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A Simulation Model for IEEE802.11n

A Description of the Signal Processing Techniques Used in Simulating the High Throughput (HT) Extension for IEEE 802.11 WLAN

11n – Talk Outline

� Plan:� History of IEEE802.11n Draft

� Description of MIMO Structures

� Signal Processing Details:� Channel Estimation

� MIMO Detection

� Space-Time Block Codes (STBC)

� Beamforming

� A Simulation Model in MATLAB/Simulink� Outline of System Model

� Performance Tests

� Demo

11n – History of 802.11n

� History of 802.11n Draft:� In late 2003, the IEEE task group, TGn, was formed, in order to develop a new specification: 802.11n

� Goal of specification: achieve rates of at least 100Mbps, potentially doubling existing rate of 54 Mbps for 11a/g.

� Many proposals were submitted by various hardware, networking companies (up to 61 proposals received at one point)

� Eventually, the proposals were reduced down to two major proposals, both with strong backing from many companies…


� Main Proposals for 802.11n:TGn Sync:

� Formed by companies including Atheros, Marvell, Sony, Toshiba

WWiSE:� Consists of Broadcom, Conexant, Airgo Networks, Texas Instruments, and others

� The goal of the two groups similar:� Come up with next generation of WLAN products, considering:

� worldwide deployment, regulatory issues� low-cost, low-power solutions� interoperability with legacy device (11a/g)


� In July 2005, a group consisting of participants from three major proposal groups, including TGn Sync and WWiSE, agreed to form a joint proposal group, which submitted a proposal to the TGn workgroup in January 2006

� This proposal combined the benefits offered by the other proposals, as well as adding further improvements

� The TGn Joint Proposal forms the basis of the emerging 802.11n standard



�Description of MIMO Structures


� MIMO Detection


� Beamforming



� Demo

11n – MIMO Structures

� MIMO Structures� MIMO structures use multiple spatial streams, transmit, receive antennas:

� Goal is to increase throughput in rich scattering environments, as well as reduce signal fading using spatial diversity.

� Each transmit stream is generated using OFDM modulation:


� Direct Map MIMO� For direct-map MIMO, spatial streams are mapped directly to transmit antennas:


� Spatial Expansion� Maps NSS spatial streams to all NTX transmit antennas (when NSS<NTX.) using spatial mapping matrices.

� Different mapping matrices, Wk, may be applied to each sub-carrier, k


� Space-Time Block Coding (STBC) Option� Uses spatial diversity through multiple transmit antennas to improve range, reduce fading (described later)

� Can be used with either direct map MIMO or spatial expansion


� TX Beamforming� Form matrices from channel estimates to emphasize dominant modes of transmission for MIMO channel

� Optimal transform can be computed using singular value decomposition (described later)




�Signal Processing Details:� Channel Estimation

� MIMO Detection


� Beamforming



� Conclusion

11n – Channel Estimation

� Channel Estimation� Goal is to estimate channel response from each transmit antenna to each receive antenna

� Note: Antennas used for MIMO are typically omni-directional� Transmit/Receive power evenly distributed in all directions


� Channel Estimation (cont.)� Can write channel estimates in matrix form as:

� Each element hxy is channel response from transmit antenna y to receive antenna x.

,

3231

2221

1211

=

hh

hh

hh

H ),( TxAntyRxAntxhwith xy ==


� Channel Estimation and Multipath� The multipath channel response (for any Tx to Rx antenna) can be represented as (from [3]):

))(()(),()(2

tetth n

tfj

n

nnc ττδατ τπ

−=−∑

Gain of path ‘n’Effect of delay of path ‘n’ ( )

on carrier phase

nτ

Delay of path ‘n’

Time-varying channel response

(Since Tx, Rx, and objects may be mobile)


� Channel Estimation and Multipath� Although channel is time-varying, we can model the channel as wide-sense stationary (or WSS) by transmitting data in chunks (or packets) with sufficiently short duration…

Equation:

Becomes:

For packet duration…

))(()(),()(2

tetth n

tfj

n

nnc ττδατ τπ

−=−∑

)()(2

n

fj

n

nnceh ττδατ τπ

−=−∑


� Channel Estimation and Multipath

� How short should packet be?

