1. DSP Group, EE, Caltech, Pasadena CA1 Precoded V-BLAST for ISI MIMO Channels Chun-yang Chen and P. P. Vaidyanathan California Institute of Technology

2. DSP Group, EE, Caltech, Pasadena CA2 Outline  Introduction  Review of the related work V-BLAST system [Wolniansky et al. 1998] Precoded V-BLAST system [Jiang et al. 2004, Xu et al. 2004] FIR MMSE DFE system for ISI MIMO channels [Al- Dhahir and Sayed 2000]  Extend the precoded V-BLAST system from flat-fading channels to ISI channels FIR based method OFDM based method  Numerical examples

3. DSP Group, EE, Caltech, Pasadena CA3 Introduction: channel models  Both transmitted symbols and received noise are assumed to be i.i.d. and zero-mean.  H is an NxM matrix and H(z) is an NxM LTI system.  We choose N>=M. H s v x MN H(z) sisi vivi xixi Flat-fading MIMO channel ISI MIMO channel

4. DSP Group, EE, Caltech, Pasadena CA4 Introduction: transceivers H v V-BLAST decoder s ^ [Wolniansky et al. 1998] Precoder s [Jiang et al. 2004, Xu et al. 2005] H(z) v DFE decoder s ^ [Al-Dhahir and Sayed 2000] Precoder s Our goal

5. DSP Group, EE, Caltech, Pasadena CA5 Review: V-BLAST system Some ISI has been canceled Decision Linear estimator of the M-th element Cancel the response of the M-th element  The V-BLAST system is a decision feed back equalizer (DFE) in spatial domain [Wolniansky et al. 1998]. H fMfM hMhM f M-1 h M-1 f1f1 … s v x (M) x (M-1) x (M-2) s(M) ^ s(M-1) ^ s(1) ^ --

6. DSP Group, EE, Caltech, Pasadena CA6 Review: V-BLAST system Noise to signal ratio [B. Hassibi, 1999] v H fMfM hMhM f M-1 h M-1 f1f1 … s x (M) x (M-1) x (M-2) s(M) ^ s(M-1) ^ s(1) ^ -- … P s P [Jiang et al. 2004, Xu et al. 2005]

7. DSP Group, EE, Caltech, Pasadena CA7 Geometric mean decomposition Unitary Identical QR GMD [Jiang et al. 2004] Geometric mean

8. DSP Group, EE, Caltech, Pasadena CA8 Review: Precoded V-BLAST system Geometric mean [Jiang et al. 2004, Xu et al. 2004] Compute the QR for the precoded channel.

9. DSP Group, EE, Caltech, Pasadena CA9 Review: FIR MMSE DFE [Al-Dhahir and Sayed 2000] previously decoded needs to be decoded Time domain feedback H T2 d: FIR order  : Decision delay H T1

10. DSP Group, EE, Caltech, Pasadena CA10 Review: FIR MMSE DFE Only the last M elements need to be decoded. Only this part needs to be upper triangular. H(z) V-BLAST receiver Time domain feedback sisi xixi vivi s i-Δ ^ precoder sisi

11. DSP Group, EE, Caltech, Pasadena CA11 Precoded V-BLAST for ISI channels First, perform this partial QR decomposition. Then, perform the geometric mean decomposition (GMD) on the upper triangular matrix. Use this P T as the precoder

12. DSP Group, EE, Caltech, Pasadena CA12 Precoded V-BLAST for ISI channels Replace the channel with the precoded channel.

13. DSP Group, EE, Caltech, Pasadena CA13 Precoded V-BLAST for ISI channels GMD Identical diagonal elements Compute the partial QR decomposition. Partial QR

14. DSP Group, EE, Caltech, Pasadena CA14 Precoded V-BLAST for ISI channels Geometric mean

15. DSP Group, EE, Caltech, Pasadena CA15 OFDM based method  By introducing OFDM, the ISI MIMO channel is converted to a block diagonal MIMO channel. H(z) P/S S/P CP Remove CP IDFT v i DFT HdHd v K: number of carriers N: number of receiving antennas M: number of transmitting antennas KMMNKN KM

16. DSP Group, EE, Caltech, Pasadena CA16 OFDM based method HdHd v P s (1) s (2) s ( KM ) … p p p V-BLAST receiver s (1) ^ s (2) ^ s ( KM ) ^ … p p p However, the size is quite large. All carriers and all antennas have identical MSE (Mean square error).

17. DSP Group, EE, Caltech, Pasadena CA17 OFDM based method The permutation matrix makes the matrix block diagonal. The block diagonal structure significantly reduces complexity when computing GMD (geometric mean decomposition).

18. DSP Group, EE, Caltech, Pasadena CA18 Numerical results FIR  d=2 OFDM K=16 Without precoder Optimal bitloading MSE-equalizing precoder  Parameters Channel matrix size : 2x2 Channel order = 3 1000 randomly generated channels

19. DSP Group, EE, Caltech, Pasadena CA19 Conclusion  The precoded V-BLAST system is generalized for ISI MIMO channels in two ways. FIR based method OFDM based method  The simulation shows MSE-equalizing precoder has better performance than bitloading.  The simulation shows the precoded OFDM V- BLAST system has the best performance among the tested systems.

20. DSP Group, EE, Caltech, Pasadena CA20 References [1] P.W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzela, “ V-Blast: An architectre for realizing very high data rates over the rich-scattering channel, ” Proc. Int. Symp. Signals, Systems and Electronics (ISSE 1998), pp.295-300. [2] B. Hassibi, “ An efficient square-root algorithm for BLAST, ” Proc. of the ICCASP, vol.2, pp. II737 - II740, June. 1999. [3] Y. Jiang, J. Li, and W. W. Hager “ Joint transceiver design for MIMO communications using geometric mean decomposition, ” IEEE Trans. Sig. Proc., pp.3791-3803, Oct. 2005. [4] F. Xu, T. N. Davidson, J. K. Zhang, S. S. Chan, and K. M. Wong, “ Design of block transceivers with MMSE decision feedback detection, ” Proc. of the ICASSP, pp. 1109 - 1112, March. 2004. [5] Y. Jiang, W. W. Hager, and J. Li, “ The Geometric Mean Decomposition and Generalized Triangular Decomposition, ” 2004 SIAM Annual Meeting, Portland, Oregon, July 12 - 16. [6] N. Al-Dhahir, A. H. Sayed, “ The finite-length multi-input multi-output MMSE- DFE, ” IEEE Trans. Sig. Proc., pp. 2921 - 2936, Oct. 2000.

21. DSP Group, EE, Caltech, Pasadena CA21 Thank you