Systolic Arrays for Lattice-Reduction-Aided MIMO Detection

  • Wang, Ni-Chun (Electrical Engineering Department, University of California-Los Angeles) ;
  • Biglieri, Ezio (Electrical Engineering Department, University of California-Los Angeles) ;
  • Yao, Kung (Electrical Engineering Department, University of California-Los Angeles)
  • Received : 2010.04.13
  • Accepted : 2010.11.11
  • Published : 2011.10.31

Abstract

Multiple-input multiple-output (MIMO) technology provides high data rate and enhanced quality of service for wireless communications. Since the benefits from MIMO result in a heavy computational load in detectors, the design of low-complexity suboptimum receivers is currently an active area of research. Lattice-reduction-aided detection (LRAD) has been shown to be an effective low-complexity method with near-maximum-likelihood performance. In this paper, we advocate the use of systolic array architectures for MIMO receivers, and in particular we exhibit one of them based on LRAD. The "Lenstra-Lenstra-Lov$\acute{a}$sz (LLL) lattice reduction algorithm" and the ensuing linear detections or successive spatial-interference cancellations can be located in the same array, which is considerably hardware-efficient. Since the conventional form of the LLL algorithm is not immediately suitable for parallel processing, two modified LLL algorithms are considered here for the systolic array. LLL algorithm with full-size reduction-LLL is one of the versions more suitable for parallel processing. Another variant is the all-swap lattice-reduction (ASLR) algorithm for complex-valued lattices, which processes all lattice basis vectors simultaneously within one iteration. Our novel systolic array can operate both algorithms with different external logic controls. In order to simplify the systolic array design, we replace the Lov$\acute{a}$sz condition in the definition of LLL-reduced lattice with the looser Siegel condition. Simulation results show that for LR-aided linear detections, the bit-error-rate performance is still maintained with this relaxation. Comparisons between the two algorithms in terms of bit-error-rate performance, and average field-programmable gate array processing time in the systolic array are made, which shows that ASLR is a better choice for a systolic architecture, especially for systems with a large number of antennas.

