The nonlinear vector precoding (VP) technique has been proven to achieve close-to-capacity performance in multiuser multiple-input multiple-output (MIMO) downlink channels. The performance benefit with respect to its linear counterparts stems from the incorporation of a perturbation signal that reduces the power of the precoded signal. The computation of this perturbation element, which is known to belong in the class of NP-hard problems, is the main aspect that hinders the hardware implementation of VP systems. To this respect, several tree-search algorithms have been proposed for the closest-point lattice search problem in VP systems hitherto. Nevertheless, the optimality of these algorithms has been assessed mainly in terms of error-rate performance and computational complexity, leaving the hardware cost of their implementation an open issue. The parallel data-processing capabilities of field-programmable gate arrays (FPGA) and the loopless nature of the proposed tree-search algorithms have enabled an efficient hardware implementation of a VP system that provides a very high data-processing throughput. 1. Introduction Since the presentation of the vector precoding (VP) technique [1] for data transmission over the multiuser broadcast channel, many algorithms have been proposed in the literature to replace the computationally intractable exhaustive search defined in the original description of the algorithm. To this respect, lattice reduction approaches have been widely used as a means to compute a suboptimum perturbation vector with a moderate complexity. The key idea of lattice-reduction techniques relies on the usage of an equivalent and more advantageous set of basis vectors to allow for the suboptimal resolution of the exhaustive search problem by means of a simple rounding operation. This method is used in [2], where the Lenstra-Lenstra-Lovász (LLL) reduction algorithm [3] is used to yield the Babai's approximate closest-point solution [4]. Similar approaches can be found in [5–7]. Despite achieving full diversity order in VP systems [8, 9], the performance degradation caused by the quantization error due to the rounding operation still remains. Moreover, many lattice reduction algorithms have a considerable computational complexity, which poses many challenges to a prospective hardware implementation. An appropriate perturbation vector can also be found by searching for the optimum solution within a subset of candidate vectors. These approaches, also known as tree-search techniques, perform a traversal through a tree of hypotheses with the aim
References
[1]
B. M. Hochwald, C. B. Peel, and A. L. Swindlehurst, “A vector-perturbation technique for near-capacity multiantenna multiuser communication, part II: perturbation,” IEEE Transactions on Communications, vol. 53, no. 3, pp. 537–544, 2005.
[2]
C. Windpassinger, R. F. H. Fischer, and J. B. Huber, “Lattice-reduction-aided broadcast precoding,” IEEE Transactions on Communications, vol. 52, no. 12, pp. 2057–2060, 2004.
[3]
A. K. Lenstra, H. W. Lenstra, and L. Lovász, “Factoring polynomials with rational coefficients,” Mathematische Annalen, vol. 261, no. 4, pp. 515–534, 1982.
[4]
L. Babai, “On lovász' lattice reduction and the nearest lattice point problem,” Combinatorica, vol. 6, no. 1, pp. 1–13, 1986.
[5]
D. Seethaler and G. Matz, “Efficient vector perturbation in multi-antenna multi-user systems based on approximate integer relations,” in Proceedings of the EURASIP European Signal Processing Conference (EUSIPCO '06), pp. 1–5, September 2006.
[6]
S. Hur, N. Kim, H. Park, and J. Kang, “Enhanced lattice-reduction-based precoder with list quantizer in broadcast channel,” in Proceedings of the IEEE 66th Vehicular Technology Conference (VTC '07), pp. 611–615, October 2007.
[7]
F. Liu, L. Jiang, and C. He, “Low complexity MMSE vector precoding using lattice reduction for MIMO systems,” in Proceedings of the IEEE International Conference on Communications (ICC '07), pp. 2598–2603, June 2007.
[8]
M. Taherzadeh, A. Mobasher, and A. K. Khandani, “LLL lattice-basis reduction achieves the maximum diversity in MIMO systems,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT '05), pp. 1300–1304, September 2005, maximum diversity; MIMO fading channels; MIMO broadcast systems; lattice-reductionaided decoding; point-to-point system;multiple-access system.
[9]
M. Taherzadeh, A. Mobasher, and A. K. Khandani, “Communication over MIMO broadcast channels using lattice-basis reduction,” IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4567–4582, 2007.
[10]
K. H. Lin, H. L. Lin, R. C. Chang, and C. F. Wu, “Hardware architecture of improved Tomlinson-Harashima Precoding for downlink MC-CDMA,” in Proceedings of the IEEE Asia Pacific Conference on Circuits and Systems (APCCAS '06), pp. 1200–1203, December 2006.
[11]
A. Burg, D. Seethaler, and G. Matz, “VLSI implementation of a lattice-reduction algorithm for multi-antenna broadcast precoding,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS 07), pp. 673–676, May 2007.
[12]
P. Bhagawat, W. Wang, M. Uppal et al., “An FPGA implementation of dirty paper precoder,” in Proceedings of the IEEE International Conference on Communications (ICC '07), pp. 2761–2766, June 2008.
[13]
L. G. Barbero and J. S. Thompson, “Rapid prototyping of a fixed-throughput sphere decoder for MIMO systems,” in Proceedings of the IEEE International Conference on Communications (ICC '06), vol. 7, pp. 3082–3087, June 2006.
[14]
L. G. Barbero and J. S. Thompson, “FPGA design considerations in the implementation of a fixed-throughput sphere decoder for MIMO systems,” in Proceedings of the International Conference on Field Programmable Logic and Applications (FPL '00), pp. 1–6, August 2006.