� Channel is time-varying due to motion of either the transmitter, receiver, or surrounding objects, changing the multipath characteristic (gain, carrier phase, path delays)

� For indoor environments (wireless LAN in offices, homes), objects are assumed to move at walking speeds... (approx. 1.2 km/h, or 0.333 m/sec)


� Channel Estimation and Multipath� How short should packet be?

� Considering wavelength (distance radio signal travels before carrier phase changes by 2*pi, from [4]):

� And since objects moving at vo=0.333 m/sec:

� fd is called Doppler Spread (represents worst-case shift in carrier frequency)

mHz

sm

f

c

c

0571.01025.5

/1039

8

=×

×==λ

Hzm

smvf o

d 8.50571.0

/333.0===

λ


� Channel Estimation and Multipath� How short should packet be?

� Doppler Spread and its reciprocal (coherence time) give indication of time duration where channel response is essentially time-invariant

� Coherence time (TC) = 1 / 5.8 Hz = 0.172 sec

� Above measure is often too long (from [2]). Better measure is:

� WLAN packets are much shorter than this (in worst case, less than 1ms for 802.11a/g)

sec0729.08.5

423.0423.0

16

92

====Hzff

Tdd

Cπ


� Channel Estimation and Multipath� One more issue… Signal fading

� Generally two model of signal propagation:� Large-scale propagation model: modelling mean signal strength over large distances (hundreds, thousands of meters)

� Small-scale fading: modelling instantaneous signal strength when travelling short distances (a few wavelengths)

� For indoor WLAN, more concerned with small-scale fading (mobile devices, notebooks, moving short distances, resulting in fading) than large-scale model (average path loss between transmitter, receiver)



� Doppler spread is one form of small-scale fading� Doppler spread leads to frequency dispersion and time selective fading

� Frequency dispersion since (from before):

� Time selective fading since multipath characteristic changes over time (paths between transmitter, receiver change), resulting in time-varying fading

� With short packet duration, time-selective fading is negligible and, using OFDM, effect of frequency dispersion is negligible

Hzm

smvf o

d 8.50571.0

/333.0===

λfd represents the max. shift in carrier frequency due to motion (hence freq. dispersion)



� One more issue… Signal fading� Other form of small-scale fading is due to the multipath

channel response itself. From before:

� Note the ‘n’ paths (copies of same signal) are combined with different gains, phases, and with different delays

� If delays are spread widely enough, transmitted symbols are time dispersed, and intersymbol interference occurs

� Tx symbols mix together, resulting in a time-varying frequency response, depending on past symbols

� Known as frequency-selective fading [2]

� Can still recover data (by modelling each multipath signal, and considering channel as linear filter [2]), but model is complex.

)()(2

n

fj

n

nnceh ττδατ τπ

−=−∑



� To get an idea of the how wide the delays may be distributed (called delay spread), can consider a large delay spread scenario (large office-type environ.):

� Assume office with length ~100m. From diagram: Shortest path (direct line-of-sight, or LOS) is 20 m Largest path (non line-of-sight, or NLOS) is:

� The propagation delay for each path is:

� So delay spread is: 504.3ns–66.7ns = 437.7ns

m3.15110752 22 =+

sec7.66sec1067.6/103

20 8

8

11 n

sm

m

c

d=×=

×== −τ

sec3.504sec1043.50/103

3.151 8

8

22 n

sm

m

c

d=×=

×== −τ

11n – Channel Estimation� Channel Estimation and Multipath

� One more issue… Signal fading� From the computed delay spread of the previous example (437.7ns), can consider that if the symbol period is much larger than this delay spread, the signal experiences flat-fading

� multipath response looks like a delta function, with some gain, phase:

� A general rule of thumb (from [2]) is that a signal faces frequency-selective fading if:

� (Symbol time) < 10*(multipath delay spread)

� And flat fading if: (from [2])

� (Symbol time) ≥ 10*(multipath delay spread)


� Use of OFDM with multipath� Using OFDM allows for both efficient use of channel bandwidth, as

well as the ability to handle frequency-selective fading.