Keywords

References

  1. G. J. Foschini and M. J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Pers. Commun., vol. 6, pp. 311-335, 1998. https://doi.org/10.1023/A:1008889222784
  2. E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, and H. V. Poor, MIMO Wireless Commun. New York, NY, USA: Cambridge University Press, 2007.
  3. Z. Guo and P. Nilsson, "A VLSI implementation of MIMO detection for future wireless communications," in Proc. IEEE PIMRC, vol. 3, 2003, pp. 2852-2856.
  4. M. Myllyla, J. Hintikka, J. Cavallaro, M. Juntti, M. Limingoja, and A. Byman, "Complexity analysis of MMSE detector architectures for MIMO OFDM systems," in Proc. the Asilomar Conf. Signals, Syst. Comput., 2005, pp. 75-81.
  5. M. Karkooti, J. Cavallaro, and C. Dick, "FPGA implementation of matrix inversion using QRD-RLS algorithm," in Proc. Asilomar Conf. Signals, Syst. Comput., 2005, pp. 1625-1629.
  6. H. Yao and G. Wornell, "Lattice-reduction-aided detectors for MIMO communication systems," in Proc. IEEE GLOBECOM, vol. 1, 2002, pp. 424-428.
  7. D. Seethaler, G. Matz, and F. Hlawatsch, "Low-complexity MIMO data detection using seysen's lattice reduction algorithm;' in Proc. IEEE ICASSP, vol. 3, 2007, pp. III-53-III-56.
  8. D. Wubben, R. Bohnke, V. Kuhn, and K.-D. Kammeyer, "Near-maximum-likelihood detection of MIMO systems using MMSE-based lattice reduction," in Proc. IEEE ICC, vol. 2, 2004, pp. 798-802.
  9. A. K. Lenstra, H. W. Lenstra, and L. Lovasz, "Factoring polynomials with rational coefficients," Mathematische Annalen, vol. 261, no. 4, pp. 515-534, 1982. https://doi.org/10.1007/BF01457454
  10. Y. H. Gan, C. Ling, and W. H. Mow, "Complex lattice reduction algorithm for low-complexity full-diversity MIMO detection," IEEE Trans. Signal Process., vol. 57, no. 7, pp. 2701-2710, 2009. https://doi.org/10.1109/TSP.2009.2016267
  11. X. Ma and W. Zhang, "Performance analysis for MIMO systems with lattice-reduction aided linear equalization," IEEE Trans. Commun., vol. 56, no. 2, pp. 309-318, 2008. https://doi.org/10.1109/TCOMM.2008.060372
  12. M. Taherzadeh, A. Mobasher, and A. Khandani, "LLL reduction achieves the receive diversity in MIMO decoding," IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4801-4805. 2007. https://doi.org/10.1109/TIT.2007.909169
  13. J. Jalden, D. Seethaler, and G. Matz, "Worst-and average-case complexity of LLL lattice reduction in MIMO wireless systems," in Proc. IEEE ICASSP, 2008, pp.2685-2688.
  14. B. Gestner, W. Zhang, X. Ma, and D. Anderson, "VLSI implementation of a lattice reduction algorithm for low-complexity equalization," in Proc. IEEE ICCSC, 2008, pp. 643-647.
  15. C. P. Schnorr and M. Euchner, "Lattice basis reduction: Improved practical algorithms and solving subset snm problems," Mathematical Programming, vol. 66, no. 1-3, pp. 181-199, 1994. https://doi.org/10.1007/BF01581144
  16. J. Jalden and P. Elia, "DMT optimality of LR-aided linear decoders for a general class of channels, lattice designs, and system models," IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 4765-4780, 2010. https://doi.org/10.1109/TIT.2010.2059493
  17. H. Vetter, V. Ponnampalam, M. Sandell, and P. Hoeher, "Fixed complexity LLL algorithm," IEEE Trans. Signal Process., vol. 57, no. 4, pp. 1634-1637, 2009. https://doi.org/10.1109/TSP.2008.2011827
  18. H. T. Kung and C. E. Leiserson, Algorithms for VLSI Processor Arrays. Introduction to VLSI Systems, Addison-Wesley, 1980, p. 271.
  19. S. Y. Kung, "VLSI array processors," IEEE ASSP Mag., vol. 2, no. 3, pp. 4-22, 1985. https://doi.org/10.1109/MASSP.1985.1163741
  20. W. M. Gentleman and H. T. Kung, "Matrix triangulation by systolic arrays," in Proc. SPIE: Real-time Signal Processing IV, vol. 298, 1981, pp. 19-26.
  21. A. El-Amawy and K. Dharmarajan, "Parallel VLSI algorithm for stable inversion of dense matrices," lEE Proc. Computers and Digital Techniques, vol. 136, no. 6, pp. 575-580, 1989. https://doi.org/10.1049/ip-e.1989.0079
  22. C. Rader, "VLSI systolic arrays for adaptive nulling," IEEE Signal Process. Mag., vol. 13, no. 4, pp. 29-49, 1996. https://doi.org/10.1109/79.526897
  23. K. Liu, S.-F. Hsieh, K. Yao, and C.-T. Chiu, "Dynamic range, stability, and fault-tolerant capability of finite-precision RLS systolic array based on givens rotations," IEEE Trans. Circuits Syst., vol. 38, no. 6, pp. 625-636, 1991. https://doi.org/10.1109/31.81857
  24. D. Boppana, K. Dhanoa, and J. Kempa, "FPGA based embedded processing architecture for the QRD-RLS algorithm," in Proc. IEEE Symposium on Field-Programmable Custom Computing Machines, vol. 0, 2004, pp. 330-331.
  25. K. Yao and F. Lorenzelli, "Systolic algorithms and architectures for high-throughput processing applications," J. Signal Process. Syst., vol. 53, no. 1-2, pp. 15-34, 2008. https://doi.org/10.1007/s11265-007-0108-z
  26. J. Wang and B. Daneshrad, "A universal systolic array for linear MIMO detections," in Proc. IEEE WCNC, 2008, pp. 147-152.
  27. K. Seki, T. Kobori, J. Okello, and M. Ikekawa, "A CORDIC-based reconfigrable systolic array processor for MIMO-OFDM wireless communications," in Proc. IEEE Workshop on Signal Process. Syst., 2007, pp. 639-644.
  28. Y. Hu, "CORDIC-based VLSI architectures for digital signal processing," IEEE Signal Process. Mag., vol. 9, no. 3, pp. 16-35, 1992.
  29. B. Cerato, G. Masera, and P. Nilsson, "Hardware architecture for matix factorization in mimo receivers," in Proc. ACM Great Lakes symposium on VLSI, New York, NY, USA, 2007, pp. 196-199.
  30. C. Heckler and L. Thiele, "A parallel lattice basis reduction for mesh-connected processor arrays and parallel complexity," in Proc. IEEE Symp. Parallel and Distributed Processing, 1993, pp. 400-407.
  31. J. W. S. Cassels, Rational quadratic forms. New York: USA, Academic Press, 1978.
  32. B. Hassibi, "An efficient square-root algorithm for BLAST," in Proc. IEEE ICASSP, vol. 2, 2000, pp. II-737-II-740.
  33. E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, "Closest point search in lattices," IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2201-2214, 2002. https://doi.org/10.1109/TIT.2002.800499
  34. L. Babai, "On lovasz' lattice reduction and the nearest lattice point problem," Combinatorica, vol. 6, no. 1, pp. 1-13, 1986. https://doi.org/10.1007/BF02579403
  35. R. Dohler, "Squared givens rotation," IMA J. Numerical Analysis, vol. 11, no. 1, pp. 1-5, Jan. 1991. https://doi.org/10.1093/imanum/11.1.1
  36. P. Luethi, A. Burg, S. Haene, D. Perels, N. Felber, and W. Fichtner, "VLSI implementation of a high-speed iterative sorted MMSE QR decomposition," in Proc. IEEE Int. Symp. Circuits and Syst., 2007, pp. 1421-1424.
  37. C. V. Ramamoorthy, J, R. Goodman, and K. H. Kim, "Some properties of iterative square-rooting methods using high-speed multiplication," IEEE Trans. Comput., vol. C-21, no. 8, pp. 837-847, 1972. https://doi.org/10.1109/TC.1972.5009039
  38. F. Lorenzelli, P. Hansen, T. Chan, and K. Yao, "A systolic implementation of the Chan/Foster RRQR algorithm," IEEE Trans. Signal Process., vol. 42, no. 8, pp. 2205-2208, 1994. https://doi.org/10.1109/78.301862