The Case for Optimum Detection Algorithms in MIMO Wireless Systems. Helmut Bölcskei

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1 The Case for Optimum Detection Algorithms in MIMO Wireless Systems Helmut Bölcskei joint work with A. Burg, C. Studer, and M. Borgmann ETH Zurich

2 Data rates in wireless double every 18 months throughput 1 Gbps 1 Mbps b g UMTS n 2-stream Edge n 4-stream HSDPA-2 HSDPA-1 3GPP LTE GSM 1 kbps year 2

3 Need for higher throughput cannot be met by simply allocating more bandwidth 20 MHz 40 MHz Interference Achieving higher throughput requires higher spectral efficiency 3

4 Spatial multiplexing: Transmit multiple data streams simultaneously and in the same frequency band 4

5 MIMO gains carry through to system level Advantages of MIMO ˆ Larger range ˆ Better quality of service ˆ Higher peak throughput ˆ Higher system capacity throughput [Mbps] x 2x 2 streams 4 streams stream range IEEE n PHY, 40 MHz bandwidth, TGn-C channel MIMO is part of IEEE n, IEEE e, and 3GPP LTE 5

6 The Digital Home : A challenging application for MIMO wireless systems Ensure a wire-like experience throughout the entire home 6

7 Meeting user expectations requires 4 spatial streams ˆ Requirement: 4 HDTV video 25 Mbps each ˆ Aggregate throughput requirement: 100 Mbps at a range of 30m range [m] g (SISO) n 2-stream aggregate throughput requirement n 4-stream application layer throughput [Mbps] / 60% MAC efficiency ˆ Current IEEE n solutions support only 2 spatial streams ˆ Products with three spatial streams have just been announced 7

8 Maximum likelihood (ML) MIMO detection Modulation and mapping Demodulation and separation y = Hs + n Maximum likelihood (ML) MIMO detection ŝ = arg min y Hs 2 s O M T 8

9 ML detection through exhaustive search Exhaustive search: Enumerate all possible candidate vectors ˆ Number of candidate vectors grows exponentially in the number of antennas ˆ A 4 4 system with 64-QAM modulation 91mm requires consideration of candidates 11.3mm 5mm 1.7M GE 5mm 4x4 IEEE n baseband ASIC [ETH Zurich, 2008] 0.3M GE 1.4 mm 1.4 mm 2x2 ML detector 64-QAM 20M GE 3x3 ML detector 64-QAM 11.3mm 1'300M GE 4x4 ML detector 64-QAM 91mm Exhaustive search is not economic for more than two spatial streams 9

10 Soft-output (APP) MIMO detection MIMO channel MIMO detector y = Hs + n MIMO detector computes log-likelihood ratios (LLR) for each bit ( ) P (xj,b = 1 y) L (x j,b ) = log P (x j,b = 0 y) Max-log approximation for LLRs L (x j,b ) = min s X (0) j,b y Hs 2 min s X (1) j,b y Hs 2 X (0) j,b, X (1) j,b... sets of vector symbols for which x j,b = 0, 1 10

11 Linear equalization decomposes the MIMO channel into parallel SISO channels detector linear equalizer soft-metric soft-metric LLRs are computed for each stream separately ˆ Compared to the remaining baseband processing, complexity of equalization is very low even for a large number of streams ˆ Complexity of LLR computation is negligible 11

12 MMSE is ill-suited for highly integrated devices 54mm ˆ Mini-PCI and half-mini PCI is becoming the de-facto standard ˆ Spacing of printed antennas can easily be below λ/4 ˆ Reduced antenna spacing leads to (severe) spatial correlation Antenna 1 18mm frame error rate Soft-output MMSE Close-tooptimum APP Antenna IEEE n, MCS27, 40 MHz, TGn-D (M T = M R = 4, 16-QAM, rate 1/2) received power [dbm] MMSE detection suffers significantly from spatial correlation 12