� OFDM (Orthogonal Frequency-Division Multiplexing) divides frequency spectrum into ‘N’ sub-band channels, which can each be viewed as a narrowband channel:

� From above eq’n, there are N sub-band symbols transmitted during each OFDM symbol time, TS

� The benefit occurs since the N sub-band symbols (ie. N modulated carriers) are sent over entire time TS, instead of sending N symbols in time, each with symbol time TS/N.

� Thus, OFDM efficiently use channel bandwidth and also provides a large symbol time to handle frequency-selective fading

∑−

=

−=

1

0

/2)()(

N

k

Tktj SekStsπ


� Channel Estimation and Multipath� Use of OFDM with multipath

� For OFDM, 20MHz mode:� N=64, TS=3.2us

� Sample period: TSAM=3.2us/64 = 50ns (20MHz bandwidth)

� For flat fading:� symbol time > 10*(delay spread)

� Consider previous delay spread (437.7ns):

� Since 3200ns < 4377ns, not quite flat fading…

� Note above delay spread is a worse-case scenario

� Also note that another technique is also used in OFDM (cyclic prefix, described next)


� Channel Estimation and Multipath� Use of OFDM with multipath

� OFDM simplifies design of receiver with multipath by allowing the effect of channel to be viewed as a circular convolution (instead of linear). This is done by adding a cyclic prefix to transmit signal (cyclically-extending data)

� For 802.11n, 800ns (16 samples) of cyclic prefix added:

� Receiver processes the 64 data samples after cyclic prefix, which contains circular convolution of channel and OFDM symbol in timedomain (multiplication in freq. domain)

� Can handle around 600ns of delay spread (around 200ns used to handle symbol timing estimate inaccuracy)

� Adding cyclic prefix reduces efficiency to: (3200/4000) = 80%, but is robust vs. multipath, simplifies receiver.



� Summary: Using OFDM with multipath

� Using OFDM with cyclic prefix:

� Despite multipath effects, time-varying channel, we can model the channel in frequency domain with multiplication

� Can represent received signal as: (in freq. domain)

� Where H(k) is channel matrix, and S(k), N(k) are transmit signal, noise vectors

� Note for each sub-band symbol (element S(k)), the effect of channel can be viewed as a constant gain, phase change (multiply by element H(k))

� Also note past symbols do not influence current symbol output (called memoryless)

)()()()( kNkSkHkR +=


� MIMO Channel Estimation� The previous equation: R(k)=H(k)S(k)+N(k) refers to a SISO channel (multipath response from any Tx antenna to any Rx antenna)

� Returning to MIMO channel estimation:

� Considering each sub-band, S(k), individually, we can see that each element of the above matrix can be represented by a complex value, indicating the gain, phase of the channel from Tx antenna ‘y’ to Rx antenna ‘x’ for that sub-band.

),(,

3231

2221

1211

TxAntyRxAntxhwith

hh

hh

hh

H xy ==

=



� MIMO Channel Estimation

� Thus, MIMO channel estimation for each sub-band, ‘k’, can be performed independently, using the channel matrix described previously. Can write:

� Where the MIMO channel estimates, H, is a set of ‘N’ matrices (indexed by ‘k’), one for each sub-band channel

),()(,

)()(

)()(

)()(

)(

3231

2221

1211

TxAntyRxAntxkhwith

khkh

khkh

khkh

kH xy ==

=


� MIMO Channel Estimation� Freq. Domain Channel Estimation

� For a SISO channel:� Considering the received signal in freq. domain:

� To estimate channel in frequency domain, consider:

� So if S(k), the Tx training sequence, is designed with unit magnitude (ie. |S(k)|2=1), then R(k)S*(k) gives an estimate for H(k), with noise term: N(k)S*(k).

