBC Error Probabilities [4/4] –
Error rate performance of distributed STBC scheme exhibits a high stability:
γ1Fractional
STBC
FractionalSTBC
γ2
ChannelEncoder
InformationSource
Space-Time
Block Decoder
Channel
Decoder
InformationSink
(a) Distributed Alamouti scheme with unequal
sub-channel gains due to different pathloss &
shadowing.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 210
−6
10−5
10−4
10−3
10−2
10−1
100
γ1
SE
R
1 Tx − SISO (γ1)
1 Tx − SISO (γ2=2−γ
1)
2 Tx − Alamouti (γ1 & γ
2=2−γ
1)
(b) SER versus the normalised power γ1 in the
first link for a distributed Alamouti system oper-
ating at 2 bits/s/Hz; SNR=30dB.
Figure 58: Topology and performance of distributed Alamouti scheme.
245
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6.2 Estimate & Forward Protocols
246
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– Considered Topology –
Following [86], the aim is to analyse the end-to-end error rate for the below general topology
assuming the estimate & forward protocol:
6th
VAA
5th
VAA
4th
VAA
(V-2)nd
VAA
(V-1)st
VAA
V-th
VAA
targ
et te
rmin
al
3rd
VAA
2nd
VAA
1st
VAA
so
urc
e t
erm
ina
l
1st
Relaying
Stage
2nd
Relaying
Stage
co
op
era
tion
rela
yin
g t
erm
inal
Figure 59: Distributed-MIMO multi-stage relaying topology.
247
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�
– End-to-End Error Rate [1/4] –
• We assume first no cooperation and unequal-power Rayleigh fading channels.
• To obtain the exact end-to-end BER is not trivial, as an error occurring in one node may or may
not be corrected by a parallel node.
• This creates dependencies between the error events at each stage in dependency of:
– the modulation scheme used,
– the prevailing channel statistics,
– the average channel attenuations,
– as well as the deployed STBC.
• The fairly complex interdependencies call for suitable simplifications, where we will weigh the
strength of a channel with a given error probability against the strength of the other channels.
• Subsequent explanations relate to Figure 60.
248
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�
– End-to-End Error Rate [2/4] –
3rd TierVAA2nd Tier
VAA
1st Tier
VAA
So
urc
e M
T
4th Tier
VAA
Targ
et M
T
(1,1)
(1,2)
(2,1)
(2,2)
(2,3)
(2,4)
(3,1)
(3,2)
P1,1
P1,2
P2,1
P2,2
P3,1
Figure 60: 3-stage distributed O-MIMO communication system without cooperation.
249
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�
– End-to-End Error Rate [3/4] –
• We assume that the system operates at low error rates which causes only one error event at a
time in the entire network.
• Let us assume that an error occurs in link (1,1); however, (1,2) is error free. Then the probability
that the error propagates further is related to the strengths of channels (2,1) and (2,3).
• It is intuitive and hence conjectured here that the probability that such error propagates is
proportional to the strength of the STBC branch it departs from, here (2,1) for one of two MISO
channels, and (2,2) for the other one.
• Therefore, the probability that an error which occurred in link (1,1) with probability P1,1
propagates through the O-MISO channel spanned by (2,1) and (2,3) is approximated as
P1,1 · γ2,1/(γ2,1 + γ2,3), where the strength of the erroneous channel (2,1) is normalised by
the total strength of both sub-channels.
• To capture the probability that such an error propagates until the t-MT, all possible paths in the
network have to be found and the original probability of error weighed with the ratios between
the respective path gains.
250
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�
– End-to-End Error Rate [4/4] –
• Taking the previously said into account and assuming that at high SNRs only one such error will
occur at any link, the end-to-end BER for the network depicted in Figure 60 can be expressed as
Pb,e2e(e) ≈[P1,1(e)
(γ2,1
γ2,1 + γ2,3
γ3,1
γ3,1 + γ3,2+
γ2,2
γ2,2 + γ2,4
γ3,2
γ3,1 + γ3,2
)+
P1,2(e)(
γ2,4
γ2,2 + γ2,4
γ3,2
γ3,1 + γ3,2+
γ2,3
γ2,1 + γ2,3
γ3,1
γ3,1 + γ3,2
)]+[
P2,1(e)(
γ3,1
γ3,1 + γ3,2
)+ P2,2(e)
(γ3,2
γ3,1 + γ3,2
)]+[P3,1(e)
]
• This can be simplified to
Pb,e2e(e) ≈[ξ1,1P1,1(e) + ξ1,2P1,2(e)
]+[
ξ2,1P2,1(e) + ξ2,2P2,2(e)]
+[ξ3,1P3,1(e)
]
where ξv,i is the probability that an error occurring in link (v, i) will propagate to the t-MT.
251
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– Clustering –
• This is easily generalised to networks of any size and any form of partial cooperation.
• To this end, remember that there are Qv∈(1,K) cooperative clusters at the vth stage, each of
which will yield an error probability of Pv∈(1,K),i∈(1,Qv).
• The end-to-end BER is hence approximated as
Pb,e2e(e) ≈K∑
v=1
Qv∑i=1
ξv,iPv,i(e) (112)
where the probabilities ξv,i are easily found from the specific network topology.
• The BERs Pv,i(e) can be found from the previously derived SERs with an appropriate number
of transmit and receive antennas per cluster, as well as prevailing channel conditions.
• The proposed approximation holds with high precision, as demonstrated by means of the
following performance graphs.
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– Performance –
0 5 10 15 20 25 30 35 40 45 50
10−4
10−3
10−2
10−1
100
End
−to
−E
nd B
ER
SNR [dB]
Exact (numerical)Approximate (analysis)
γ1,1
= 4, γ1,2
= 1γ2,1
= 1, γ2,2
= 4
γ1,1
= 0.1, γ1,2
= 0.05γ2,1
= 10, γ2,2
= 20
(a) Numerically obtained and derived end-to-
end BER versus the SNR in the first link for a
two-stage network without cooperation.
0 5 10 15 20 25 30 35 40 45 50
10−4
10−3
10−2
10−1
100
End
−to
−E
nd B
ER
SNR [dB]
Exact (numerical)Approximate (analysis)
γ1,1
= 1.9, γ1,2
= 0.1γ2,1
= 0.1, γ2,2
= 1.0γ2,3
= 1.0, γ2,4
= 1.9γ3.1
= 1.9, γ3,2
= 0.1
γ1,1
= 1.6, γ1,2
= 0.4γ2,1
= 0.4, γ2,2
= 1.0γ2,3
= 1.0, γ2,4
= 1.6γ3.1
= 1.6, γ3,2
= 0.4
γ1,1
= 21, γ1,2
= 22γ2,1
= 13, γ2,2
= 14γ2,3
= 15, γ2,4
= 16γ3.1
= 7, γ3,2
= 8
(b) Numerically obtained and derived end-to-
end BER versus the SNR in the first link for a
three-stage network without cooperation.
Figure 61: End-to-end BER of various 2- & 3-stage relaying topologies.
253
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– Throughput Maximisation –
• In [86], the end-to-end throughput-maximising optimised fractional power and optimised
fractional frame duration have been obtained as
α′v =
∏Kw=1,w �=v Rw · log2(Mw)∑K
k=1
∏Kw=1,w �=k Rw · log2(Mw)
(113)
β′v =
⎡⎢⎢⎢⎢⎢⎢⎣
K∑w=1
α′w
√√√√√√√√√√
Qv∑i=1
∑j∈i
ξ−1v,i K
−1v,i,jA
−1v Bv,i,j
Qw∑i=1
∑j∈i
ξ−1w,iK
−1w,i,jA
−1w Bw,i,j
⎤⎥⎥⎥⎥⎥⎥⎦
−1
(114)
where the notation j ∈ i represents the j th sub-channel belonging to the ith cluster, Further-more, Kv,i,j =
∏j′∈i,j′ �=j
γv,j
γv,j−γv,j′and
Av =
{Mv−1
Mv log2(Mv) for M-PSK2qv
log2(Mv) for M-QAMBv,i,j =
{ gPSK,v
Rv
γv,j∈i
tv
SN for M-PSK
gQAM,v
Rv
γv,j∈i
tv
SN for M-QAM
254
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6.3 Decode & Forward Protocols
255
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– Decode & Forward Methods –
• The most tractable DF methods are:
– repetition based (repeat codeword during relaying)
– channel code based (relay parity information)
– space-time code based (construct ST codeword or multiplex)
repetition
s-MT
r-MT t
channel code
s-MT
r-MT t
same data parity data
ST code
s-MT
r-MT t
ST data
Supportive Case:
256
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– Channel Coded: Topology –
• We will follow [89] and assume the following:
– 2-hop relay;
– K relay stations;
– variable relaying gains;
– Rayleigh fading channels throughout;
– BPSK, channel coder, MRC at destination.
• Optimised power allocation at source and relays; pertinent to realistic systems.
Source
Rayleigh
Relay #1
Destination
Relay #K
257
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– Channel Coded: System Model –
• Source first broadcasts s(t) to both the destination and relays at time t.
• Upon receiving signals from the source, each relay decodes the received signal, re-encodes it
and transmits it as xr,k(t)
• The power of source and relays are constrained, where
– P is the overall power;
– α0 · P is the power allocated to the source;
– αr,k · P is the power allocated to the k−th relay;
– α0 +∑K
k=1 αr,k = 1.
• The respective fading channel powers are:
– γ0 is the average fading channel power between source and destination;
– γ1,k is average fading channel power between source and k−th relay;
– γ2,k is average fading channel power between k−th relay and source;
258
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– Channel Coded: Approximate DF Model [1/4] –
• We define:
– SNRin,1,k the input SNR at the decoder of the k−th relay;
– SNRout,1,k the output SNR of the decoder of the k−th relay;
• Relationship between these SNRs for DF is SNRout,1,k = f (SNRin,1,k).