13 MMSE fails to provide robustness against varying propagation conditions 10 0 MMSE diversity order x4 MMSE signal power (db) BER ML diversity order 4x5 MMSE 4x4 Maximum likelihood location SNR [db] Diversity: Resilience against bad channels more reliable operation 13

14 The business case for high-end MIMO receivers throughput [Mbps] x4 MMSE 4x4 APP 4x5 MMSE 30.4m 35.7m 41.2m 4x4 MMSE 4x5 MMSE 4x4 APP range [m] Additional receive antennas can partially compensate for sub-optimal receiver algorithms ˆ Each additional antenna costs 0.7 USD 1.0 USD ˆ Overall manufacturing chipset cost is 9 USD ˆ Space limitations can become critical (antenna spacing) Boosting MMSE performance by using additional antennas is expensive and not always possible 14

15 Impact of RF non-idealities mean SNR [db] RF limitations: SNR is limited to approximately 35 db 40 db SNR limited by poor RF noise figure Close-tooptimum APP received power [dbm] average received power [dbm] IEEE n, MCS 31 (600 Mbps), M T = M R = 4, Greenfield, 20MHz bandwidth, 1000B packets frame error rate Soft-output MMSE In IEEE n, APP detection is needed for operation in the highest rate modes 15

16 Performance of MMSE receiver is sensitive to interference Consider a 4 5 MIMO system interfered by a single-stream system ˆ Information-theoretic arguments: Interference knocks out one receive antenna ˆ Reduction to an effective 4 4 system MMSE detector ˆ Diversity is lost and robustness is reduced Optimum APP detector ˆ Receiver performs well even with an effectively symmetric antenna configuration ˆ Graceful performance degradation 16

17 Sphere decoding: Exploiting the structure of the detection problem Transmitter MIMO Channel Receiver ŝ = arg min y Hs 2 s O M T The MIMO ML-detection problem corresponds to finding the closest point in a skewed, finite lattice 17

18 A brief history of the sphere decoding algorithm ˆ 1981: M. Pohst describes an algorithm to efficiently identify the closest point in an infinite lattice ˆ 1993: E. Viterbo and E. Biglieri apply the Pohst algorithm to lattice decoding and introduce the sphere constraint ˆ 1999: E. Viterbo and J. Boutros employ sphere decoding for lattice decoding in fading channels ˆ 2000: M. O. Damen et al. describe the application of sphere decoding to space-time codes 18

19 A brief history of the sphere decoding algorithm cont d ˆ 2003: B. Hochwald and S. ten Brink propose the first soft-output sphere decoder ˆ 2005: A. Burg et al. provide the first VLSI implementation of hard-output sphere decoding ˆ 2008: C. Studer et al. develop single tree search soft-output sphere decoding and provide a corresponding VLSI implementation 19

20 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: d i (s (i) ) = d i+1 (s (i) ) + e i 2, i = M T,..., 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 leads to efficient tree pruning 20

21 Computing the LLRs by applying the sphere decoding algorithm L (x j,b ) = min y Hs 2 min y Hs 2 s X (0) j,b } {{ } λ ML s X (1) j,b }{{} λ ML j,b Repeated Tree Search (RTS) [Wang and Giannakis, 2004] 1 Use the sphere decoding algorithm to find λ ML 2 Restart the search to identify the QM T remaining minima and constrain the search to X (xml j,b ) by operating on pre-pruned trees 21

22 The single tree search (STS) philosophy [Studer et al., 2006] Repeated tree search is highly inefficient ˆ For example, a 4-stream system employing 64-QAM modulation requires 24+1 sphere decoder runs ˆ A given node may be visited more than once in consecutive runs STS algorithm: Ensure that each node is visited at most once ˆ Search for the ML solution and all counterhypotheses concurrently ˆ Maintain a list containing the ML hypothesis x ML and its metric λ ML the metrics of the counterhypotheses λ ML j,b ˆ Search a subtree only if the result can lead to an update of either λ ML or of at least one of the metrics λ ML j,b 22