)()()()( kNkSkHkR +=

)()()()()()()( ***kSkNkSkSkHkSkR +=

)()(|)(|)( *2kSkNkSkH +=



� Issue for Channel Estimation� The main issue in extending channel estimation from single antenna to multiple antennas is to separate the transmit antenna signals (or, more correctly, transmitted data streams) at the receiver.

� Can see that if each receive antenna receives signals from multiple transmit streams, we need to distinguish which component of the received signal represents which transmit stream.

� To determine the approach to use in determining the MIMO channel estimates, we first consider the training sequence…



� High-Throughput Long Train Field (HT-LTF)

� For 20MHz mode:

� HT-LTF for the TGn Joint proposal uses the same training sequence across tones as the IEEE 802.11a standard (extended from 52 to 56 carriers), for all spatial streams.

� The sequence is:

� To allow for MIMO channel estimation, the above training sequence is coded across both space (transmit spatial streams) and time (OFDM symbols).

28:28

1,1,1,1, 1, 1,1,1, 1,1, 1,1,1,1,1,1,1, 1, 1,1,1, 1,1, 1,1,1,1,1,0,

1, 1, 1,1,1, 1,1, 1,1, 1, 1, 1, 1, 1,1,1, 1, 1,1, 1,1, 1,1,1,1,1, 1, 1HTLTF−

− − − − − − − − =

− − − − − − − − − − − − − − −


� MIMO Channel Estimation� The training pattern used is shown below:

� Rows represent spatial dimensions (space)

� Columns represent training symbols (time).

� The same training pattern is used for each tone, k.

� Orthogonality of rows used to separate spatial streams

� improves performance compared to using frequency-division, time-division to isolate streams

−

−

−

−

=

1111

1111

1111

1111

HTLTFP space

time

11n – Channel Estimation� MIMO Channel Estimation

� With received symbol vectors put in matrix form, the received signal matrix can be written as (for each tone k):

� where: SHTLTF,k= SkPHTLTF, is the training sequence, and Sk= HTLTFk (training value for tone k)

� Least-squares channel estimates can be obtained with:

� Where: (with U = SkPHTLTF)

� And since Sk = 1 or -1:

kkHTLTFkHTLTF NHSR += ,,

kHTLTFk NPSH += )(

HTLTFkHTLTFHTLTFkHTLTFkHTLTF WNWPSHWR += )(,

HTLTFkWNH +=

HH

HTLTF UUUW1)( −=

H

HTLTFHTLTF

H

HTLTFkHTLTF PPPSW1)( −=


� MIMO Channel Estimation� Below are examples of PHTLTF, WHTLTF with different numbers of spatial streams:

� NSTS = 2:

� NSTS = 4:

� Note, in general:

−=

11

11HTLTFP

−⋅=

11

11

2

1HTLTFW

−

−

−

−

=

1111

1111

1111

1111

HTLTFP

−

−

−

−

⋅=

1111

1111

1111

1111

4

1HTLTFW

T

HTLTF

DLTF

kHTLTF PN

SW1

=


� MIMO Channel Estimation� Thus, we can obtain MIMO channel estimates in the frequency domain using the approach described above.

� During data transmission, multiple spatial streams may be used simultaneously for increased throughput

� In this case, the reception of each spatial stream sees the signals from the other spatial streams as interference.

� The process of separating each data stream from the other streams (as well as performing channel equalization) is referred to as MIMO detection, which is discussed next.





� MIMO Detection


� Beamforming



� Conclusion

11n – MIMO Detection

� MIMO Detection� MIMO detection refers to the process of determining the transmitted data symbols from received signal

� Involves separating each transmitted data stream from other streams (called interference cancellation), as well as channel equalization

� There are many different forms of MIMO detectors. The following detectors are discussed here:

� Linear detectors

� Zero-forcing (ZF) detector

� Minimum mean-square error (MMSE) detector

� ML detectors

� Maximum-likelihood (ML) detector


� MIMO Detection� MIMO System

� The basic MIMO system can be written as:

� Where:� r is N-dimensional received signal vector.

� s is M-dimensional transmitted signal vector.