• For convolutional codes, the above relationship can be upper-bounded at high SNR
by [90]:
SNRout,1,k ≤ SNRin,1,k · R · dfree, (115)
where R is the channel code rate and dfree its free distance.
• For other types of block and channel codes as well as tighter bounds, one can use the
theory invoked in [91].
259
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– Channel Coded: Approximate DF Model [2/4] –
• Soft-output at the decoder k at time-sample moment i for BPSK modulation can be
modelled as
sk(i) = sk(i) (1 − nk(i)) , (116)
where sk(i) is the exact transmitted symbol.
• Furthermore, nk(i) is an equivalent noise with mean μn,k and variance σ2n,k, which
can be calculated as [92]
μn,k =1l
l∑i=1
|sk(i) − sk(i)| , (117)
σ2n,k =
1l
l∑i=1
(sk(i) − sk(i) − μn,k)2 , (118)
where l is the code sequence length.
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– Channel Coded: Approximate DF Model [3/4] –
• The signals transmitted from the k−th relay is hence given as
xr,k(i) = βksk(i), (119)
where βk is a normalisation factor calculated from the transmit power constraint at the
relay as
β2k
((1 − μn,k)
2 + σ2n,k
)≤ αr,k · P. (120)
• After some manipulations, one can calculate the end-to-end SNR at the destination [89]:
γ ≤(
γ0 +K∑
k=1
γ1,kγ2,kαr,kRdfree
γ2,kαr,k + γ1,kαr,kRdfree + N0/P
)α0 · P
N0, (121)
where N0 is the noise power spectral density.
261
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– Channel Coded: Approximate DF Model [4/4] –
• From this, we can finally calculate the optimum distributed power allocation coefficients
for source and relays:
αopt0 =
8γ20 + Rdfree
∑Kk=1 γ1,kγ2,k ± 8γ0
√γ2
0 + 14Rdfree
∑Kk=1 γ1,kγ2,k
8γ20 + 2Rdfree
∑Kk=1 γ1,kγ2,k ± 8γ0
√γ2
0 + 14Rdfree
∑Kk=1 γ1,kγ2,k
and
αoptr,k =
Rdfreeγ1,kγ2,k
8γ20 + 2Rdfree
∑Kk=1 γ1,kγ2,k ± 8γ0
√γ2
0 + 14Rdfree
∑Kk=1 γ1,kγ2,k
.
• It can be observed that the power allocation factor for k−th relaying node is
proportional to the channel and coding gain of the k-th relay link.
• The power gains w.r.t. equal power allocation for different channel configurations are
shown in the subsequent slide.
262
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– Channel Coded: Power Gains –
1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
2.5
3
3.5
4
Number of Relays K
SN
R G
ain
[d
B]
γ0=γ
1,k=γ
2,k=1
γ0=4γ
1,k=4γ
2,k=1
4γ0=γ
1,k=4γ
2,k=1
γ0=γ
1,k=4γ
2,k=1
Figure 62: Power gains can be achieved by using prior theory, where this gain will monotonically
increase as the number of relays increases.
263
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– Space-Time Coded: Code Design [1/4] –
• We will follow [103] and assume the following:
– two-hop relay system with K relaying nodes;
– Rayleigh fading channel;
– relay only re-transmits if received correctly;
– MLSE detector at destination.
• Upper bound to the pairwise error probability (PEP) has been derived.
Source
Rayleigh
Relay #1
Destination
Relay #K
264
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– Space-Time Coded: Code Design [2/4] –
• According to [103], the received sequence vector at the destination is
yd =√
P2XDIh + n, (122)
where X is the space-time code sequence, n the noise, h the channel vector from the relays to
the destination, and DI = diag(I1, . . . , IK) the relay state matrix.
• Ik = 1 with probability (1 − Pk)L if relay decoded information successfully from source and
Ik = 0 otherwise with probability 1 − (1 − Pk)L, where L is the frame length and for M-QAM
Pk ≤ 2Ng(2)bP1|h1,k|2
, (123)
where b = 3/(M − 1), g(2) = 4Y/π∫ π/2
0sin2 θdθ − 4Y 2/π
∫ π/4
0sin2 θdθ and
Y = 1 − 1/√
M . Ik is hence Bernoulli distributed.
• We will subsequently assume that all channel realisations are symmetric, i.e.
|h1,k|2 = |h1,K |2 and Pk = PK .
265
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– Space-Time Coded: Code Design [3/4] –
• Maximum likelihood decoding is applied, where the PEP can be bounded by:
Pr(X1 → X2|I,h) = Pr(‖y −
√P2X1DIh‖2 >‖y −
√P2X2DIh‖2|I,h,X1
)
≤K∑
k=0
(1 − L · PK)k(L · PK)K−k · Ω (P2/N) (124)
where
Ω(x) =∑
I:nI=k
⎛⎝ 2k − 1
k − 1
⎞⎠
xk∏k
i=1 λIi
. (125)
Here, nI is the number of active relays (assuming that the space-time codeword is full-rank) and
λIi are the nonzero eigenvalues of sent signal matrix corresponding to state I.
• Above equation allows us to gain insights into the design criteria of the space-time code word.
266
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– Space-Time Coded: Code Design [4/4] –
• Following [103] and assuming α to be the fractional power of the first stage, we rewrite the PEP
as
Pr(X1 → X2|I,h) ≤ SNR−KK∑
k=0
(2Lg(2)
bα|h1,K |2
)K−k
· Ω(1 − α) (126)
• The diversity gain is given as
D = limSNR→∞
− log(PEP )/ log(SNR) = K, (127)
which indicates that any full-rank MIMO code will achieve full diversity if used for the decode and
forward space-time protocol.
• The coding gain is given as
C = 1/n
√√√√ K∑k=0
(2Lg(2)
ba1|h1,K |2
)K−k
· Ω(1 − α) (128)
which indicates that − among all determinant-maximising space-time codes − special decode
and forward space-time codes need to be constructed to maximise coding gain. 267
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– Space-Time Coded: Correlation Impact [1/3] –
• We will follow [104] and assume the following:
– two-hop relay system with K relaying nodes;
– correlated Rayleigh fading channel;
– each relay node has potentially more than one antenna;
– (Q-)OSTBCs at relays with MRC at destination.
• Upper bound to the BER with correlation has been derived.
Source
Rayleigh
Relay #1
Destination
Relay #K
268
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– Space-Time Coded: Correlation Impact [2/3] –
• According to [104], the BER can be Chernoff upper-bounded in the high SNR region by
BER ≤ Ne
(SNRd2
min
4M
)−M
βdeg, (129)
where Ne and dmin are the number of nearest neighbours and the minimum Euclidean
distance in the constellation diagram, M is the total number of antenna elements in the relay
stage, βdeg = det[E{vec{H}vec{H}H}]−1, H = [H(1)T , . . . ,H(K)T ]T
,
vec{H(k)} = S(k)1/2vec{Hw
(k)}, Hw(k) is spatially white and S(k) is the covariance
matrix from the k−th relaying terminal capturing correlation.
• Having 4 antennas, we can e.g. (1) take one terminal with 4 antennas or (2) two terminals with
two antennas each. The degradation coefficient can be calculated from the above [104]:
β(1)deg = (1 − 6ρ + 15ρ2 − 20ρ3 + 15ρ4 − 6ρ5 + ρ6)−1, (130)
β(2)deg = ((4α2
1 − 4α31 + α4
1)(1 − 4ρ + 6ρ2 − 4ρ3 + ρ4))−1, (131)
where ρ is the correlation coefficient and α1 is the channel gain from relay #1 (α2 = 2 − α1).
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– Space-Time Coded: Correlation Impact [3/3] –
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
0
101
102
103
104
Correlation Coefficient ρ
Deg
rati
on
Co
effi
cien
t β d
eg
4 Antennas in 1 Relaying Terminal2 Antennas in 2 Relaying Terminals with a
1=1 & a
2=1
2 Antennas in 2 Relaying Terminals with a1=0.5 & a
2=1.5
Figure 63: Correlation has bigger impact than power imbalance!
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– Distributed Multiplexing: Topology –
• We will follow [93] and assume the following:
– two-hop relay system with K relaying nodes over Rayleigh channel;
– relays multiplex sub-stream from received full data stream;
– N receive antennas at the receiving node;
– receiving node deploys zero-forcing (ZF) or minimum mean square error (MMSE).
• Assuming no channel coding, the error rates for multiplexed streams are derived.
Source
Rayleigh
Relay #1
Destination
Relay #K
Antenna #1
Antenna #N
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– Distributed Multiplexing: System Model –
• Communication is performed in two steps:
– In the first phase, the source broadcasts a 2K−ary symbol x representing K bits,
x1, . . . , xK , with energy Es.
– In the second phase, relay k detects only xk and forwards its estimate xk to the
destination with enery Er ; all relays do this simultaneously using the same channel.
• At the destination, each multiplexed signal stream is detected by using ZF or MMSE and
then subtracted to detect the subsequent sub-stream.
• The ordering of the sub-streams and hence their order of substraction is traditionally
based on each sub-streams SNR; however, [93] propose to order according to the
log-likelihood ratio.
272
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– Distributed Multiplexing: Performance –
Figure 64: Spectral efficiency 4b/s/Hz, ds,r = 5m, dr,d = 100m, N=8; C-SM = cooperative spatial
multiplexing, C-DIV = cooperative diversity; all use 256-QAM between source and relay; C-SM uses
16-QAM for 2 relays and BPSK for 8 relays; C-DIV uses Alamouti STBC with 256-QAM [93].
273
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6.4 Asynchronous Protocols
274
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– Synchronisation Methods –
• Of major concern for distributed relaying networks is how to maintain synchronisation between
cooperative nodes and nodes belonging to the same relaying stage, whether cooperating or not.
