The Case for Optimum Detection Algorithms inMIMO Wireless Systems

Helmut Bolcskei

joint work with A. Burg, C. Studer, and M. Borgmann

ETH Zurich

Data rates in wireless double every 18 months

1990 1995 2000 2005 2010 20151 kbps

1 Mbps

1 Gbps

GSM

802.11802.11b 802.11g

802.11n

2-stream

UMTS HSDPA-1HSDPA-2

Edge

3GPP LTE

802.11n

4-stream

year

thro

ughp

ut

2

Need for higher throughput cannot be met bysimply allocating more bandwidth

40 MHz

20 MHz

Interference

Achieving higher throughput requires higher spectral efficiency

3

Spatial multiplexing: Transmit multiple data streamssimultaneously and in the same frequency band

4

MIMO gains carry through to system level

Advantages of MIMO

� Larger range

� Better quality of service

� Higher peak throughput

� Higher system capacity

10 20 30 40 50 60 700

100

200

300

400

500

600

range

thro

ughp

ut[M

bps]

4stre

am

s2stream

s

1 stream

2x

2x

IEEE 802.11n PHY, 40 MHz bandwidth,TGn-C channel

MIMO is part of IEEE 802.11n, IEEE 802.16e, and 3GPP LTE

5

The “Digital Home”: A challenging application forMIMO wireless systems

Ensure a wire-like experience throughout the entire home

6

Meeting user expectations requires 4 spatial streams

� Requirement: 4 HDTV video streams @ 25 Mbps each

� Aggregate throughput requirement: 100 Mbps at a range of 30m

0 50 100 150 200 250 300 350 400

10203040506070

application layer throughput [Mbps] / 60% MAC efficiency

rang

e [m

]

aggregatethroughputrequirement

802.11g(SISO)

802.11n2-stream

802.11n4-stream

+

� Current IEEE 802.11n solutions support only 2 spatial streams

� Products with three spatial streams have just been announced

7

Maximum likelihood (ML) MIMO detection

Dem

odula

tion a

nd s

epara

tion

Modula

tion a

nd m

appin

g

y = Hs + n

Maximum likelihood (ML) MIMO detection

s = arg mins∈OMT

||y −Hs||2

8

ML detection through exhaustive search

Exhaustive search: Enumerate all possible candidate vectors

� Number of candidate vectors grows exponentially in the number ofantennas

� A 4×4 system with 64-QAM modulationrequires consideration of 16’777’216candidates

4x4 IEEE 802.11nbaseband ASIC

[ETH Zurich, 2008]

5mm

5mm

1.4 mm1.4 mm2x2 ML

detector64-QAM

3x3 MLdetector64-QAM

4x4 MLdetector64-QAM

91mm

91m

m

11.3mm

11.3m

m

20M GE

1'300M GE1.7M GE

0.3M GE

Exhaustive search is not economic for more than two spatial streams

9

Soft-output (APP) MIMO detection

MIMO

channel

MIMO

detector

y = Hs + n

MIMO detector computes log-likelihood ratios (LLR) for each bit

L (xj,b) = log(P (xj,b = 1|y)P (xj,b = 0|y)

)Max-log approximation for LLRs

L (xj,b) = mins∈X (0)

j,b

||y −Hs||2 − mins∈X (1)

j,b

||y −Hs||2

X (0)j,b ,X

(1)j,b ... sets of vector symbols for which xj,b = 0, 1

10

Linear equalization decomposes the MIMO channelinto parallel SISO channels

linear equalizersoft-metric

detector

soft-metric

LLRs are computedfor each stream

separately

� Compared to the remaining baseband processing, complexity ofequalization is very low even for a large number of streams

� Complexity of LLR computation is negligible

11

MMSE is ill-suited for highly integrated devices

� Mini-PCI and half-mini PCI is becoming the de-facto standard

� Spacing of printed antennas can easily be below λ/4� Reduced antenna spacing leads to (severe) spatial correlation

Antenna 1

Antenna 2

18mm

54m

m

-75 -70 -65received power [dBm]

fram

e erro

r rat

e

Soft-outputMMSE

Close-to-optimum APP

10-1

100

10-2

IEEE 802.11n, MCS27, 40 MHz, TGn-D (MT = MR = 4, 16-QAM, rate 1/2)

MMSE detection suffers significantly from spatial correlation

12

MMSE fails to provide robustness against varyingpropagation conditions

location

signa

l pow

er (d

B)

10 15 20 25 30 35

100

SNR [dB]

