Abstract — Tree search based detection techniques allow to achieve near-capacity performance in iterative receivers for multiple antenna (MIMO) systems. In order to solve the detection problem not only effectively but efficiently, the use of MMSE preprocessing is fundamental. However, straightforward implementations lead to a bias on the calculated metrics, resulting in performance deterioration. In this paper, we study how unbiased MMSE tree search detection can be used to achieve excellent performance-complexity trade-offs. We compare the performance and complexity of list sphere, list sequential and M-algorithm based detection. The latter two provide very good performance at low (maximum) complexity, making them attractive for the use in next generation wireless systems. I.

Lattice reduction is a powerful concept for solving diverse problems involving point lattices. Signal processing applications where lattice reduction has been successfully used include global positioning system (GPS), frequency estimation, color space estimation in JPEG pictures, and particularly data detection and precoding in wireless communication systems. In this article, we first provide some background on point lattices and then give a tutorial-style introduction to the theoretical and practical aspects of lattice reduction. We describe the most important lattice reduction algorithms and comment on their performance and computational complexity. Finally, we discuss the application of lattice reduction in wireless communications and statistical signal processing. Throughout the article, we point out open problems and interesting questions for future research.

Lattice reduction-aided decoding enables significant complexity saving and near-optimum performance in multi-input multi-output (MIMO) communications. However, its remarkable performance largely remains a mystery to date. In this paper, a first step is taken towards a quantitative understanding of its performance limit. To this aim, the proximity factors are defined to measure the worst-case gap to maximum-likelihood (ML) decoding in terms of the signal-to-noise ratio (SNR) for given error rate. The proximity factors are derived analytically and found to be bounded above by a function of the dimension of the lattice alone. As a direct consequence, it follows that lattice reduction-aided decoding can always achieve full receive diversity of MIMO fading channels. The study is then extended to the dualbasis reduction. It is found that in some cases reducing the dual can result in smaller proximity factors than reducing the primal basis. The theoretic bounds on the proximity factors are further compared with numerical results.

Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-SNR regime in terms of the Diversity-Multiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and non-asymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information

Abstract — List sequential (LISS) detection is an effective means of achieving near-capacity performance in iterative detection-decoding for MIMO systems. Using a length bias term calculated via an auxiliary stack has been shown to substantially narrow the tree search and thus reduce detection complexity. We present a novel approach to determine an approximation of the bias term, based on information available during the tree search in the main stack of the LISS detector. We also extend the LISS MIMO detector from ZF to MMSE based detection and show that by following this approach, a far better performance-complexity trade-off can be achieved. I.

We consider multiple–symbol differential detection (MSDD) for multiple–input multiple–output Rayleigh–fading channels. MSDD, which jointly processes blocks of N received symbols to detect N −1 data symbols, allows for power–efficient transmission without requiring channel state information at the receiver. In previous work, we showed that computational efficient sphere decoding algorithms can be used to accomplish MSDD. In this paper, we analyze the computational complexity of this sphere–decoding based MSDD. In particular, we prove by means of a lower bound that the complexity of the Fincke–Pohst multiple–symbol differential sphere decoder (FP–MSDSD), while being very low over wide ranges of N and signal–to–noise ratios, is exponential in N in principle. We further derive both exact and simple approximate expressions for the complexity of FP–MSDSD, which allow for quick assessment of ranges of useful window sizes N of FP–MSDSD and show that the exponential rate of growth of the complexity of FP–MSDSD is asymptotically equal to that of brute–force MSDD. I.

In this work, we consider maximum likelihood (ML) sequence detection in MIMO linear channels corrupted by additive white Gaussian noise. While sphere decoding (SpD) algorithms have been developed to reduce the average complexity of ML detection, the average complexity of classical SpD can itself be impractical in low-SNR settings or when the channel is ill-conditioned. In response, sequential decoding algorithms that employ a preprocessing stage based on minimum mean-squared error generalized decision-feedback equalization (MMSE-GDFE) have been proposed. They are capable of near-ML detection at a complexity that remains low over a wide SNR range and/or with ill-conditioned channels. While it has always been assumed that MMSE-GDFE pre-processing compromises the ML-optimality of the downstream minimum-distance detector, we establish, in this work, that MMSE-GDFE pre-processing preserves ML-optimality under uncoded BPSK/QPSK signaling, regardless of channel dimension and rank. The implication is that, when BPSK/QPSK signaling is used, MMSE-GDFE pre-processing can be used in conjunction with efficient SpD algorithms for true ML detection. This is particularly attractive in moderate-to-low SNR ranges or with ill-conditioned or under-determined linear channels. 1

***Seoul National University In this paper, we propose a near maximum likelihood (ML) decoding technique, which reduces the computational complexity of the exact ML decoding algorithm. The computations needed for the tree search in the ML decoding is simplified by reducing the dimension ofthe search space prior to the tree search. In order to compensate performance loss due to the dimension reduction, a list stack algorithm (LSA) is considered, which produces a list ofthe top K closest points. The combination of both approaches, called reduced dimension list stack algorithm (RD-LSA), is shown to provide flexibility and offers a performance-complexity trade-off. Simulations performed for V-BLAST transmission demonstrate that significant complexity reduction can be achieved compared to the sphere decoding algorithm (SDA) while keeping the performance loss below an acceptable level. Index Terms- Maximum likelihood, Dimension reduction, MIMO, Tree search, Sphere decoding

Multicarrier modulation (MCM) over a doubly dispersive (DD) channel yields complicated inter-carrier interference (ICI) and intersymbol interference (ISI) responses. With appropriately designed MCM pulse shapes, however, ISI can be mostly suppressed, as can ICI outside a small subcarrier radius. In this case, the channel can be well described by a quasi-banded subcarrier coupling matrix. Several sequence detectors (SDs) have been proposed to leverage this quasi-banded structure, including linear, decision feedback (DF), and maximum likelihood (ML) schemes. Relative to linear and DF schemes, the ML schemes offer superior performance, but are significantly more complex, even when efficient Viterbi or sphere-detection algorithms are used. In this paper, we propose a new SD algorithm for the quasi-banded application with a frame error rate (FER) that is nearly indistinguishable from ML and an average complexity that is on par with DF SD. 1 1.

Abstract—It is well known that maximum-likelihood (ML) decoding in many digital communication schemes reduces to solving an integer least-squares problem, which is NP hard in the worstcase. On the other hand, it has recently been shown that, over a wide range of dimensions and signal-to-noise ratios (SNRs), the sphere decoding algorithm can be used to find the exact ML solution with an expected complexity that is often less than 3.However, the computational complexity of sphere decoding becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In this paper, we target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoding algorithm. The search tree is pruned by computing lower bounds on the optimal value of the objective function as the algorithm proceeds to descend down the search tree. We observe a tradeoff between the computational complexity required to compute a lower bound and the size of the pruned tree: the more effort we spend in computing a tight lower bound, the more branches that can be eliminated in the tree. Using ideas from semidefinite program (SDP)-duality theory and estimation theory, we propose general frameworks for computing lower bounds on integer least-squares problems. We propose two families of algorithms, one that is appropriate for large problem dimensions and binary modulation, and the other that is appropriate for moderate-size dimensions yet high-order constellations. We then show how in each case these bounds can be efficiently incorporated in the sphere decoding algorithm, often resulting in significant improvement of the expected complexity of solving the ML decoding problem, while maintaining the exact ML-performance. Index Terms—Branch-and-bound algorithm, estimation, convex optimization, expected complexity, integer least-squares,