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1 Signal Detection Based on Belief Propagation in a Massive MIMO System Takeo Ohgane Hokkaido University, Japan 28 October 2013

2 Background (1) 2 Massive MIMO An order of 100 antenna elements channel capacity issue Fading reduction effect H : N x N channel matrix (i.i.d. complex Gaussian random variables) H H H NI log det I + N H H H log det (I + I) = N log(1 + )

3 Background (2) 3 Promising application Multiuser MIMO Very large array antenna Fewer users

4 Problem 4 If the number of users increase... Detection of a large number of streams is required.

5 Objective 5 Spatial demultiplexing MAP detection: O(L N ) Spatial filtering (MMSE, ZF): O(N 3 ) QR decomposition based algorithms: O(N 3 )! Less complex method Detection based on belief propagation (BP): O(N 2 )! N. Srinidhi, S. K. Mohammed, A. Chockalingam, and B. S. Rajan, Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search, Proc. IEEE ISIT, pp , June/July 2009.! C. Knievel, M. Noemm, and P. A. Hoeher, Low-Complexity Receiver for Large-MIMO Space- Time Coded Systems, Proc. IEEE VTC-Fall, Sept ! Capability of pure BP-based algorithm

6 Contents!6 Factor graph expression BP-based detection algorithm EXIT analysis Performance evaluation Conclusions

7 Factor graph expression (1)!7 s1 TX s2 Estimated symbols and received signals are mutually related. r1 RX r2 ex) r1 RX r2 s1 s2 Problem is to estimate s1 and s2 from r1 and r2. (1)} s1 s2 (3) (2) a priori values

8 Factor graph expression (2)!8 s1 s2 s3 s4 Symbol node TX s1 s2 s3 s4 RX r1 r2 r3 r4 r1 r2 r3 r4 Observation node

9 Factor graph expression (3)!9 MIMO detection vs LDPC decoding Message node b1 b2 b3 b4 Symbol node s1 s2 s3 s4 c1 Check node c4 b1+b2+b3=0 b3+b4=0 r1 r2 r3 r4 Observation node ri=hi1s1+hi2s2+hi3s3+hi4s4

10 BP-based detection (1)!10 Message update at observation node (1) soft replica generation s1 si sn ik ŝ k extrinsic value pq i1 ij in ri pq : LLR (2) parallel interference cancellation (PIC) ˆr (j) i = r i (3) detection N k=1,k=j h ik ŝ k log P (ˆr(j) i s j = 1) P (ˆr (j) i s j = 0) = ij O(N 2 )

11 BP-based detection (2)!11 Message update at symbol node (1) a posteriori LLR calculation N si j = kj k=1 1j Nj ij ij j final decision r1 ri rn (2) message calculation ij = j ij extrinsic value

12 Block diagram of BP-based detection!12 LLR calculation a posteriori LLR calculation parallel interference cancellation uncoded channel decoder coded soft replica generation observation node LLR calculation symbol node coded

13 An example of reliability improvement 1! I(beta) Trajectory Symbol node 0.2 Observation SNR = 6 db I(alpha)

14 EXIT analysis 1! I(beta) SNR = 20 db SNR = 10 db SNR = 6 db SNR = 2 db Observation node Symbol node I(alpha)

15 Simulation parameters!15 BP with PIC MMSE Number of antennas 10 x 10, 30 x 30, 50 x 50, 100 x 100, 200 x 200 Modulation QPSK Channel statistics quasi-static Rayleigh fading Noise AWGN Frame length symbols Number of frames 10,000 Channel encoding Channel decoding Convolutional code (constraint length 3, coding rate 1/2) Max-Log MAP decoder

16 BER performance (100 x 100, coded case) 1!16 Average BER 1x10-1 1x10-2 BP w/ PIC 1 iteration 3 iterations 5 iterations 7 iterations 1x10-3 SISO AWGN MMSE 1x SNR [db]

17 BER performance (100 x 100, uncoded case) 1 BP w/ PIC 1 iteration 3 iterations!17 1x10-1 Average BER 1x10-2 1x10-3 BP w/ PIC 5 iterations 7 iterations MMSE SISO AWGN 1x SNR [db]

18 BER performance (10 x 10, uncoded case) 1 1x10-1 BP w/ PIC 1 iteration 3 iterations 5 iterations 7 iterations!18 Average BER 1x10-2 MMSE 1x10-3 SISO AWGN 1x SNR [db]

19 BER performance (10 x 10, coded case) 1!19 Average BER 1x10-1 1x10-2 1x10-3 SISO AWGN BP w/ PIC 1 iteration 3 iterations 5 iterations 7 iterations MMSE 1x SNR [db]

20 Conclusions!20 We have clarified the capability of pure BP-based detection for spatially multiplexed streams. BP-based detection is implementable in O(N 2 ) achieves better performance than spatial filtering with MMSE works only when size of array is large converges more quickly with channel encoding Future works effects of channel correlation higher level modulation

turbo 1993code Berrou 1) 2[dB] SNR 05[dB] 1) interleaver parallel concatenated convolutional code ch

1 -- 2 6 LDPC 2012 3 1993 1960 30 LDPC 2 LDPC LDPC LDPC 6-1 LDPC 6-2 6-3 c 2013 1/(13) 1 -- 2 -- 6 6--1 2012 3 turbo 1993code Berrou 1) 2[dB] SNR 05[dB] 1) 6 1 2 1 1 interleaver 2 2 2 parallel concatenated