BE

R

10-1

10-2

10-3

10-4

10-5

10-6

4x4MMSE

4x4 Maximumlikelihood

4x5MMSE

MMSE diversity order

ML diversityorder

Diversity: Resilience against bad channels ⇒ more reliable operation

13

The “business case” for high-end MIMO receivers

10 20 30 40 50 60050

100150200250300350400

range [m]

thro

ughp

ut[M

bps]

30.4m 35.7m 41.2m

4x4

MMSE

4x5

MMSE 4x4 APP

4x

4M

MS

E

4x

5M

MS

E4

x4

AP

P

Additional receive antennas canpartially compensate forsub-optimal receiver algorithms

� Each additional antenna costs 0.7 USD–1.0 USD� Overall manufacturing chipset cost is ≈ 9 USD� Space limitations can become critical (antenna spacing)

Boosting MMSE performance by using additional antennas isexpensive and not always possible

14

Impact of RF non-idealities

RF limitations: SNR is limited to approximately 35 dB–40 dB

-90 -80 -70 -60 -50 -40 -30 -20 -1005

101520253035404550

received power [dBm]

mea

n SN

R [dB

]

0

SNR limited by poorRF noise figure

-65 -60 -55 -50average received power [dBm]

Close-to-optimum APP

10-1

100

10-2fra

me e

rror r

ate

Soft-outputMMSE

IEEE 802.11n, MCS 31 (600 Mbps), MT = MR = 4, Greenfield, 20MHz bandwidth, 1000B packets

In IEEE 802.11n, APP detection is needed for operation in the highestrate modes

15

Performance of MMSE receiver is sensitive tointerference

Consider a 4× 5 MIMO system interfered by a single-stream system

� Information-theoretic arguments: Interference “knocks out” onereceive antenna

� Reduction to an effective 4× 4 system

MMSE detector� Diversity is lost and robustness is reduced

Optimum APP detector

� Receiver performs well even with an effectively symmetric antennaconfiguration

� Graceful performance degradation

16

Sphere decoding: Exploiting the structure of thedetection problem

Tra

nsm

itte

r

Receiv

er

MIMO

Channel

s = arg mins∈OMT

||y −Hs||2

The MIMO ML-detection problem corresponds to finding the closestpoint in a skewed, finite lattice

17

A brief history of the sphere decoding algorithm

� 1981: M. Pohst describes an algorithm to efficiently identify theclosest point in an infinite lattice

� 1993: E. Viterbo and E. Biglieri apply the Pohst algorithm to latticedecoding and introduce the sphere constraint

� 1999: E. Viterbo and J. Boutros employ sphere decoding for latticedecoding in fading channels

� 2000: M. O. Damen et al. describe the application of spheredecoding to space-time codes

18

A brief history of the sphere decoding algorithmcont’d

� 2003: B. Hochwald and S. ten Brink propose the first soft-outputsphere decoder

� 2005: A. Burg et al. provide the first VLSI implementation ofhard-output sphere decoding

� 2008: C. Studer et al. develop single tree search soft-output spheredecoding and provide a corresponding VLSI implementation

19

Sphere decoding reduces to a tree-search problem

1 Translate the problem into a tree search (triangularization)2 Nodes are associated with Partial Euclidean Distances (PEDs) d(s)3 Update rule: di(s(i)) = di+1(s(i)) + |ei|2, i = MT , . . . , 1 (tree level)4 ML detection corresponds to finding the leaf with the smallest PED

Partial Euclidean

distance

A branch-and-bound strategy realized through a sphere constraint leadsto efficient tree pruning

20

Computing the LLRs by applying the spheredecoding algorithm

L (xj,b) = mins∈X (0)

j,b

||y −Hs||2︸ ︷︷ ︸λML

− mins∈X (1)

j,b

||y −Hs||2︸ ︷︷ ︸λML

j,b

Repeated Tree Search (RTS) [Wang and Giannakis, 2004]

1 Use the sphere decoding algorithm to find λML

2 Restart the search to identify the QMT remaining minima and

constrain the search to X (xMLj,b ) by operating on pre-pruned trees

21

The single tree search (STS) philosophy [Studer etal., 2006]

Repeated tree search is highly inefficient

� For example, a 4-stream system employing 64-QAM modulationrequires 24+1 sphere decoder runs