• Several approaches are possible, some of which are dealt with subsequently:
– Natural Synchronisation: Assuming that terminals belonging to the same relaying hop
require the same processing time, i.e. reception, decoding, re-encoding, transmission, then
path differences leading to relative delays less than the symbol duration are acceptable.
– Extended Cyclic Prefix: As long as the cooperative scheme uses OFDM and the CP is
longer than the channel’s power delay profile plus the maximum expected asynchronism, ISI
is mitigated inherently. In addition, Cyclic Delay Diversity can be used!
– Asynchronous STC: It is also possible to design space-time coding schemes which are
robust to asynchronisms, however, mostly at the cost of a loss in spectral efficiency and/or
performance.
275
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– Natural Synchronisation [1/3] –
We will estimate the allowed spatial separation between relaying terminals belonging to the same
relaying stage for the best and worst case, so that natural synchronisation is still possible:
s-MT t-MTr-MT1r-MT2
Best Case (relaying in series)
r-MT1
r-MT2Worst Case (relaying in parallel)
s-MT t-MT
Δ d
d d
Figure 65: Best and worst case for natural synchronisation between terminals.
276
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– Natural Synchronisation [2/3] –
• The time synchronisation error ought to be below sampling rate ΔT , which allows an optical
path difference of ΔT · c, where c ≈ 3 · 108m/s is the speed of light.
• Assuming equal processing time in each r-MT, the topological distribution has to obey:∣∣∣(ds→r2 + dr2→t) − (ds→r1 + dr1→t)∣∣∣ ≤ ΔT · c (132)
• For the best case, i.e. both r-MTs are on the line between s-MT and t-MT, they can be separated
by any distance because |(ds→r2 + dr2→t) − (ds→r1 + dr1→t)| = 0.
• For the worst case, i.e. one r-MT lies on the line between s-MT and t-MT and the other r-MT is
on the ellipse with the s-MT and t-MT in its foci. For simplicity, we assume that the first r-MT is
exactly in the middle between s-MT and t-MT and the second r-MT is perpendicular. For this
case, the allowed spatial separation between both r-MTs is easily obtained as:
Δd ≤√(
ΔT · c2d
+ 1)2
− 1 (133)
where d is the distance between the t-MT (s-MT) and the first r-MT.
277
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– Natural Synchronisation [3/3] –
0 10 20 30 40 50 60 70 80 90 10010
20
30
40
50
60
70
80
90
100
Distance d between s−MT and r−MTs (r−MTs and t−MT) in [m]
Allo
wed
spa
tial s
epar
atio
n Δ
d b
etw
een
r−M
Ts
in [m
]
HiperLAN2: Ts⋅ c = 15m
UMTS: Tc⋅ c = 75m
(a) Allowed spatial separation between r-MTs
for WLAN and UMTS according to the topology
in Figure 65.
0 10 20 30 40 50 60 70 80 90 1000
20
40
60
80
100
120
140
160
180
200
Distance d between s−MT and r−MTs (r−MTs and t−MT) in [m]
Fra
ctio
n Δ
d / d
in [%
]
HiperLAN2: Ts⋅ c = 15m
UMTS: Tc⋅ c = 75m
(b) Fraction of the allowed spatial separation
between r-MTs w.r.t. the absolute distance be-
tween s-MT and r-MT for WLAN and UMTS ac-
cording to the topology in Figure 65.
Figure 66: Study of allowed spatial separation for natural synchronisation.
278
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– CDD/OFDM Inherent Synchronisation [1/2] –
• Cyclic delay diversity (CDD) is the application of delay diversity (DD) to OFDM; DD has been
pioneered by A. Wittneben in 1993 and CDD by Armin Dammann and Stefan Kaiser in 2001.
• It is a transmit diversity scheme, where the same signal stream is transmitted from each
available antenna with a controlled mutual timing offset.
• This makes the channel more frequency selective and hence yields a performance gain when
detected with MLSE or MMSE equaliser.
• Furthermore, CDD has the following properties:
– The optimum delays between the transmit antennas depend on the modulation scheme (and
fading channel).
– There is no modification required to the receiving side.
– Although the deployment of MLSE and MMSE is possible without an outer channel code, this
will rarely be the case.
– A delay spread of less than the cyclic prefix length is tolerated, which makes it very attractive
for distributed deployment with loose synchronisation.
279
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– CDD/OFDM Inherent Synchronisation [2/2] –
Target MT
Relaying MT#2
Relaying MT#1
Modulator S/P IFFT CP
Data Bits
Modulator S/P IFFT CPδ
remove
CPFFT P/S MLSE/MMSE
Delay
Power Delay Profile
Length of
cyclic prefix (CP)
Figure 67: Cyclic delay diversity transmitter and receiver.
280
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– Asynchronous Space-Time Code Design [1/4] –
• Various Asynchronous space-time code designs have been proposed in recent years, most
notably [105]−[115] and also [103].
• We will concentrate on [103] according to below topology, where we assume Rayleigh channels
and orthogonal and hence loosely synchronised relay frames. This greatly facilitates
asynchronous communication.
Source
Rayleigh
Relay #1
Destination
Relay #K
Duration: T T/K T/K T/K
281
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– Asynchronous Space-Time Code Design [2/4] –
• According to [103], the received sequence vector at the k−th relay is
yk =√
P1h1,ks + nr,k, (134)
where s is the source symbol sequence, nr,k the noise at the relay and h1,k the channel from
source to relay.
• It is assumed that the k−th relay performs a ’sequence-contraction’ by means of a linear
transformation tk, i.e. tkyk, where necessarily L = K .
• For subsequent analysis, a codeword vector x is defined as
x = [t1T , . . . , tKT ]T s = Ts and X = diag(x), (135)
where T is a K × K linear transformation matrix.
• From above, xk = tks and xmk is the k−th element of the xm codeword.
282
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– Asynchronous Space-Time Code Design [3/4] –
• Using a maximum likelihood decoder, the PEP can be upper bounded by:
PEP = Pr(Xm → Xj) (136)
≤ NK
∏Kk=1,xmk �=xjk
(1
P1|h1,k|2+ 1
P2|h2,k|2)
∏Kk=1,xmk �=xjk
|xmk−xjk|24
. (137)
• The diversity gain is hence given as
D = limSNR→∞
− log(PEP )/ log(SNR) = minm�=j
rank(Xm − Xj), (138)
which indicates that the difference matrix xm − xj should be full-rank for any codeword x.
• The coding gain is given as
C = K
√√√√ K∏k=1
|xmk − xjk|2, (139)
which requires the minimum product distance to be maximized.
283
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– Asynchronous Space-Time Code Design [4/4] –
0 5 10 15 20 25 3010
−5
10−4
10−3
10−2
10−1
100
SNR per time slot [dB]
BE
R
Asynchronous Space−Time Code, delay < slot durationSynchronous Space−Time Code, no delaySynchronous Space−Time Code, delay = 60 % of slot duration
Figure 68: BER for two relays using optimum Vandermonde matrices T for constructing x [103].
284
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Open Issues
285
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– Open Issues –
Again, there are endless unsolved problems. However, I believe that these are some
interesting open issues:
• Analysis and optimisation of
– robust synchronisation schemes,
– differentially modulated cooperative (space-time) schemes,
– random beamforming with sensor nodes.
• Advanced topics, such as
– design of (sub-)optimum multi-user cooperative transceivers,
– capacity-approaching distributed channel and space-time code design.
286
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PART 7MAC & X-Layer Design
287
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– Preliminary Note –
• The MAC layer is central to the throughput and delay of a wireless system.
• There are dozens contributions available today, which is why we only concentrate on
some basic MAC and cross-layer design issues.
• We proceed with the following topic:
1. cooperative-diversity slotted ALOHA MAC with routing protocol;
2. throughput of cooperative PHY-optimized CSMA/CA based MACs;
• These are contributions which we found very interesting but have no time to dwell on:
– Larsson: selection diversity including fading and capture effects [116];
– Dianati et al.: analytical analysis of node-cooperative ARQ scheme, which introduces
a CFC (Claim for Cooperation) into the CSMA/CA MAC structure and shows that
performance gains can thereby be achieved [119].
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– MAC is Centre of Gravity! –
The MAC decides upon:
• transmit power levels → error rates, interference behaviour
• frame lengths → throughput, interference behaviour
• scheduling timings → delay, interference behaviour
• IP packet ’buffering’ → QoS
CSMA-type MAC
(conventional)
Reservation-type MAC
(distr. & coop.)
Control Signalling
Data Traffic
synchr/hop reserv/etc. not useful
bursty data ‘regularized’ data
Hybrid
MAC
?
?
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7.1 Cooperative-DiversityALOHA MAC & Routing
290
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– Rational of Protocol [1/2] –
• The cooperative-diversity slotted ALOHA (CDSA) protocol has these properties [118]:
– if packet in a traditional ad hoc network gets lost along the chosen route, then a full
re-transmissions process is initiated;
– however, nodes adjacent to the troubled link may have received the packet correctly and −with a proper MAC protocol − can help relaying this packet to the destination;
– their MAC protocol is based on a modified slotted ALOHA MAC, coupled with a suitable
routing metric.
• With reference to the figure on the subsequent slide, the following can be observed:
– A wants to transmit to H and determines from the routing table that this shall happen via D;
– however, the link between A and D is in a deep fade hence corrupting reception;
– nonetheless, B, C and E have well received and decoded the packet;
– all three check the packet header and decide whether to forward the packet eventually;
– according to subsequent MAC and routing rules, only one of them chooses to forward.
291
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– Rational of Protocol [2/2] –
A
B
I
J
H
C
D
F
E
G
X
source destination
active
relay
active
relay
intended
receiver
Figure 69: Illustration of cooperative routing/MAC approach [118].
