Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios

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In this paper, we explore the fundamental performance tradeoff of the delay-limited Multi-Input-Multi-Output (MIMO) Automatic Retransmission reQuest (ARQ) channel. In particular, we extend the diversity-multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e. diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow fading MIMO channels. In particular, we show that: 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-multiplexing tradeoff, and hence, renders operating at high multiplexing gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed. Finally, we complement our information theoretic analysis with an Incremental Redundancy LAttice Space-Time (IR-LAST) coding scheme which is shown, through a random coding argument, to achieve the optimal tradeoff(s). An integral component of the optimal IR-LAST coding scheme is a list decoder, based on the MMSE lattice decoding principle, for joint error detection and correction. Throughout the paper, our theoretical claims are validated by numerical results.

A universal framework is developed for constructing full-rate and full-diversity coherent space-time codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines space-time layering concepts with algebraic component codes optimized for single-input-single-output (SISO) channels. Each component code is assigned to a "thread" in the space-time matrix, allowing it thus full access to the channel spatial diversity in the absence of the other threads. Diophantine approximation theory is then used in order to make the different threads "transparent" to each other. Within this framework, a special class of signals which uses algebraic number-theoretic constellations as component codes is thoroughly investigated. The lattice structure of the proposed number-theoretic codes along with their minimal delay allow for polynomial complexity maximum-likelihood (ML) decoding using algorithms from lattice theory. Combining the design framework with the Cayley transform allows to construct full diversity differential and noncoherent space-time codes. The proposed framework subsumes many of the existing codes in the literature, extends naturally to time-selective and frequency-selective channels, and allows for more flexibility in the tradeoff between power efficiency, bandwidth efficiency, and receiver complexity. Simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios.

We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm decomposes into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. We argue that the minimum mean square error decision feedback (MMSE-DFE) frontend is instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for using lattice reduction methods to reduce complexity, at the expense of a marginal performance loss, and solving under-determined linear systems. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSE-Fano decoder is established via simulation results and analytical arguments in several MIMO and ISI scenarios.

We construct a full data rate space-time (ST) block code over = 2 transmit antennas and = 2 symbol periods, and we prove that it achieves a transmit diversity of 2 over all constellations carved from [ ]. Further, we optimize the coding gain of the proposed code and then compare it to the Alamouti code. It is shown that the new code outperforms the Alamouti code at low and high signal-to-noise ratio (SNR) when the number of receive antennas 1. The performance improvement is further enhanced when or the size of the constellation increases. We relate the problem of ST diversity gain to algebraic number theory, and the coding gain optimization to the theory of simultaneous Diophantine approximation in the geometry of numbers. We find that the coding gain optimization is equivalent to finding irrational numbers "the furthest" from any simultaneous rational approximations.

Theoretical and practical aspects of diagonal algebraic space-time block codes over n transmit and m receive antennae are examined. These codes are obtained by sending a rotated version of the information symbols over the principal diagonal of the n × n space-time matrix over n transmit antennae and n symbol periods. The output signal-to-noise ratios of two pre-decoding filters and two decoding algorithms are derived. Analysis of the information loss incurred by using the codes considered is used to clarify their structures, and the expected performances. Different algebraic real and complex rotations presented in the literature are analyzed and compared as regards the achieved coding gains, the complexities, performances, and peak-to-mean envelope power ratios. I. Introduction H igh-rate data transmission achieved using multiple antennae with diversity techniques has been the subject of many works in the last five years [1]-[6]. Although diversity techniques are a mature topic (see [7] and references therein), fewer results pertaining to diversity techniques applied to sufficiently spaced transmit antennae have been reported. Space-time (ST) codes were proposed by Tarokh et al. in [3] in order to exploit the transmit diversity in a multi-antenna system while transmitting at high data rates. Block ST codes based on orthogonal design (OD) were proposed in [8]. They achieve maximum transmit diversity and have the great advantage of optimal linear processing decoding. These codes were proved to maximize the output signal-to-noise ratio (SNR) when the receiver uses linear decorrelators [9]; however, they have small data rates compared to the capacity of the multi-antenna system [1]. In [10], DaSilva and Sousa proposed a diagonal scheme over n = 2,. .. , 5 transmit antennae that transmits the components of rotated n-dimensional BPSK modulations over the different transmit antennae. The rotations used in [10] were optimized either by exhaustive search

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