� N is complex additive white Gaussian noise vector

� H is the N x M matrix of channel estimates

nHsr +=

11n – MIMO Detection� MIMO Detection

� Linear detectors� Linear detectors have the form:

� With r=Hs+n (from before)

� The performance is measured using the mean-square error (MSE):

� The linear detectors are differentiated by the choice of detector matrix C

Cry =

][2

sCrEMSE −=


� Zero-forcing (ZF) detector� The matrix C is chosen to completely cancel interference (or CH=I) [1]. If the system is overdetermined (M≤N), a unique solution exists, given by:

� This is known as the Moore-Penrose pseudoinverse of H

� The performance, using MSE, can be written as:

HHHHHC

1)( −=

1

0

2

2

2

][

])([

][

−==

−+=

−=

RNCnE

snHsCE

sCrEMSE


� Minimum mean-square error (MMSE) detector� The matrix C is chosen considering both interference cancellation as well as minimizing signal loss, noise enhancement. This is done by choosing C to minimize the mean-square error of the detector:

� Where Rr is the received autocorrelation matrix, and E[ssH]=I. The above MSE can be minimized by choosing: C=HH Rr

-1. This can be written as:

� Or:

HRHIRHCRRHC

CHCHICCR

sCrsCrEMSE

r

HH

r

H

rr

H

HHH

r

H

111)()(

]))([(

−−−−+−−=

−−+=

−−=

1)( −+= INHHHC o

HH

H

o

HHINHHC

1)( −+=


� MIMO Detection

� Maximum likelihood (ML) detector

� The ML detector performs an exhaustive search of all possible sequences for transmitted data symbol, s. This can be written as:

� The ML detector offers improved performance compared to the linear detectors. With the correct symbol chosen, the MSE can be seen to be:

2minarg Hsrs

Ss−=

∈

0

2

2

2

][

])([

][

NnE

HsnHsE

HsrEMSE

==

−+=

−=


� MIMO Detection

� Maximum likelihood (ML) detector

� Although the ML detector has better performance, the algorithm complexity makes it unattractive for practical applications.

� The ML detector runs in exponential time, while the ZF, MMSE linear detectors run in polynomial time

� The ML detector complexity is O(BM), where B is the constellation size per dimension, and M is the transmitted symbol dimension size.

� The linear detector complexity is NM, where N is the received symbol dimension size.





� MIMO Detection


� Beamforming



� Conclusion

11n – Space-Time Codes

� Space-Time Block Codes (STBC)� Space-time block codes are used to achieve spatial diversity through the use of multiple transmit antennas

� The most common STBC code is the Alamoutispace-time code, which is used in the IEEE802.11n draft proposals.


� Space-Time Block Codes (STBC)� The Alamouti code is considered a direct, open-loop approach for transmit diversity [1]

� Direct, since it does not convert spatial diversity into frequency or temporal diversity.

� Open-loop, since it does not require channel information to generate the code

� The basic form for the Alamouti code encodes one spatial stream into two space-time streams (shown next)


� Space-Time Block Codes (STBC)� The Alamouti code to encode one spatial stream into two space-time streams can be described as follows:

� Given two input symbols in time: x1 and x2, the STBC output symbols, y1 and y2, are:

� After STBC is applied, the first spatial stream sends x1and x2, the second sends –x2

* and x1* (Note that the first

antenna sends the original sequence unaltered, and the second stream provides space-time coding)

−=

∗

2

1

1x

xy

=

∗

1

2

2x

xy


� Space-Time Block Codes (STBC)� To see the effect of the code, we consider the received symbols: (Note: system is 2x1 MISO, or 2Tx-by-1Rx ant.)