292
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– Routing Metric –
• A minimum-cost routing algorithm is considered with a route cost given by the pair (H, L),
where
– H is the number of hops towards the destinations; and
– L =∑
i 1/SNRi, where SNRi is the average SNR of the i-th hop.
• The link cost tuples are ordered such that (Hi, Li) < (Hj , Lj) if
– Hi < Hj , i.e. minimum-hop routing takes priority;
– Hi = Hj and Li < Lj , i.e. a lower link cost is chosen for the same hop count.
• The route may hence dynamically be changed by means of Routing Relays (RR), which
happens iff
– the RR overhears a packet from the transmitter and can decode it;
– the RR’s hop count towards destination is not bigger than from the transmitter;
– the RR’s link cost is also not larger than that of the transmitter.
293
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�
�
– MAC Protocol [1/2] –
• PRD (Packet-Reached-Destination) is populated with positive acknowledgement of final
destination;
• ACK1 is for the intended receiver (not destination) to acknowledge successful reception;
• RRF (Request-for-Relay-Forwarding) / PRD slot is populated as follows:
– if Tx receives PRD in first slot, then Tx will send second PRD to stop further transmissions;
– if Tx does not get PRD in first slot but an ACK1, then it will not transmit anything;
– if Tx receives nothing, then it will transmit RRF to get help from RR.
• One or more ACK2.i mini-slots are used for RRs to compete to relay packet, where
– if RRF does not match received packet, the RR will drop the packet;
– otherwise, it will decide whether to transmit or not and if it does then it sends ACK2.i.
Message PRD ACK1PRD/
RRFACK2.1 ACK2.k CRF
One Cooperative MAC Slot
294
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– MAC Protocol [2/2] –
• the CRF (Clear-to-Relay-Forwarding) mini-slot is used to select suitable RR, where
– Tx chooses RR which responded in at least one ACK2.i mini-slot with probability p;
– if there are no such mini-slots (either due to non-availability or ACK collisions), then the entire
re-transmission cycle is re-initiated.
• after having sent the ACK in at least one of the mini-slots, the RR will wait for the CRF, where
– if there is no CRF, then the RR will discard the packet;
– if CRF is present, then the RR will check whether it is the correct packet and will forward it;
• this handshaking procedure is necessary because RRs may not be able to hear their mutual
ACKs.
Message PRD ACK1PRD/
RRFACK2.1 ACK2.k CRF
One Cooperative MAC Slot
295
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– Performance [118] –
296
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7.2 CSMA-TypePHY/MAC Optimisation
297
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– Approach for CSMA-type MAC [1/3] –
We are interested in a general mathematical framework which quantifies:
• throughput (for bursty data)
• delay (for signalling and bursty data)
in dependency of
• node density, distribution & traffic
• transmission & interference radii
• pathloss/shadowing/fading models
which allows us to
• characterise performance of CSMA/4W-HS/SW-ARQ/etc protocols
• synthesise an optimum MAC
298
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�
– Approach for CSMA-type MAC [2/3] –
Distributed
STC
Co
op
era
tio
n
So
urc
e N
od
e
Desti
nati
on
No
de
Coo
pera
tion
Coo
per
atio
n
Cooperation
Distributed
STC
STC
Sou
rce N
od
e
Destin
atio
n N
od
e
Figure 70: Multi-hop CSMA/CA scenario with two different transmit power levels (coverage areas).
299
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– Approach for CSMA-type MAC [3/3] –
low modulation index (BPSK) high modulation index (64QAM)
→ low error rate (low prob. of loss) → high error rate (high prob. of loss)
→ long packets (high prob. of collision) → short packets (low prob. of collision)
with channel code without channel code
→ low error rate (low prob. of loss) → high error rate (high prob. of loss)
→ long packets (high prob. of collision) → short packets (low prob. of collision)
Can we capture this trade-off analytically?
300
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– CSMA-type PHY/MAC Optimisation [1/6] –
’1’: normalised packet length D: delay period
a: slot duration (=log2(M)/Nb) T : transmission period
p: persistency factor B: busy period
Pf : frame error probability I : idle period
D(1)
D(2)
D(1)
IT(1)
T(1)
T(2)
B(1)
B(2)
Busy Period Idle Period
a1 Sub-delayTransmission
Period
Figure 71: Time sequence of events for basic p−persistent CSMA/CA.
301
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– CSMA-type PHY/MAC Optimisation [2/6] –
The useful average end-to-end network throughput can be derived as
S = B × 1N
× U
B + I + C(140)
where
• B is the number of bits per packet;
• N is the average number of hops from source to destination;
• U is the average useful transmission time;
• B is the average busy time;
• I is the average idle time;
• C is the average cooperation time;
302
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– CSMA-type PHY/MAC Optimisation [3/6] –
• We can derive the average idle period I to be
I =a
1 − (1 − g)Mt(141)
• We can derive the average busy period B to be
B = E[D(1)] + (J − 1)E[D(2)] + J (1 + a) (142)
where the average number of busy sub-periods is given as
J =N
(1 − g)(1+1/a)(Mt−1)(143)
and
E[D(j)] =
⎧⎨⎩ d(1) j = 1
d(1 + 1/a) j = 2, 3, ...(144)
where
303
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�
�
– CSMA-type PHY/MAC Optimisation [4/6] –
d(X) =a
N − (1 − g)X(Mt−1)(145)
·∞∑
k=1
{N(1 − p)k − p
[(1 − p)k − (1 − g)k
p − g
]}
·{
(1 − p)k − p(1 − g)X
[(1 − p)k − (1 − g)k
p − g
]}Mt−1
− a(1 − g)X(Mt−1)
N − (1 − g)X(Mt−1)
∞∑k=1
[p(1 − g)k − g(1 − p)k
p − g
]Mt
• Similarly, we can derive the average useful period U to be
E[U (j)] =
⎧⎨⎩ u(1) j = 1
u(1 + 1/a) j = 2, 3, ...(146)
where
304
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– CSMA-type PHY/MAC Optimisation [5/6] –
u(X) =p · (1 − Pf )
N − (1 − g)X(Mt−1)
∞∑k=0
{(1 − p)k+1 (147)
−p(1 − g)X
[(1 − p)k+1 − (1 − g)k+1
p − g
]}Mt−2
·{(1 − g)k(1 − p)k[N(1 − g)X − 1]
+Mt
{(1 − p)k − (1 − g)X
[p(1 − p)k − g(1 − g)k
p − g
]}
·{
N(1 − p)k+1 − p
[(1 − p)k+1 − (1 − g)k+1
p − g
]}}
−Mtgp(1 − g)X(Mt−1)
N − (1 − g)X(Mt−1)
∞∑k=1
[p(1 − g)k+1 − g(1 − p)k+1
p − g
]Mt−1
·[(1 − g)k − (1 − p)k
p − g
]
305
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– CSMA-type PHY/MAC Optimisation [6/6] –
• The average cooperation time C is easily calculated as:
C =U · Nc
α, (148)
where
– U is the average useful transmission time;
– Nc is the number of cooperating links per relaying stage;
– α is the strength of the cooperative data-pipe w.r.t. the relaying pipe.
• Here, we assumed that a reservation based MAC protocol is used per cooperative stage.
• For the design and analysis of a CSMA-based MAC at the cooperative stage, please,
consult [130].
306
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– Performance: Transmission Range [1/6] –
no relaying (20m)
1-hop relaying (10m)
2-hop relaying (6.7m)
Figure 72: We have choice of a single hop, dual hop, triple hop, etc.
307
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– Performance: Transmission Range [2/6] –
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18
20
Transmission Range [m]
Net
wo
rk S
pec
tral
Th
rou
gh
pu
t [b
/s/H
z]
SNR = −10dB : BPSKSNR = −10dB : QPSKSNR = −10dB : 16QAMSNR = +10dB : BPSKSNR = +10dB : QPSKSNR = +10dB : 16QAM
Figure 73: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, no cooperation (just relaying).
308
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– Performance: Cooperation [3/6] –
0 2 4 6 8 10 12 14 16 18 200
5
10
15
20
25
30
35
40
45
50
Transmission Range [m]
Net
wo
rk S
pec
tral
Th
rou
gh
pu
t [b
/s/H
z]
SNR = −10dB : BPSKSNR = −10dB : QPSKSNR = −10dB : 16QAMSNR = +10dB : BPSKSNR = +10dB : QPSKSNR = +10dB : 16QAM
Figure 74: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, three nodes cooperate, α → ∞.
309
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– Performance: Cooperation Pipe [4/6] –
0 2 4 6 8 10 12 14 16 18 200
5
10
15
20
25
30
35
Transmission Range [m]
Net
wo
rk S
pec
tral
Th
rou
gh
pu
t [b
/s/H
z]
α = 1 : BPSKα = 1 : QPSKα = 1 : 16QAMα = 10 : BPSKα = 10 : QPSKα = 10 : 16QAM
Figure 75: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, three nodes cooperate, SNR= 10dB.
310
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– Performance: Channel Code [5/6] –
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Transmission Range [m]
Net
wo
rk S
pec
tral
Th
rou
gh
pu
t [b
/s/H
z]
w/out code : BPSKw/out code : QPSKw/out code : 16QAMwith code : BPSKwith code : QPSKwith code : 16QAM
Figure 76: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, no cooperation, SNR= −10dB.
311
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– Performance: Channel Code [6/6] –
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18
20
Transmission Range [m]
Net
wo
rk S
pec
tral
Th
rou
gh
pu
t [b
/s/H
z]
w/out code : BPSKw/out code : QPSKw/out code : 16QAMwith code : BPSKwith code : QPSKwith code : 16QAM
Figure 77: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, no cooperation, SNR= +10dB.
