Mohamed Oussama Damen

On maximum-likelihood detection and the search for the closest lattice point

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.

Diagonal algebraic space-time block codes

We construct a new family of linear space-time (ST) block codes by the combination of rotated constellations and the Hadamard transform, and we prove them to achieve the full transmit diversity over a quasi-static or fast fading channels. The proposed codes transmit at a normalized rate of 1 symbol/s. When the number of transmit antennas n=1, 2, or n is a multiple of four, we spread a rotated version of the information symbol vector by the Hadamard transform and send it over n transmit antennas and n time periods; for other values of n, we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n /spl times/ n ST code matrix. The codes maintain their rate, diversity, and coding gains for all real and complex constellations carved from the complex integers ring Z [i], and they outperform the codes from orthogonal design when using complex constellations for n > 2. The maximum-likelihood (ML) decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity. It is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity.

A unified framework for tree search decoding: rediscovering the sequential decoder

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.

The MIMO ARQ Channel: Diversity–Multiplexing–Delay Tradeoff

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 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 minimum mean-square error (MMSE) lattice decoding principle, for joint error detection and correction. Throughout the paper, our theoretical claims are validated by numerical results

A "better than" Nyquist pulse

A novel ISI-free pulse is presented that has smaller maximum distortion, a more open receiver eye, and a smaller probability of error in the presence of symbol timing error than the Nyquist pulse for the same excess bandwidth.

Delay-Tolerant Distributed-TAST Codes for Cooperative Diversity

In cooperative networks using a decode-and-forward strategy, the multiple relays effectively transmit a distributed space-time code, the performance of which can be severely degraded when timing synchronization among the relays is not assured (e.g., in cases of broadcast to dispersed recipients or in networks without a shared, high-quality timing reference). Recent work by Xia and Hammons have investigated the design of distributed space-time codes that are delay tolerant, in the sense that full spatial diversity is achieved regardless of timing offsets. In general, the previously known space-time block codes belonging to the class of C-linear codes, however, which are important because they achieve full spatial diversity and admit near-optimal lattice decoding algorithms, are not delay tolerant. In this paper, we present a new family of such codes that are fully delay tolerant. The new codes generalize the threaded algebraic space-time (TAST) codes introduced by El Gamal and Damen. Like their brethren, the new distributed-TAST codes are effective and flexible, enabling use of different signaling constellations, transmission rates, numbers of transmit and receive antennas, and decoders of varying levels of complexity.

Parametric construction of Nyquist-I pulses

A novel parametric approach for constructing families of intersymbol-interference (ISI)-free pulses is presented and examined. Some new pulses so constructed have smaller maximum distortion, a more open receiver eye, and a smaller probability of error in the presence of symbol-timing error than the Nyquist raised-cosine pulse for the same excess bandwidth. The parametric approach gives more degrees of freedom in the design of ISI-free pulses, and subsumes previous ISI-free pulses as special cases. A number of theorems that relate time-domain behaviors of a pulse to the pulses frequency spectrum are proved. A previously known result relating pulse tail-time decay to discontinuity of the pulse-frequency spectrum is corrected and clarified.

Linear threaded algebraic space-time constellations

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 gains offered by the proposed designs in average power and peak power limited systems.

On diagonal algebraic space-time block codes

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 /spl times/ n space-time matrix over n transmit antennae and n symbol periods. The output signal-to-noise ratios of two predecoding 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.

Further results on the sphere decoder

The fast development of digital communications hardware allows for the application of very powerful algorithms at the expense of a small increase in complexity compared to the traditionally implemented algorithms. In this paper we give further results on the sphere decoder (SD) algorithm, and its applications to a broad range of digital communications problems related to the separation of m independent sources by n sensors. First, we discuss practical implementation issues and propose an efficient method to initialize the SD parameters based on computing an estimate of the packing radius of the lattice. We relate the initializing method to the expected performance of the SD, and show that at high SNR, one obtains near optimum performance. The complexity of the SD is then shown to be much less than the upper bound on the complexity of the Fincke and Pohst (1985) algorithm for the problem of finding short length vectors in an m-dimensional lattice. Simulations show that the SD of an m-dimensional lattice needs at most O(m/sup 4.5/) arithmetic operations at low SNR, and O(m/sup 3/) at high SNR. The obtained results offer a very powerful tool to reach near the maximum likelihood (ML) decoding performance in several cases such as lattice codes decoding over the Gaussian and Rayleigh fading channels, multiuser detection, uncoded multi-antenna systems detection and space-time codes decoding, and vector quantization.