� A given node may be visited more than once in consecutive runs

STS algorithm: Ensure that each node is visited at most once

� Search for the ML solution and all counterhypotheses concurrently

� Maintain a list containing

the ML hypothesis xML and its metric λML

the metrics of the counterhypotheses λMLj,b

� Search a subtree only if the result can lead to an update of eitherλML or of at least one of the metrics λML

j,b

22

VLSI implementation of the STS algorithm [Studeret al., 2008]

Hard-output STS

Technology 0.25 µm, 1P/5M

System 4×4, 16-QAM

Decoding norm `∞ `2

Clock freq. 87 MHz 71 MHz

Area 36 kGE 57 kGE

MHz/kGE 2.41 1.25

Hardware complexity of STS is only 30% of that of RTS based onhard-output sphere decoding

23

LLR clipping reduces complexity and providesscalability

In practice, wordwidth of LLRs must be constrained

LLR clipping

LLR clipping can be built into the STS algorithm ⇒ additional constraintfor pruning the tree

LLR clipping allows to realize aperformance/complexity tradeoff atrun-time

16 16.5 17 17.5 18 18.5 190

50100150

200250300350

400450

0.10.2

0.4

24

816

32

64

aver

age n

umbe

r of v

isite

d nod

es

required SNR [dB] for 1% FER

STS

List sphere decoder[Hochwald and ten Brink, 2005]

0.05 0.025

24

Early termination and scheduling

Sphere decoding has variable detection effort

Achieving fixed throughput under latency constraints

� A scheduler with FIFO distributes runtime across symbols

� Latency constraints: Need to constrain the decoding effort throughearly termination

STS

STSScheduler Collector

terminate terminated early

FIFOterminated early

early termination

early termination+ scheduling

25

Application of STS to IEEE 802.11n

� Data rates range from 6 Mbps to 600 Mbps

MMSE� MMSE is set to operate at a certain highest rate mode

� No performance improvement possible for lower-rate modes

STS: Adjust the decoding effort at runtime

� Use LLR clipping to reduce complexity in the highest rate modes ⇒graceful performance degradation, but still better than MMSE

� LLR clipping adjusts decoding effort to achieve close-to-optimumperformance for lower-rate modes

26

Application of STS to IEEE 802.11n

Instantiation of 10 STS units� Meet throughput and latency requirements for 40 MHz bandwidth

� Enable 600 Mbps operation with real-world RF

4x4 IEEE 802.11nbaseband ASIC

[ETH Zurich, 2008]

5mm

5mm

1.7M GE

4x4 STSdetector0.6M GE

4x4 MMSEdetector0.05M GE

2.3M GE(estimated)

Commercially available 2-stream solutions require roughly 2M GEs

27

Headaches

STS exploits (finite-alphabet) structure of transmitted vectors

� RF non-idealities limit transmit SNR to 32 dB. Transmit noiseappears spatially colored at the receiver

� Interference appears as spatially colored noise

� Phase-noise and residual frequency offset distort the discretelocations of the constellation points

MMSE� Linear detection suffers from fixed-point effects

� MMSE detection requires accurate noise estimation

28

Iterative detection and decoding

Iterate between MIMO detector and FEC decoder

MIMOdetector deinterleaverLLRs

FECdeocoder

(BCJR,LDPC)

LLRsinterleaver

vectorsymbols

� Strong channel code: More iterations can compensate forsuboptimal MIMO detector

In practice, the code is given by the standard and code rates can beclose-to one for the highest (data) rate modes

29

Tradeoff between detector complexity and numberof iterations

Guaranteed throughput requirement

� Need multiple instantiations of MIMO detectors and FEC decoders

� Area scales linearly with the number of iterations

Maximum latency constraints

� Increase throughput of the MIMO detector and the FEC decoder

� Additional area increase due to latency constraints

� Maximum throughput of the sequential FEC decoder is limited

30

Tradeoff between detector complexity and numberof iterations cont’d

Additional hardware overhead� Iterations require additional storage for baseband samples

� For strong codes, hardware complexity for FEC decoding is high

� Complexity of soft-in soft-out MIMO and FEC decoders is higherthan for non-iterative schemes

� Iterative detection and decoding leads to significant increase inhardware complexity compared to one-shot operation

� If iterations are needed, the number of iterations must be kept low

31

High-performance MIMO detector is key forefficient implementation of iterative receiver

STS I=1

MM

SEI=2

STS

I=2

MM

SEI=

410 11 12 13 14 15 16 17 18 2019

SNR [dB]

fram

e erro

r rat

e 10-1

100

10-2

10-3

MM

SE I=1

For the same performance, MMSE detection requires more iterationsthan soft-in soft-out STS sphere decoding

32