312
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Open Issues
313
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– Open Issues –
The design and analysis of suitable cooperative MAC protocols is still in its infancy. I believe
that these are some interesting open issues:
• For existing MAC protocols, analysis of
– throughput & delay for finite user populations,
– throughput & delay for realistic queuing models,
– throughput & delay for cooperative systems,
• Design of optimum MAC incorporating
– x-layer optimised PHY and network layer design,
– cooperative links in an explicit way.
314
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PART 8SYSTEM CONSIDERATIONS
315
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– Preliminary Note –
• In the end, it will be the entire system which will facilitate/realise cooperative
communication.
• The available literature on cooperative and/or relaying systems is very unevenly spread,
i.e. there is an overabundance of information on WLAN relaying and virtually nothing on
LTE activities.
• Picking a few, we will proceed with the following topics:
1. scaling laws for large-scale systems;
2. IEEE 802.16j − WiMAX;
3. economical studies on relaying systems;
4. other multi-hop systems;
5. practical multi-hop systems.
316
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8.1 Scaling Laws
317
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�
– Rational behind Scalability –
• The France Telecom Group constitutes one of the biggest integrated operators worldwide.
• France Telecom’s cellular networks are composed of several million of nodes and enjoy planning
and optimization prior to roll-out.
• The number of subscribers has dramatically increased over the past years, hence requiring
cellular capacity to be augmented.
• The invoked solution consisted of introducing a hierarchical communication structure in form of
cells, where several users are connected to a base station (BS), several of these BSs are then
connected to a network controller, and the network controllers are then meshed by means of a
backbone.
• The question hence arises whether the approach taken is optimum or whether another solution
would have been more appropriate?
• We will hence try to address the issue of scalability but first defining it, then applying it to various
network laws and finally use these insights to optimise performance.
318
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– Definition of Scalability [1/3] –
• To attempt a more general definition than [131] and [132], we will follow [133] and first introduce
η12 =FA(N2, S2)/N2
FA(N1, S1)/N1(149)
to be the relative efficiency between two systems
– obeying the same type of architecture A;
– consisting of N1 and N2 nodes, respectively;
– tackling some problems of size S1 and S2, respectively; and
– being gauged by some ’positive’ average network-wide attribute F .
• The problem size is determined by the ’problem’ the system aims to solve and is related to the
attribute; e.g., the problem of a network to deliver a given amount of data from every node in a
cellular system, etc.
• The ’positive’ attribute could, e.g., be the total average network throughput, the inverse of the
average end-to-end delay, etc.
319
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�
�
– Definition of Scalability [2/3] –
• To facilitate a definition, we assume that
– The difference between the number of nodes in the two systems approaches infinity, i.e., with
N1 = N and N2 = N + Δ, we require Δ → ∞. The requirement on Δ approaching
infinity stems from the fact that the below-given ratio (150) can often only be calculated in
closed form under this assumption.
– N is sufficiently large such that the attribute F holds with sufficiently high probability. The
requirement on N being sufficiently large stems from the the fact that many network-wide
attributes, such as average throughput and delay, can only be quantified if the number of
involved nodes is sufficiently large (often even infinite).
– The problem size of the larger system does not decrease, i.e. S2 ≥ S1. This means that the
system with a larger number of nodes is not required to perform a more trivial task.
• With these assumptions, we now define an architecture A to be scalable w.r.t. attribute F if
η � limΔ→∞
FA(N + Δ, S2)/(N + Δ)FA(N, S1)/N
≥ O(1). (150)
320
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�
�
�
– Definition of Scalability [3/3] –
• The first question we pose is when a network has to be considered large. To exemplify this
problem, let us presuppose systems with and without internal conflicts [134].
• For instance, two systems without conflicts are
1. our circle of true friends, comprising a small number of elements; and
2. the soldiers of an ant colony, comprising a large number of elements.
• On the other hand, two systems with conflicts, frictions and competition are, for example,
1. a few children left on their own, comprising a small number of elements; and,
2. a state without government, comprising a large number of elements.
• As such, ’large’ is hence not about size; it is rather about managing existing and emerging
conflicts, and hence the amount of overheads needed to facilitate (fair) communication.
• This overhead is well reflected in the efficiency η, which needs to be maximised for a given
attribute F . Using different scaling laws, we will use different attributes to judge upon the
scalability of considered architectures.
321
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�
– Capacity Scaling Laws –
• By plugging the capacity expressions from Slide 125 into (150), we can judge upon the
scalability of various topologies:
– Gupta’s law [16], η = O(1/√
Δlog Δ) < O(1) (not scalable);
– Franceschetti’s law [109], η = O(1/√
Δ) < O(1) (not scalable);
– Aeron’s law [110], η = O(1/ 3√
Δ) < O(1) (not scalable);
– Ozgur’s law [28], η = O(1) = O(1) (scalable!);
• In using (150), we have assumed
– above architectures A are either flat or clustered;
– the attribute F is the average network capacity Θ;
– and, with the average network capacity being the ’problem’ to be solved in the
network, the problem size S is related to the total number of nodes in the network N
(thus certainly not decreasing with an increasing number of nodes).
322
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�
�
– Value Scaling Laws [1/3] –
• Mainly economically driven, various efforts in the past by e.g. Sarnoff, Reed and Metcalf
have been dedicated to establishing the value of a network in dependency of the
number of its elements N :
– Sarnoff’s Law [135] quantifies the value of a broadcast network to be proportional to
N , which stems from the fact that the N members only communicate with the BS.
– Reed’s Law [136] claims that with N members you can form communities in 2N
possible ways; the value hence scales with 2N .
– Metcalfe’s Law [137], unjustifiably blamed for many dot-com crashes, claims that N
members can have N(N − 1) connections; the value hence scales with N2.
• Since a large-scale cellular network is not truly of broadcast nature, nor do nodes form
all possible communities, nor does every node communicate with every other node,
another value scaling law is required to quantify the network’s behaviour.
323
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�
�
�
– Value Scaling Laws [2/3] –
• Odlyzko and Tilly have proposed a value scaling which is proportional to N log N [138].
• Their argumentation bases on Zipf’s Law [139], an important law in biology & medicine
with discrete samples, which states that if one orders a large collection of entities by
size or popularity, the entity ranked k-th, will be in value about 1/k of the first one.
• The added value of a node to communicate with the remaining nodes is hence∑Nn=1 1/n ∝ log N (this can equally be formulated for continuous values leading to
the same result since∫ Nn=1 1/n dn ∝ log N ).
• The total value V of the network with N nodes hence scales with
V ∝ N log N. (151)
• With reference to (150) and (151), the relative efficiency can hence be calculated as
η = O(log Δ) > O(1), revealing that w.r.t. network value the architecture is scalable.
324
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�
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�
– Value Scaling Laws [3/3] –
• Odlyzko and Tilly’s law can also be used to describe the routing behaviour in multi-hop
cellular networks.
• All mobile terminals which require energy k · Emin ≤ Ek < (k + 1) · Emin to route
the information from source to the basestation/gateway are placed in zone k.
basestation or gateway
mobile node of zone 1
mobile node of zone 2
mobile node of zone 3
source mobile node
Figure 78: The value of the network with N of such zones is hence proportional to N log N .
325
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�
�
�
– Clustering: Odlyzko & Tilly’s Law [1/2] –
• Based on Odlyzko and Tilly’s value scaling law, we introduce a normalized network
value V ′, which we define as the ratio between the value given in (151) and the number
of links per unit area needed to support such connected community. This definition
hence incorporates the required links into the value of the spanned network.
• For an unclustered network, we can calculate the normalized network value V ′ as
V ′ =N log N
N log N= 1. (152)
• For a clustered network, we assume C clusters and hence M = N/C nodes per
cluster. Assuming that the value of the nodes within a cluster as well as the cluster
heads obeys Zipf’s Law, the normalized network value V ′ is
V ′ =C log C · M log M
C log C + M log M. (153)
326
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�
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�
– Clustering: Odlyzko & Tilly’s Law [2/2] –
100
101
102
103
104
10−2
10−1
100
101
102
103
Number of Clusters [logarithmic]
No
rmal
ized
Net
wo
rk V
alu
e [l
og
arit
hm
ic]
N = 100 NodesN = 1000 NodesN = 10000 Nodes
Figure 79: Relative value of clustered network, where maximum occurs at C =√
N .
327
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�
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�
– Clustering: Fully-Meshed Cluster-Heads [1/2] –
• We now wish to shed light onto the requirements of the architecture’s data pipes in
hierarchical cellular/WLAN systems with meshed network controllers.
• We assume that each mobile node communicates only with its respective cluster head
and all cluster heads communicate among each other using a data pipe which is
α−times stronger than the mobile node’s one.
• This leads to a 2-tier hierarchy using a 2-phase communication protocol with N total
nodes, C clusters with one cluster head and M = N/C − 1 ≈ N/C nodes per
cluster.
• The normalised throughput is hence
Θ =N
M + M · C · (C − 1)/α. (154)
328
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�
�
�
– Clustering: Fully-Meshed Cluster-Heads [2/2] –
100
101
102
103
104
10−2
10−1
100
101
102
Number of Clusters [logarithmic]
No
rmal
ized
Net
wo
rk T
hro
ug
hp
ut
[lo
gar
ith
mic
]
nodes @ 1 kbps & cluster−heads @ 1 kbpsnodes @ 1 kbps & cluster−heads @ 100 kbps (Zigbee)nodes @ 1 kbps & cluster−heads @ 1 Mbps (Bluetooth)
Figure 80: Normalised throughput of clustered network, where maximum occurs at C =√
α.
329
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– Clustering: Multi-Hop Network [1/2] –
• We assume that all mobile nodes can communicate with their cluster heads over a
single hop (1-hop clusters), but that all cluster heads can only reach the base station or
gateway via multiple hops (using again α−times stronger pipes).