23 VLSI implementation of the STS algorithm [Studer et al., 2008] Hard-output STS Technology 0.25 µm, 1P/5M System 4 4, 16-QAM Decoding norm l l 2 Clock freq. 87 MHz 71 MHz Area 36 kge 57 kge MHz/kGE Hardware complexity of STS is only 30% of that of RTS based on hard-output sphere decoding 23

24 LLR clipping reduces complexity and provides scalability In practice, wordwidth of LLRs must be constrained LLR clipping LLR clipping can be built into the STS algorithm additional constraint 450 for pruning the tree LLR clipping allows to realize a performance/complexity tradeoff at run-time average number of visited nodes List sphere decoder [Hochwald and ten Brink, 2005] STS required SNR [db] for 1% FER 24

25 Early termination and scheduling Sphere decoding has variable detection effort Achieving fixed throughput under latency constraints ˆ A scheduler with FIFO distributes runtime across symbols ˆ Latency constraints: Need to constrain the decoding effort through early termination terminate terminated early STS early termination FIFO Scheduler STS Collector terminated early early termination+ scheduling 25

26 Application of STS to IEEE n ˆ Data rates range from 6 Mbps to 600 Mbps MMSE ˆ MMSE is set to operate at a certain highest rate mode ˆ No performance improvement possible for lower-rate modes STS: Adjust the decoding effort at runtime ˆ Use LLR clipping to reduce complexity in the highest rate modes graceful performance degradation, but still better than MMSE ˆ LLR clipping adjusts decoding effort to achieve close-to-optimum performance for lower-rate modes 26

27 Application of STS to IEEE n Instantiation of 10 STS units Meet throughput and latency requirements for 40 MHz bandwidth Enable 600 Mbps operation with real-world RF 5mm 5mm 4x4 MMSE detector 0.05M GE 1.7M GE 4x4 IEEE n baseband ASIC [ETH Zurich, 2008] 4x4 STS detector 0.6M GE 2.3M GE (estimated) Commercially available 2-stream solutions require roughly 2M GEs 27

28 Headaches STS exploits (finite-alphabet) structure of transmitted vectors ˆ RF non-idealities limit transmit SNR to 32 db. Transmit noise appears spatially colored at the receiver ˆ Interference appears as spatially colored noise ˆ Phase-noise and residual frequency offset distort the discrete locations of the constellation points MMSE ˆ Linear detection suffers from fixed-point effects ˆ MMSE detection requires accurate noise estimation 28

29 Iterative detection and decoding Iterate between MIMO detector and FEC decoder vector symbols MIMO detector LLRs deinterleaver FEC deocoder (BCJR, LDPC) interleaver LLRs ˆ Strong channel code: More iterations can compensate for suboptimal MIMO detector In practice, the code is given by the standard and code rates can be close-to one for the highest (data) rate modes 29

30 Tradeoff between detector complexity and number of iterations Guaranteed throughput requirement ˆ Need multiple instantiations of MIMO detectors and FEC decoders ˆ Area scales linearly with the number of iterations Maximum latency constraints ˆ Increase throughput of the MIMO detector and the FEC decoder ˆ Additional area increase due to latency constraints ˆ Maximum throughput of the sequential FEC decoder is limited 30

31 Tradeoff between detector complexity and number of iterations cont d Additional hardware overhead ˆ Iterations require additional storage for baseband samples ˆ For strong codes, hardware complexity for FEC decoding is high ˆ Complexity of soft-in soft-out MIMO and FEC decoders is higher than for non-iterative schemes ˆ Iterative detection and decoding leads to significant increase in hardware complexity compared to one-shot operation ˆ If iterations are needed, the number of iterations must be kept low 31

32 High-performance MIMO detector is key for efficient implementation of iterative receiver 10 0 frame error rate MMSE I=4 MMSE I=2 STS I=2 STS I=1 MMSE I= SNR [db] For the same performance, MMSE detection requires more iterations than soft-in soft-out STS sphere decoding 32

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