� The received symbols (in time), in terms of x1, x2, are (assuming channel does not change over two symbols):

� In the receiver, the transmitted data can be recovered by forming the received vector [r1, r2

*]T with one receive antenna. This can be expressed as:

[ ] 1

2

1

211 nx

xhhr +

−⋅=

∗[ ] 2

1

2

212 nx

xhhr +

⋅=

∗

+

⋅

−=

∗∗∗∗∗

2

1

2

1

12

21

2

1

n

n

x

x

hh

hh

r

r


� Space-Time Block Codes (STBC)� Note the 2x1 MISO channel is effectively viewed as a 2x2 MIMO channel, with channel matrix:

� In the above, the columns of Heff are orthogonal. Hence, the matched filter can be seen to be Heff

H, since: Heff

HHeff =||H||2I, where ||H||2=||h1||

2+||h2||2.

� Thus, after matched filtering:

−=

∗∗

12

21

hh

hhHeff

+

=

∗∗∗

2

1

2

1

2

1

n

nH

x

xHH

y

yH

effeff

H

eff

+

=

∗∗

2

1

2

12

n

nH

x

xH

H

eff


� Space-Time Block Codes (STBC)� From last slide:

� From the above, we see that the channel is diagonalized (no interference between x1, x2

*).

� Also, note the noise remains white after the matched filter, since:

+

=

∗∗∗

2

1

2

12

2

1

n

nH

x

xH

y

yH

eff

[ ]eff

HH

eff

HHnnHEnnE =][

rr

[ ]

IHN

HINH

HnnEH

o

effo

H

eff

eff

HH

eff

2=

⋅⋅=

=


� Space-Time Block Codes (STBC)� Because the channel is diagonalized and noise remains white, the joint ML detection becomes greatly simplified

� The ML detection result can be found by using a pair of slicers (one for y1, one for y2

*)

� Thus, the ML solution could be found by computing 2Bdistances (assuming each slicer does B distance comparisons), compared to a search of B2 points


� Space-Time Block Codes (STBC)� The optional STBC coding rates consist of either STBC coding, or hybrid STBC / Spatial-Division Multiplexing (SDM).

� Other optional coding rates consist of:

� NSS=2 to NSTS=3 (One 2x1 STBC, one spatial stream)

� NSS=2 to NSTS=4 (Two 2x1 STBC)

� NSS=3 to NSTS=4 (One 2x1 STBC, two spatial streams)

� Note: above rates use Spatial-Division Multiplexing


� Space-Time Block Codes (STBC)� For an example of hybrid STBC / Spatial-Division Multiplexing, consider the coding option which maps NSS=2 streams into NSTS=4 streams.

� The coding is:

� Note the first two output streams are the STBC coding of first input stream, while the second two output streams are the STBC coding of second input stream.

� The STBC provides transmit diversity so that only two antennas are needed at the receiver (4x2 MIMO)

−

−=

∗

+

∗

+

12,2

2,2

12,1

2,1

1

n

n

n

n

x

x

x

x

y

=

∗

+

∗

+

n

n

n

n

x

x

x

x

y

2,2

12,2

2,1

12,1

2


� Space-Time Block Codes (STBC)� The received symbols are (for first antenna):

� And for the second antenna:

[ ] 12,1

2,2

12,2

2,1

12,1

4,13,12,11,112,1 +

∗

+

∗

+

+ +

⋅= n

n

n

n

n

n n

x

x

x

x

hhhhr[ ] n

n

n

n

n

n n

x

x

x

x

hhhhr 2,1

12,2

2,2

12,1

2,1

4,13,12,11,12,1 +

−

−⋅=

∗

+

∗

+

[ ] n

n

n

n

n

n n

x

x

x

x

hhhhr 2,2

12,2

2,2

12,1

2,1

4,23,22,21,22,2 +

−

−⋅=

∗

+

∗

+ [ ] 12,2

2,2

12,2

2,1

12,1

4,23,22,21,212,2 +

∗

+

∗

+

+ +

⋅= n

n

n

n

n

n n

x

x

x

x

hhhhr


� Space-Time Block Codes (STBC)� To recover the transmitted data, we can form the receive vector: [r1,2n r

*1,2n+1 r2,2n r

*2,2n+1]

T. This can be written as:

� From the above, can see that the first two columns and last two columns are orthogonal

� This shows there is no interference between x1,2n, x*1,2n+1,

as well as between x2,2n, x*2,2n+1.