• The average distance from any point of the cell to the gateway can be calculated as
L = 23√
π, which allows the normalised throughput to be calculated as
Θ =3 · C · α
3 · α + C · √log C. (155)
• Comparing with a flat topology, which has a normalized throughput of
Θ′ = 3/√
log N , it can be shown that clustering improves performance if the number
of nodes N and super-nodes C relate as follows:
N > exp
[(3C
+√
log C
α
)2]
. (156)
330
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�
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�
– Clustering: Multi-Hop Network [2/2] –
100
101
102
103
104
10−1
100
101
102
103
104
Number of Clusters [logarithmic]
No
rmal
ized
Net
wo
rk T
hro
ug
hp
ut
[lo
gar
ith
mic
]
nodes @ 1 kbps & cluster−heads @ 1 kbpsnodes @ 1 kbps & cluster−heads @ 100 kbps (Zigbee)nodes @ 1 kbps & cluster−heads @ 1 Mbps (Bluetooth)
Figure 81: Normalised throughput of multi-hop network, where maximum occurs at C ≈ 10α.
331
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8.2 IEEE 802.16j − WiMAX
332
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– IEEE 802.x Families –
• Numerous working groups (WGs) have been created within the IEEE 802 LAN/MAN
Standards Committee family, some with overlapping goals and correlated technical
proposals [140, 141].
• IEEE 802.16 WG = Broadband Wireless Access Standards; established in 1999; aim
was to prepare formal specifications for the global deployment of broadband Wireless
Metropolitan Area Networks; official name is ”WirelessMAN”, pushes from industrial
forum lead to naming of ”WiMAX” (Worldwide Interoperability for Microwave Access).
• IEEE 802.20 WG = Mobile Broadband Wireless Access (MBWA); establishment 2002
and draft specs approved in 2006; aim to facilitate low-cost, always-on, and truly mobile
broadband wireless IP-based services; nicknamed as ”Mobile-Fi”.
• The goals of IEEE 802.20 and IEEE 802.16e are fairly similar; both are often referred to
as ”mobile WiMAX”.
333
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�
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�
– IEEE 802.16 Letter Salad [1/2] –
• 802.16 point to multipoint broadband wireless transmission in the 10-66GHz band; only
LOS capability; single-carrier PHY.
• 802.16a was an amendment to 802.16 and delivered a point to multipoint capability in
the 2-11 GHz band; also nLOS and extension to OFDM/OFDMA.
• 802.16c was a further amendment to 802.16, delivered a system profile for the 10-66
GHz 802.16 standard.
• 802.16d was a revision project with the aim to align 802.16x with ETSI’s HIPERMAN
standard; earlier 802.16x documents were withdrawn.
• 802.16e was an amendment to .16d including mobility, better QoS, scalable OFDMA.
• 802.16f incorporates a management information base.
• 802.16g incorporates management plane procedures and services
334
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– IEEE 802.16 Letter Salad [2/2] –
• 802.16h incorporates improved coexistence mechanisms for license-exempt operations.
• 802.16i incorporates mobile management information base.
• 802.16j incorporates Multihop Relay Specification and will be dealt with later.
• 802.16k bridging of 802.16.
• 802.16m is an advanced air interface:
– data rates of 100 Mbit/s for mobile applications;
– data rates of 1 Gbit/s for fixed applications;
– cellular, macro and micro cell coverage;
– expected bandwidth of 20MHz or higher;
– expected completion by Sept. 2008 and approval by Dec 2008.
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– IEEE 802.16j Working Group –
• IEEE 802.16j’s Relay Task Group Leadership Team:
– Mitsuo Nohara (Chair), KDDI Corp.
– Peiying Zhu (Vice Chair), Nortel
– Mike Hart (Editor/Secretary), Fujitsu Laboratories of Europe Ltd.
– Jung Je Son (Editor/Secretary), Samsung Electronics
• This initiative is hence mainly driven by manufacturers. With the exception of a few,
operators are generally very wary of IEEE 802.x’s activities.
• IEEE 802.16’s Relay Task Group is currently developing a draft under the P802.16j
Project Authorization Request (PAR), approved by the IEEE-SA Standards Board in
March 2006.
• This PAR deals with ”Air Interface for Fixed and Mobile Broadband Wireless Access
Systems - Multihop Relay Specification.”
336
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– Overview of IEEE 802.16j [1/4] –
• Subsequent slides base on [142, 143] which will not be explicitly referenced again.
• The aim of [143] is to provide specifications for mobile multi-hop relay (MMR) features,
functions and interoperable relay stations to enhance coverage, throughput and system
capacity of IEEE 802.16 networks.
Coverage extension at cell edge
Penetration into inside room
Shadow of buildings
Coverage hole
Underground
Valley between buildings
Coverage extension to isolated area
M ultihop Relay
M obile Access
BS RS
RS
RS
RS
RS
RS
337
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– Overview of IEEE 802.16j [2/4] –
• MMR-Base Station (MMR-BS):
A base station that is compliant with amendment IEEE 802.16j to IEEE Standard
802.16e.
• Relay Station (RS) types:
– fixed relay station (FRS): relay station that is permanently installed at a fixed location;
– nomadic relay station (NRS): relay station that is intended to function from a location
that is fixed for periods of time comparable to a user session;
– mobile relay station (MRS): relay station that is intended to function while in motion.
• Mobile Multihop Relay (MMR):
The system function that enables mobile stations to communicate with a base station
through intermediate relay stations.
338
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– Overview of IEEE 802.16j [3/4] –
• In particular, [143] specifies OFDMA PHY and MAC enhancement to the IEEE 802.16
standard for licensed bands to enable the operation of relay stations.
RS TypeFixed / nom adic / m obile
M odulationOFDM A
Term inalConventional802.16 M S/SS
Backward com patibility kept
339
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– Overview of IEEE 802.16j [4/4] –
• The proposed main features are:
– terminals that can talk with relay station: conventional .16 MS/SS only;
– modulation: OFDMA only;
– relay station type: fixed, nomadic and mobile;
– tree structure: one of the end of relayed data path should be at basestation;
– backward compatible to point-to-point mode;
– efficiently provide relay connection to mobile station via a small number of hops).
• The required working scope is hence:
– PHY: enhance normal frame structure;
– MAC: add new protocols for the relay.
340
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– Technical Scope of IEEE 802.16j [1/4] –
• As we have learned from previous sections of this tutorial, multi-hop enables link budget
gains, which can be exemplified by [142]:
128
130
132
134
136
138
140
142
0 0.2 0.4 0.6 0.8 1
Norm alised RS Position
Total pathloss (dB)
Direct Link Relayed Link
Relayed Link (s=1.1) Relayed Link (s=1.2)
BSRS
M S
rd
r1
r2
rd=s(r1+ r2)
rnbdBL log10
Effect of RS positioning
Propagation loss m odel:
W here: b=15.3, n=3.76
341
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– Technical Scope of IEEE 802.16j [2/4] –
• The scope of the IEEE 802.16j is best defined by [142]:
L
L
3
RS
RS
RS
RS
No changes to 802.16e OFDM A PM P (access) links
No changes to SS/M S
Definition of new “802.16j Relay”link air interface•Support fixed, portable, and m obile RSs•Based on OFDM A PHY•M AC to support m ulti-hop com m unication (BS -> RS and RS -> RS)•Security and M anagem ent
Definition of new RS entity:•Supports PM P links •Supports M M R links•Supports aggregation of traffic from m ultiple RSs
BS
Changes to BS:•Add support forM M R links•Add support foraggregation of trafficfrom m ultiple RSs
342
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– Technical Scope of IEEE 802.16j [3/4] –
• Envisaged relay station types and capabilities [142]:
Higher user throughputHigher user throughputat low SINR regionat low SINR region
Cell coverage Cell coverage extensionextensionObjectiveObjective
OnlyOnly UnicastUnicastTraffic CHTraffic CH
Both Broadcast Control CHBoth Broadcast Control CHandand UnicastUnicastTraffic CHTraffic CH
RelayingRelayingChannelsChannels
RSRSCapabilitiesCapabilities
Low CapabilityLow Capability
•Relay data traffic
only
•Control m essages
are provided
through a direct
link from BS
•RS-M S link control
by BS
High CapabilityHigh Capability
•Transm it DL
control M essages
•Provide M S w ith
Netw ork_Entry
procedure
on behalf of BS
•RS-M S link control
by RS
… … …
Centralised vs. distributed control
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– Technical Scope of IEEE 802.16j [4/4] –
• Example scenario with before-mentioned capabilities [142]:
344
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– Technical Challenges of IEEE 802.16j [1/2] –
• Use of advanced antenna techniques at PHY:
– MIMO, beamforming, interference nulling, etc.
• Advanced approaches at MAC/Link Layer:
– scheduling, radio resource management, power control, etc.
– centralised versus distributed control approaches, etc.
• Novel approaches for routing protocols:
– centralised versus distributed flow control;
– hierarchical or other topologies.
• QoS has to be dealt with appropriately:
– network-wide load balancing;
– congestion and flow control.
345
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– Technical Challenges of IEEE 802.16j [2/2] –
• Frequency planning has to be done appropriately:
– shared or separate PMP and relay link bands;
– interference mitigation in access (RS/MS) and BS/RS link;
– frequency reuse / spatial multiplexing in BS/RS link.
• Other important issues are:
– call admission and traffic shaping policies;
– transport layer protocols for multi-hop networks;
– network auto-reconfiguration under the control of BS;
– network management for portable / mobile RS;
– security considerations for portable / mobile RS.
346
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– 802.16j Simulations: DL Coverage [1/2] –
• The Motorola folks at IEEE 802.16j studied the downlink coverage reliability for a 2 hop
system with 6 relay stations with the below-given specs [142]:
• modelling assumptions:
– fc =2.5GHz, B = 10MHz, omni-directional antenna;
– BS-RS: LOS; RS-MS & BS-MS: nLOS; RS location: 0.6 x cell radius;
• coverage reliability:
– carrier-to-interference-and-noise-ratio (CINR) at 95% coverage;
– 95% of the users in a cell receive equal or more than the CINR value.