[15]
L. G. Barbero and J. S. Thompson, “Extending a fixed-complexity sphere decoder to obtain likelihood information for turbo-MIMO systems,” IEEE Transactions on Vehicular Technology, vol. 57, no. 5, pp. 2804–2814, 2008.
[16]
K. W. Wong, C. Y. Tsui, R. S. K. Cheng, and W. H. Mow, “A VLSI architecture of a k-best lattice decoding algorithm for MIMO channels,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '02), vol. 3, pp. 273–276, May 2002.
[17]
M. Wenk, M. Zellweger, A. Burg, N. Felber, and W. Fichtner, “K-best MIMO detection VLSI architectures achieving up to 424？Mbps,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '06), pp. 1151–1154, September 2006.
[18]
Q. Li and Z. Wang, “Improved k-best sphere decoding algorithms for MIMO systems,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '06), pp. 1159–1162, May 2006.
[19]
Z. Guo and P. Nilsson, “Algorithm and implementation of the k-best sphere decoding for MIMO detection,” IEEE Journal on Selected Areas in Communications, vol. 24, no. 3, pp. 491–503, 2006.
[20]
M. Shabany and P. G. Gulak, “Scalable VLSI architecture for k-best lattice decoders,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '08), pp. 940–943, May 2008.
[21]
C. A. Shen and A. M. Eltawil, “A radius adaptive k-best decoder with early termination: algorithm and VLSI architecture,” IEEE Transactions on Circuits and Systems I, vol. 57, no. 9, pp. 2476–2486, 2010.
[22]
S. Chen, T. Zhang, and Y. Xin, “Relaxed k-best MIMO signal detector design and VLSI implementation,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 15, no. 3, pp. 328–337, 2007.
[23]
M. Mahdavi, M. Shabany, and B. V. Vahdat, “A modified complex k-best scheme for high-speed hard-output MIMO detectors,” in Proceedings of the 53rd IEEE International Midwest Symposium on Circuits and Systems (MWSCAS '10), pp. 845–848, August 2010.
[24]
C. A. Shen, A. M. Eltawil, and K. N. Salama, “Evaluation framework for k-best sphere decoders,” Journal of Circuits, Systems and Computers, vol. 19, no. 5, pp. 975–995, 2010.
[25]
D. A. Schmidt, M. Joham, and W. Utschick, “Minimum mean square error vector precoding,” in Proceedings of the IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '05), vol. 1, pp. 107–111, September 2005.
[26]
E. Viterbo and J. Boutros, “A universal lattice code decoder for fading channels,” IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1639–1642, 1999.
[27]
M. O. Damen, H. El Gamal, and G. Caire, “On maximum-likelihood detection and the search for the closest lattice point,” IEEE Transactions on Information Theory, vol. 49, no. 10, pp. 2389–2402, 2003.
[28]
C. P. Schnorr and M. Euchner, “Lattice basis reduction: improved practical algorithms and solving subset sum problems,” in Proceedings of the International Symposium on Fundamentals of Computation Theory (FCT '91), vol. 529, pp. 68–85, September 1991.
[29]
J. Zhang and K. J. Kim, “Near-capacity MIMO multiuser precoding with QRD-M algorithm,” in Proceedings of the 39th Asilomar Conference on Signals, Systems and Computers (ACSSC '05), vol. 1, pp. 1498–1502, November 2005.
[30]
R. Habendorf and G. Fettweis, “Vector precoding with bounded complexity,” in Proceedings of the 8th IEEE Signal Processing Advances in Wireless Communications (SPAWC '07), pp. 1–5, June 2007.
[31]
M. Barrenechea, M. Mendicute, J. Del Ser, and J. S. Thompson, “Wiener filter-based fixed-complexity vector precoding for the MIMO downlink channel,” in Proceedings of the IEEE 10th Workshop on Signal Processing Advances in Wireless Communications (SPAWC '09), pp. 216–220, ita, June 2009.
[32]
M. Barrenechea, M. Mendicute, I. Jimenez, and E. Arruti, “Implementation of complex enumeration for multiuser mimo vector precoding,” in Proceedings of the EURASIP European Signal Processing Conference (EUSIPCO '11), pp. 739–743, August 2011.
[33]
P. Y. Tsai, W. T. Chen, X. C. Lin, and M. Y. Huang, “A 4 × 4 64-QAM reduced-complexity k-best MIMO detector up to 1.5？Gbps,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '10), pp. 3953–3956, May 2010.
[34]
S. Mondal, W. H. Ali, and K. N. Salama, “A novel approach for k-best MIMO detection and its VLSI implementation,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '08), pp. 936–939, May 2008.
[35]
S. Mondal, A. M. Eltawil, and K. N. Salama, “Architectural optimizations for low-power k-best MIMO decoders,” IEEE Transactions on Vehicular Technology, vol. 58, no. 7, pp. 3145–3153, 2009.
[36]
S. Mondal, A. Eltawil, C. A. Shen, and K. N. Salama, “Design and implementation of a sort-free K-best sphere decoder,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 18, no. 10, pp. 1497–1501, 2010.
[37]
M. Barrenechea, Design and implementation of multi-user mimo precoding algorithms [Ph.D. dissertation], University of Mondragon, Mondragon, Spain, 2012.
[38]
A. Burg, M. Wenk, M. Zellweger, M. Wegmueller, N. Felber, and W. Fichtner, “VLSI implementation of the sphere decoding algorithm,” in Proceedings of the 30th European Solid-State Circuits Conference (ESSCIRC '04), pp. 303–306, September 2004.