� Note there is still interference between x1,n, x2,n (spatial division multiplexing). MIMO detection is used to recover spatial streams.

+

⋅

−−

−−

=

∗

+

∗

+

∗

+

∗

+

∗∗∗∗

∗∗∗∗

∗

+

∗

+

12,2

2,2

12,1

2,1

12,2

2,2

12,1

2,1

3,24,21,22,2

4,23,22,21,2

3,14,11,12,1

4,13,12,11,1

12,2

2,2

12,1

2,1

n

n

n

n

n

n

n

n

n

n

n

n

n

n

n

n

x

x

x

x

hhhh

hhhh

hhhh

hhhh

r

r

r

r





� MIMO Detection


� Beamforming



� Conclusion

11n – Beamforming

� TX Beamforming� Beamforming refers to a technique where channel information is used to form spatial mapping matrices for the transmitter

� The goal is to improve the recovery of the received signal at the receiver.

11n – Beamforming

� TX Beamforming� Spatial matrices, Vk, (where k is subcarrier index) are applied to the signal, xk, before transmission. The received signal with beamforming can be written as:

� Spatial matrices are chosen to emphasize dominant modes of transmission for MIMO channel

� Optimal matrices can be computed using singular value decomposition (SVD):

� Other techniques can also be used (implementation left to designer)

kkkkk nxVHy +=

11n – Beamforming

� TX Beamforming

� Singular Value Decomposition (SVD) allows any NRX x NTX

matrix to be decomposed into:

� Where:

� Hk is NRX x NTX matrix of channel in frequency-domain for subcarrier k

� ∑k is diagonal matrix of “singular values”, σ0, σ1, … σN-1where σ0, … σN-1 are real, non-negative

� Uk is NRX x N matrix, Vk is NTX x N matrix (both orthonormalmatrices), where N = min{NRX, NTX}

� Note: singular values can be organized in descending order: σ0> σ1 > … σN-1, with the columns of Uk and Vk ordered appropriately.

H

kkkk VUH Σ=

11n – Beamforming

� TX Beamforming� Using SVD, the optimal choice for the spatial matrices for transmit beamforming are Vk . The received signal can be written as (note: Vk

HVk =I):

� Thus, singular values in ∑k reflect received signal strengths for each spatial stream (since Uk is orthonormal matrix).

kkkkk nxVHy +=

kkkk

kkk

H

kkk

nxU

nxVVU

+Σ=

+Σ=

11n – Beamforming

� TX Beamforming� If the number of spatial streams, NSS, is chosen smaller than min{NRX, NTX}, the NSS column vectors in Vk associated with the largest singular values can be used for spatial matrices (can write this as: [Vk]Nss)

� The above choice maximizes the receive signal strength for the spatial streams used:

kkNsskkk nxVHy += ][

kkNsskk

kkNssk

H

kkk

nxU

nxVVU

+Σ=

+Σ=

][

][

11n – Beamforming

� TX Beamforming

� Two forms of beamforming are implicit and explicit:

� In explicit beamforming, the station to use transmit beamforming (STA A) receives either channel matrices or pre-computed spatial matrices from remote station (STA B).

� In implicit beamforming, the transmitting station uses the fact that the channel from its antenna ‘j’ to the remote antenna ‘k’ should be the same as the channel from remote antenna ‘k’ to local antenna ‘j’ when the remote transmits (known as channel reciprocity).

11n – Beamforming

� TX Beamforming� Assuming channel reciprocity, the transmitting station can use transpose of its own channel matrices as estimate of the remote channel matrices:

� Where k denotes data subcarrier

� Note, however, with implicit beamforming:� transmit and receive chains of both stations have attenuation, delay differences, which needs to be considered.

� calibration process used to compensate for this (restore reciprocity).

T

ABkBAk HH >−>− = ,,

11n – Beamforming

� TX Beamforming� From before, channel reciprocity can be written as:

� The above refers to actual over-the-air channels (ie. effect of Tx, Rx chains not considered).