• interference calculations:
– single hop: no interference for intracell; from BSs in other cell for intercell.
– dual hop: no interference for intracell because of orthogonal time-slots; from one RS
in each cell for intercell.347
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– 802.16j Simulations: DL Coverage [2/2] –
• The underlying scenario and its CINR gains are as follows [142]:
1
2
5
7
6
3
4BS
RS1
RS2
RS3
RS4
RS5
RS6
(a) Scenario.
-7
-6
-5
-4
-3
-2
-1
0
1
0 500 1000 1500 2000
C ell Radius (m )
CINR (d
B) at95%
Coverage
S ingle hop 2-hop
(b) Performance Gains.
348
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– 802.16j Simulations: Efficiency & Outage [1/2] –
• The Intel folks at IEEE 802.16j studied the spectral efficiencies and link capacity outage
probabilities with the below-given specs [142]:
• assumption of a one-dimensional network from MMR-BS to MS/SS via N DF RSs
located equidistantly;
• channel includes pathloss, lognormal shadowing;
• no consideration of spatial reuse, interference, synchronization error;
• spectral efficiency denotes the maximum achievable rate per Hz;
• outage is defined as the event in which the achieved end-to-end data rate falls below the
target data rate.
M -BS RS 1 RS 2 RS 3 RS N M S/SS
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– 802.16j Simulations: Efficiency & Outage [2/2] –
• The spectral efficiencies and outages are as follows [142]:
0 2 4 6 8 10 120
1
2
3
4
5
6
7
Num ber of hops
Spectral efficiency (bps/Hz)
channel type = 1
path loss & shadowing only
d = 0.5 km
d = 1 km
d = 2 km
d = 3 km
Inter-term inal distance
(c) Spectral Efficiencies.
Relay gains w /o SS change
r
(d) Rate Outage Probabilities.
350
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– 802.16j Simulations: DL & UL Throughput [1/2] –
• The Samsung folks at IEEE 802.16j studied the downlink and uplink throughput gain for
2-hop fixed relays in a Manhattan-like environment with the below-given specs [142]:
• The underlying system model was as follows:
– TDD OFDMA based on IEEE Std 802.16e-2005;
– rate adaptation control scheme for both DL & UL;
– 49 BSs, housing block size of 200 m, road width of 30 m;
– frequency reuse among relays of 1 (Kr = 1) or 4 (Kr = 4).
BSX RS
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– 802.16j Simulations: DL & UL Throughput [2/2] –
• Env1 (high BS/RS antennas): gains of 20% in DL and 38% in UL;
Env2 (low BS/RS antennas): gains of 22% in DL and 36% in UL:
UplinkDownlink
0
10
20
30
40
50
60
Single-hop Repeater Relay (Kr=4) Relay(Kr=1)
Cell Throughput (M
bps)
Env1 Env2
0
10
20
30
40
50
60
Single-hop Repeater Relay (Kr=4) Relay(Kr=1)
Cell Throughput (M
bps)
Env1 Env2
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– 802.16j Simulations: RSSI & Throughput [1/3] –
• The Taiwanese academics at IEEE 802.16j studied the downlink and uplink received
signal strength and throughput in DL and UL [142]:
• 14 fixed relay stations have been deployed within the coverage of each BS, where the
baseline system is again IEEE 802.16e-2005 OFDMA.
Fixed Relay Station (FRS)
Base Station (BS)
Coverage of BS
M obile Station (M S)
BS coverage: 1 km
FRS coverage: 0.6 km (along main street)
M S speed: 30 km/hr
Handoff type: Hard Handoff
M S arrival: Poisson process
Traffic model: Full buffer m odel
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– 802.16j Simulations: RSSI & Throughput [2/3] –
• Downlink improvement on average received signal quality: > 20dB;
Downlink throughput enhancement: up to 116.41%.
– Exam ple I: Sub-channels are exclusively allocated to each FRS
– Exam ple II: All sub-channels can be reused by each FRS
Received signal qualityis im proved by Relay
CDF of Received Signal Quality Cell Throughput (M bps)
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– 802.16j Simulations: RSSI & Throughput [3/3] –
• Uplink average MS transmit power saved: ≈ 10dB (Example I);
Uplink throughput enhancement: up to 41.66% (Example II).
– Exam ple I: Only power control is considered
– Exam ple II: Both power and adaptive rate control are considered
M S transm it powerissaved by Relay
CDF of M S Transm it Power Cell Throughput (M bps)
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– 802.16j Protocol Stack –
• Above results have been considered promising and prior mentioned challenges have
been addressed, having led to [143]. An example protocol stack is shown below and all
specs can be found in [143].
R- PHY
R-MAC
MAC-CPS
MAC-CS
802.16 MR-BS Access Relay Station
PHY
MAC-CPS-liteMAC-SS
PHY
MAC-CPS
MAC-CS
802.16e MS
MAC-SS
Intermediate Relay Station
MAC-CPS-lite
R- PHY
R-MAC
R- PHY
R-MAC
R- PHY
R-MAC
Figure 82: Example multi-hop relay data protocol stack for simple relay station.
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8.3 Economical Studies
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– IEEE 802.16j Study: Motivation [1/3] –
• Numerous published documents have observed the short comings of current cellular
systems. This has been summarised in [142].
• As such, current deployments suffer from:
– limited spectrum and/or insufficient wire-line capacity;
– low SINR at cell edge;
– coverage holes due to shadowing.
• Reducing the cell size improves conditions, but:
– limited availability of wire-line infrastructure in developing markets;
– limited access to traditional cell site locations;
– prohibitive installation and operating costs (backhaul is large fraction);
– expensive redundant equipment, backhaul, backup power at cell sites for backup.
358
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– IEEE 802.16j Study: Motivation [2/3] –
• Economical coverage, capacity and QoS enhancement have been exemplified in [142]:
BS
L
L
RSL
RS
RS
RS
Fault tolerance via
m ulti-path redundancy
Load sharing am ong RSs
RS
RS
RS
RS
Flexible placem ent of cell sites
due to fewer access lim itations
Spectrally efficient architectures and
spatial frequency reuse
RS RS
Replacem ent of low rate,
unreliable links with m ultiple
high rate, reliable links
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– IEEE 802.16j Study: Motivation [3/3] –
• Lower CAPEX and OPEX due to:
– wireless backhaul;
– lower site acquisition costs;
– less costly antenna structure for RS;
– lower cost and complexity of RS;
– faster deployment.
• Improved return on investment (ROI):
– relay-augmented network could provide higher average revenue per user (ARPU)
through higher grades of service
– and at lower overall incremental costs.
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– IEEE 802.16j Study: Analysis [1/5] –
• The case of pure WiMAX and MMR-enabled WiMAX has been studied in [142]:
LO S
LOS
Legend
Relay Station Cell
M M R Base Station Cell
Base Station Cell
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– IEEE 802.16j Study: Analysis [2/5] –
• The following CAPEX and OPEX assumptions have been made [142]:
Administrative, backhaul, access points, and network costs
Base station
W ired backhaul provision(depending on wired backhaul traffic assum ptions)
Site acquisition & construction per cell
RS Cell
M M RConv.W iM AX
M M R-BSCell
BS Cell
<<>Current value
<<SameCurrent value
CapEx N/A>Current value
<<SameCurrent valueO pEx
Legend: > greater than
<< significantly less than
362
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– IEEE 802.16j Study: Analysis [3/5] –
• Case Scenario 1: Heavy Traffic, Urban Environment:
– capacity limited;
– traffic load is still less than capacity of MMR deployment;
– MMR-BS cell structure dimensioned for min 3.7dB SNR at cell edge;
– conventional WiMAX cell structure splits aggressively due to high traffic demand.
• Case Scenario 2: Light Traffic, Urban/Suburban/Rural Environment:
– range limited;
– traffic load based on mix of current customer demand and varying customer
densities;
– MMR-BS cell structure dimensioned for min 3.7dB SNR at cell edge;
– conventional WiMAX cell structure splits modestly due to low traffic demand.
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– IEEE 802.16j Study: Analysis [4/5] –
• CAPEX and Year 7 OPEX of MMR versus conventional WiMAX (Scenario 1) [142]:
0
1
2
3
4
5
6
7
8
9
10
56 33 12
Num ber of RS per M M R-BS
Relative Cost (norm
alized w.r.t. 1st bar)
M M R CapEx
M M R OpEx
Conv CapEx
Conv OpEx
364
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– IEEE 802.16j Study: Analysis [5/5] –
• CAPEX and Year 7 OPEX of MMR versus conventional WiMAX (Scenario 2) [142]:
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
56 33 12
Num ber of RS per M M R-BS
Relative Cost (norm
alized w.r.t. 1st bar)
M M R CapEx
M M R OpEx
Conv CapEx
Conv OpEx
365
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– IEEE 802.16j Study: Conclusions [142] –
• Conventional WiMAX:
– CAPEX is a significant cost relative to OPEX.
• MMR-based WiMAX:
– CAPEX grows with decreasing MMR-BS:RS ratio;
– CAPEX only slightly larger than OPEX under light load;
– CAPEX considerably less than OPEX under heavy load.
• Comparison between both:
– CAPEX and OPEX of MMR always less than conventional WiMAX;
– economic gains from capacity improvement significantly larger than those
from range extension.
366
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– KTH’s Study: Assumptions [1/2] –
Bogdan Timus aimed at addressing the following set of pertinent questions in [152]:
• Can the large scale use of fixed relays lead to a good (feasible) business case?
• Under which circumstances, i.e. should they be used in rural or urban environments, for
coverage or capacity enhancement?
• What fundamental aspect(s) makes relaying better than other techniques, e.g. direct
communication?
