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.

We present some general techniques for constructing full-rank, minimal-delay, rate at least one space-time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field embedded in matrix rings. The first half of the paper deals with constructions using field extensions of . Working with cyclotomic field extensions, we construct several families of STBCs over a wide range of signal sets that are of full rank, minimal delay, and rate at least one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field extensions. In the later half of the paper, we discuss two ways of embedding noncommutative division algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4 4 real orthogonal design is obtained by the left regular representation of quaternions. Alamouti's code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the th root of a transcendental element and study the capacity of the STBCs obtained from this construction. Another family of cyclic division algebras discovered by Brauer is discussed and several examples of STBCs derived from each of these constructions are presented.

Abstract—In this paper, the fundamental performance tradeoff of the delay-limited multiple-input multiple-output (MIMO) automatic retransmission request (ARQ) channel is explored. 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

Abstract—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 is decomposed 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 forward and feedback (matrix) filters of the minimum mean-square error decision feedback equalizer (MMSE-DFE) are instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity, at the expense of a marginal performance loss. 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-DFE Fano decoder is established via simulation results and analytical arguments in several multiple-input multiple-output (MIMO) and intersymbol interference (ISI) scenarios. Index Terms—Closest lattice point search (CLPS), Fano decoder, lattice codes, sequential decoding, sphere decoding, tree search. I.

Abstract—A space–time code is proposed that exhibits the highest coding gain among competing full-rate full transmit diversity space–time codes for the two transmit and receive antenna coherent quasi-static fading channel. The proposed code is derived from a layered architecture with real rotation of quadrature amplitude modulation (QAM) information symbols in two dimensions. The existing codes of similar architecture concentrate on application of complex full modulation diversity rotations or asymmetric real rotations. An analytic evaluation illustrates the significant improvement in coding gain achieved with the proposed code. Moreover, the coding gain of the proposed code is independent of its rate. This implies that the proposed code achieves the optimal diversity–multiplexing tradeoff curve for the two transmit antenna system. A stacked extension of the proposed code offers a reduced complexity capacity optimal alternative to the full diversity codes for larger number of transmit antennas. Performance enhancement in several scenarios is verified through simulations. Index Terms—Capacity optimal codes, coding gain, diversity–multiplexing tradeoff, fading channel, real rotation, space–time coding, transmit diversity. I.

Space--time (ST) constellations that are linear over the field of complex numbers are considered. Relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established. The fundamental tradeoff between rate and diversity is investigated under different constraints on the peak power, receiver complexity, and rate scaling with the signal-to-noise ratio (SNR). A new family of constellations that achieve optimal or near-optimal performance with respect to the different criteria is presented. The proposed constellations belong to the threaded algebraic ST (TAST) signaling framework, and achieve the optimal minimum squared Euclidean distance and the optimal delay. For systems with one receive antenna, these constellations also achieve the optimal peak-to-average power ratio for quadrature amplitude modulation (QAM) and phase-shift keying (PSK) input constellations, as well as optimal coding gains in certain scenarios. The framework is general for any number of transmit and receive antennas and allows for realizing the optimal tradeoff between rate and diversity under different constraints. Simulation results demonstrate the performance gaines offered by the proposed designs in average power and peak power limited systems.

Abstract—Training codes are introduced for the multiple-antenna, noncoherent, multiple block-Rayleigh-fading channel in which the fading coefficients, which are constant over a fixed number of dimensions (coherence interval) for each block and then change independently to a new realization, are known neither at the transmitter nor at the receiver. Each codeword of a training code consists of a part known to the receiver—used to form a minimum mean-squared error (MMSE) estimate of the channel—and a part that contains codeword(s) of a space–time block or trellis code designed for the coherent channel (in which the receiver has perfect knowledge of the channel). The channel estimate is used as if it were error-free for decoding the information-bearing part of the training codeword. Training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have

Abstract—It is known that the Alamouti code is the only complex orthogonal design (COD) which achieves capacity and that too for the case of two transmit and one receive antenna only. Damen et al. proposed a design for two transmit antennas, which achieves capacity for any number of receive antennas, calling the resulting space–time block code (STBC) when used with a signal set an information-lossless STBC. In this paper, using crossed-product central simple algebras, we construct STBCs for arbitrary number of transmit antennas over an a priori specified signal set. Alamouti code and quasi-orthogonal designs are the simplest special cases of our constructions. We obtain a condition under which these STBCs from crossed-product algebras are information-lossless. We give some classes of crossed-product algebras, from which the STBCs obtained are information-lossless and also of full rank. We present some simulation results for two, three, and four transmit antennas to show that our STBCs perform better than some of the best known STBCs and also that these STBCs are approximately 1 dB away from the capacity of the channel with quadrature amplitude modulation (QAM) symbols as input. Index Terms—Division algebras, information-lossless codes, multiple-input multiple-output (MIMO), space–time block codes.

Abstract—We construct unitary noncoherent space–time constellations, which can be considered as a concatenation of a training blockwith an orthogonal design. With a simple construction, our constellations are easy to design, enjoy full antenna diversity, allow for a simplified maximum-likelihood (ML) detector, and achieve error performance comparable to existing designs that rely on computer search. To exploit the constellation structures and improve coding gains, we further pursue a trellis-coded modulation (TCM) approach. Based on the sequence pairwise error analysis, we identify two simple parameters to quantify the asymptotic error performance, which enables us to compare among different TCM schemes or uncoded alternatives. Index Terms—Fading channel, noncoherent, performance analysis, space–time (ST), trellis-coded modulation (TCM). I.

Multiple-input multiple-output (MIMO) wireless systems obtain large diversity and capacity gains by employing multielement antenna arrays at both the transmitter and receiver. The theoretical performance benefits of MIMO systems, however, are irrelevant unless low error rate, spectrally efficient signaling techniques are found. This paper proposes a new method for designing high data-rate spatial signals with low error rates. The basic idea is to use transmitter channel information to adaptively vary the transmission scheme for a fixed data rate. This adaptation is done by varying the number of substreams and the rate of each substream in a precoded spatial multiplexing system. We show that these substreams can be designed to obtain full diversity and full rate gain using feedback from the receiver to transmitter. We model the feedback using a limited feedback scenario where only finite sets, or codebooks, of possible precoding configurations are known to both the transmitter and receiver. Monte Carlo simulations show substantial performance gains over beamforming and spatial multiplexing.