� Including Tx, Rx chains, the observed channels are:

� Where Ck,A:Tx, for example, is the transmit chain amplitude, phase response for STA A. (Can consider these matrices diagonal [6])

� These observed channels generally do not exhibit reciprocity.

T

ABkBAk HH >−>− = ,,

TxAkBAkRxBkBAk CHCH :,,:,,

~>−>− =

TxBkABkRxAkABk CHCH :,,:,,

~>−>− =

11n – Beamforming

� TX Beamforming� In order to have observed matrices with channel reciprocity, can add correction factors KK,A, KK,B to the STA A, STA B transmitters respectively, so that:

� Suitable correction factors are (from [6]):

� Since:

� Above satisfied by over-the-air channel reciprocity

( ) ( )TBkABkAkBAk KHKH ,,,,

~~>−>− =

T

RxAkTxAkAk CCK :,

1

:,,

−=T

RxBkTxBkBk CCK :,

1

:,,

−=

( ) ( )T

RxAkBAkRxBk

T

RxAkTxAkTxAkBAkRxBkAkBAk CHCCCCHCKH :,,:,:,

1

:,:,,:,,,

~>−

−

>−>− ==

( ) ( ) ( )T

RxAk

T

ABkRxBk

T

RxAk

T

ABk

T

TxBk

T

TxBkRxBk

T

BkABk CHCCHCCCKH :,,:,:,,:,

1

:,:,,,

~>−>−

−

>− ==





� MIMO Detection


� Beamforming

�A Simulation Model in MATLAB/Simulink� Outline of System Model


� Demo

11n – Simulation Model� Outline of Simulation Model

� The following slides show the structure of the simulation model developed in MATLAB/Simulink.

� The supported features of the TGn Joint proposal are listed below:

� MIMO structures� Direct-map, spatial expansion, space-time coding, and Tx beamforming are supported

� Preamble formats� Mixed-mode supported (Greenfield not supported)

� MCS rates 0-31 supported� 20MHz supported (40MHz not supported)

� Note: The simulation model was developed based on the IEEE 802.11a simulation model by Martin Clark, available on MATLAB Central.

11n – Simulation Model

� Block Diagram of Simulation Model


� Simulation Model – Space-Time Coding

� The block diagram above shows the space-time coding module.


� Simulation Model – Spatial Expansion, BF

� The block diagram above shows the module performing spatial expansion, beamforming.


� Simulation Model – MIMO Detection

� The block diagram above shows the channel estimation, MIMO detection module.





� MIMO Detection


� Beamforming

�A Simulation Model in MATLAB/Simulink� Outline of System Model


� Demo


� Performance Tests� The following slides show performance test results for the simulation model. The settings for the test are shown below:

� Receiver Type: MMSE

� PPDU Length: 1,000 Bytes

� Channel Model: AWGN, D(NLOS)

� Per tone Channel Estimation (no smoothing)

� No Impairments


� Performance Tests – AWGN Channel


� Performance Tests–Channel D, n-LOS


� Performance Tests–Channel D, n-LOS, BF


� Performance Tests–Ch D, n-LOS, STBC





� MIMO Detection


� Beamforming



�Demo

References

� References� [1] Barry, J., Lee, E., Messerschmitt, D., Digital Communications, 3rd ed. New York: Springer, 2004.

� [2] Rappaport, T.S., Wireless Communications. Principles and Practice 2nd Ed., Prentice Hall, New Jersey, 2002.

� [3] Terry, J., Heiskala, J., OFDM Wireless LANs: A Theoretical and Practical Guide. Indianapolis: Sams, 2002.

� [4] V. Erceg, et al., “IEEE 802.11 Wireless LANs TGnChannel Models”, May 10, 2004.

� [5] Joint Proposal: High throughput extension to the 802.11 Standard: PHY doc.: IEEE 802.11-05/1102r4.

References

� References (cont.)� [6] TGn Sync Proposal Technical Specification document: IEEE 802.11-05/1095r44.

� [7] Advanced Wireless Technologies: MIMO Comes of Age: Document FPG 2003-242.2

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