• How large are the gains obtained with advanced techniques as compared to traditional
relaying techniques?
• How sensitive are the results to traditional network design parameters, such as antenna
height, maximum transmission power, etc.?
367
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– KTH’s Study: Assumptions [2/2] –
• Example of empirical CAPEX and OPEX costs according to [152]:
e
e
e
368
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– KTH’s Study: Conclusions [1/2] –
The answer to the questions posed on Slide 367 can be summarised as [152]:
• Large-scale unplanned deployment of fixed relays on lamp-posts is worthy only if the
total cost of the relay is
– about 10 % of the BS cost
– and 50 − 100 % of the additional BS planning cost;
– the relay cost should hence be in the range of 3000 Euros over 10 years of operation.
• Large scale planned deployment of fixed relays brings cost savings w.r.t. cellular
systems:
– for coverage extension cases;
– relay cost is about 10 % of the BS cost;
– tight re-use of radio resources is pivotal.
369
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– KTH’s Study: Conclusions [2/2] –
• With respect to advanced cooperative techniques compared to simple relaying:
– cooperative MIMO techniques bring minor cost gains w.r.t. simple relaying;
differences are more visible if relay roll-out is planned;
– TDMA scheduling without coordination between cells does not suffice.
• Most influential system performance parameters:
– for planned roll-out, the transmission power, antenna gain and relay height are much
more important than choice of relaying technique;
– for un-planned roll-outs, there is little difference between above and below rooftop
relay deployments.
• A conclusive study entirely reflecting reality is missing; however, it is obvious that ...
A hybrid deployment with fixed relays and BSs isunlikely to bring a magnitude of cost savings!
370
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8.4 Other Multi-Hop Systems
371
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– Short-Range WLAN/Bluetooth/Zigbee –
• A huge body of research papers and standard specifications are available on
WLAN/Bluetooth/Zigbee/etc.
• They all failed to produce commercially viable multi-hop products to-date.
• This is mainly attributed to:
– scalability issues,
– long discovery times,
– large latency, etc.
• We will not go in further details as this is out of the scope of this tutorial.
372
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– Japan’s Virtual Cellular Network [1/2] –
• Adachi et al. introduced the concept of Virtual Cellular Network [155]:
– in-depth technical and performance analysis, together with entire protocol stack;
– reduced transmission power and signalling overhead in the case of cell splitting;
W ireless port
Central port
Control stationCore Network
Virtual cell
W ireless port
Central port
Control stationCore Network
Virtual cell
373
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– Japan’s Virtual Cellular Network [2/2] –
• At high load, the VCN outperforms traditional cellular systems [155]:
1E-05
1E-04
1E-03
1E-02
1E-01
1E+00
2 4 6 8 10Offered load G
Blocking probability
C =8
C =4
C =2
M ulti-hop VCN
Present cellular NW
K =20
J=4
SF=16
L=2
α =3.5
σ =6dB
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– 3GPP ODMA [1/3] –
• Opportunity Driven Multiple Access (ODMA) [1]:
– communications relaying protocol proposed for UMTS TDD mode;
– introduced at ETSI SMG2 ’96, proposed as UMTS standard, discontinued in R’99;
– aim was to increase range of high data rate services.
ODM ATERM INAL
H igh BitRate DataTDD
Coverage
Low BitRate DataTDD
Coverage
TDD ODM A
High Bit Rate
TDD ODM A
High Bit Rate
BorderRegion
NOcoverage
Layer 1 SynchInform ation
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– 3GPP ODMA [2/3] –
• A seminal (but largely forgotten) work of [153] demonstrated already in 2000 that
ODMA-type relaying decreases coverage holes (black squares):
(a) Conventional Cellular System. (b) ODMA-Based Cellular System.
376
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– 3GPP ODMA [3/3] –
• Relays neighbourhood discovery activity levels are influenced by [154]:
– number of neighbours;
– gradient to the base information of the neighbours;
– speed of the terminal; and
– battery power level.
• The lessons learned from ODMA are:
– only draft idea was proposed with many issues left for further study;
– concerns over complexity, battery life of users on standby, and signaling overhead
issues;
– routing is one of the key issues requiring more attention.
377
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– 3GPP/3GPP2 LTE [1/3] –
• The requirements on the Long Term Evolution (LTE) of 3G is tough [156]:
Metric
Peak data rate
Mobility support
Control plane latency (Transition time to active state)
User plane latency
Control plane capacity
Coverage(Cell sizes)
Spectrum flexibility
Requirement
DL: 100MbpsUL: 50Mbps(for 20MHz spectrum)
Up to 500kmph but opti-mized for low speeds from 0 to 15kmph
< 100ms (for idle to active)
< 5ms
> 200 users per cell (for 5MHz spectrum)
5 – 100km with slight degradation after 30km
1.25, 2.5, 5, 10, 15, and 20MHz
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– 3GPP/3GPP2 LTE [2/3] –
• LTE positions w.r.t. HSPA+ and WiMAX as follows [157]:
Com m on and Distinctive Features
M IM OBeam form ing
M IM OBeam form ing
M IM OBeam form ing
Antennaconcepts
TDD3.5-10 M Hz
OFDM (DL & UL)
QPSK-64QAMTurbo codesHARQ II
Quality-basedscheduling
W iM AX
Quality-basedscheduling
Quality-basedscheduling
M AC
QPSK-64QAMTurbo codes HARQ II
QPSK-64QAMTurbo codes HARQ II
Physical layer
FDD and TDD1.25-20 M Hz
FDD5 M Hz
Duplex andBandwidth
OFDM (DL)FDM A (UL)
CDM A (DL & UL)M ultiple access
LTEHSPA+
TXTX
tim efrequency
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– 3GPP/3GPP2 LTE [3/3] –
• LTE Phase II will start in Q4 2007 with proposals due in 2008/09.
• Research inputs are currently being requested in [157]:
– advanced antenna solutions;
– interference coordination, cancellation & avoidance;
– relaying techniques;
– simplified network operation; etc.
• Generally, operators ...
– ... do not feel entirely comfortable with relaying concepts based on mobile
relays, because QoS can only be guaranteed statistically;
– ... feel that fixed relays could be beneficial, despite the requirement of
planning and site acquisition;
– ... feel that other capacity-enhancing techniques will have a bigger impact.
380
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8.5 Practical Multi-Hop Systems
381
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– Ricochet –
• Ricochet [158] is a US company which was well ahead of its time by rolling-out a
broadband wireless network throughout major US cities more than 10 years ago.
• They simply formed a mesh network by means of relay-capable nodes attached to
lamp-posts. Technology was at its finest, including routing and MAC protocols, but the
technology just did not take of back then.
• Ricochet service is no longer available in the originally conceited form, because
Metricom, Ricochet’s parent company, went bankrupt. Aerie Networks has then bought
the Ricochet infrastructure and is attempting to restart it out in select markets (e.g.
Denver).
• Today, Ricochet has addressed some prior concerns; for instance, when consulting the
company’s website today, data security is well advertised. Ricochet has again taken up
business in a few US cities and is likely to grow over the upcoming years.
382
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– Coronis –
• Coronis’ Wavenis automatic metering solution is today the only commercially viable
multi-hop communications system [159]:
Providers
SMS /
GSM
PC/server
Wavecell
25/500mW
Wavetalk
25/500mW
Mesh
topology
Waveflow
25mW
Tree
topology
Star
topology
4km
200m
Network Installation & Configuration
Network
Management
383
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– Easy-C [1/2] –
• A German government funded project called “Enablers of Ambient Services and
Systems (EASY), Part C: Wide Area Coverage,” is currently kicking-off and addressing
the following requirements [160]:
– high spectral efficiency;
– fairness (e.g. good performance also for cell-edge users);
– low capital and operational cost per bit;
– low latency; etc.
• They aim at investigating the following techniques [160]:
– advanced multi-antenna (MIMO) techniques;
– multi-cell joint detection for interference cancellation;
– multi-cell interference coordination;
– cooperative relaying.
384
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– Easy-C [2/2] –
• A PHY-layer oriented testbed will be setup in downtown Dresden, Germany, comprising
10 sites with 30 cells, surrounded by another tier of 27 interferers [160]:
385
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Open Issues
386
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– Open Issues –
The design and deployment of entire systems facilitating relaying and cooperation are
entirely in its infancy! There are hence endless open questions, some pertinent of which are:
• Routing protocols:
– design of applicable routing protocols;
– incorporate incentive schemes into routing protocols.
• Deployment experiences:
– nobody knows until today whether a large-scale cooperative roll-out really works;
– exposure or really influential system parameters through real-world roll-outs.
387
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PART 9THE ROAD AHEAD
388
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– Only Some Thoughts –
• Capacity and algorithmic PHY layer designs are fairly well explored; despite numerous
unsolved problems, novel contributions are likely to be incremental.
• RF, MAC, routing protocols, cross-layer design and roll-outs are areas which are still in
their infancy; there is hence a lot of room for innovative contributions.
• What we may need today in these type of networks are entirely novel approaches for
system analysis, such as from physics or biology.
• A personal answer to the question posed at the beginning:
– Ripe: Technology (already available for a long time since there is no magic);
– Hype: Expectations (inflated research body on this subject).
We need commercially viable products if cooperative systems do not want to fall for
the same fate as traditional ad hoc networks, which have been researched for several
decades without any tangible product on the civil market today.
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– Credits –
The following people’s input (text, figures, research results) have been used with thanks
throughout this presentation:
• Dr Athanasios Gkelias, Imperial College, UK
• Dr Yonghui Li, University of Sydney, Australia
• Thomas Watteyne, France Telecom R&D, France
• Timus Bogdan, KTH, Sweden
• Roger B. Marks, Mitsuo Nohara, Jose Puthenkulam, Mike Hart, all involved in IEEE
802.16j.
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