In this paper, we study the design of linear dispersion (LD) codes for uplink multiuser channels with multiple antennas at the base station and each mobile unit. In the considered scheme, each user employs LD codes to transmit the data, i.e., the transmitted codeword is a linear combination over space and time of certain dispersion matrices with the transmitted symbols. The linear space-time spreading can also be utilized to separate multiple users at the base station. We propose a simulation-based optimization method together with gradient estimation to systematically design the multiuser linear space-time coding under either optimal or suboptimal receivers. We perform the gradient estimation through the score function method. The proposed method can also be applied to design codes under different fading statistics. Simulation results show that under the optimal maximum-likelihood (ML) receiver, the codes obtained by the new algorithm provides roughly the same performance as the low-dimensional spread modulation, as well as the interference-resistant modulation. Moreover, the new codes perform significantly better with suboptimal multiuser receiver structures.

The training-based scheme constitutes an efficient method for noncoherent multiantenna communications. In this paper, we propose a superimposed training-based linear dispersion (STLD) transmission scheme, where the transmitted symbols are superposition of the training pilots and the data symbols. The STLD system enjoys simple encoding and efficient suboptimal decoding. Since for noncoherent multiple-input multiple-output systems employing the STLD scheme, analytical expressions of block- or bit-error probabilities do not exist, deterministic optimization methods cannot be used to design the optimal STLD system. We therefore propose to design the optimal STLD systems using simulation-based optimization techniques, together with gradient estimation. Simulation results show that with either maximum-likelihood or suboptimal decoding, the STLD systems obtained by the proposed design algorithm generally outperform the conventional training-based scheme employing space-time codes designed for coherent channels.

The Cayley unitary (CU) codes constitute a systematic way of constructing unitary space-time modulations for noncoherent MIMO communications. For MIMO systems employing CU codes, there is no explicit expression for block (or bit) error probabilities. Hence, deterministic optimization tools cannot be employed to design the optimal CU codes. In this work, we propose to optimize the design of CU codes through simulation-based optimization techniques, in particular, stochastic approximation together with gradient estimation. The proposed methodology can be employed to design optimal CU codes under the maximum likelihood decoding or the suboptimal linearized sphere decoding. Simulation results show that new CU codes obtained by the proposed design significantly outperform those in the literature designed by maximizing the expected distance between codeword pairs. The new CU codes also enjoy comparable performance over training-based designs

In this paper we propose a systematic procedure for designing minimum-error-rate lattice (space-time) codes. By employing stochastic optimization techniques we design lattice (space-time) codes with minimum error rate when maximum likelihood (ML) detection is employed. Our design methodology can be tailored to optimize lattice (space-time) codes for any fading statistics and SNR of interest

The Cayley differential (CD) codes constitute a systematic way to construct differential unitary space-time modulations for noncoherent communication in multiple-antenna systems. The original CD codes are designed based on the criterion of maximizing the expected distance between codeword pairs. However, in practical systems, it is more sensible to design the codes according to the minimum error rate criterion. The main difficulty in such a design is that the error probability does not admit a closed-form expression and, thus, conventional optimization methods cannot be applied. In this paper, we formulate the minimum error-rate CD code design as an unconstrained stochastic optimization problem, and employ the stochastic approximation technique with gradient estimation to solve it. Simulation results show that codes generated by the proposed design procedure generally outperform the CD codes designed by maximizing the expected distance between codeword pairs and the Cayley threaded algebraic space-time codes that satisfy the full rank criterion. The new CD codes also enjoy better or comparable performance over other group based or nongroup designs.

In this paper, we propose to design linear-dispersion (LD) codes by minimizing the union bound based on the exact pairwise error probability (PEP). We find that the original programming is not convex, and we present a convex relaxation to the optimization problem. We employ the gradient descent methods to numerically search the optimum dispersion matrices. Simulation results show that codes optimized by the new criterion generally outperform the codes designed based on algebraic number theory. When the knowledge of spatial-fading correlation is available in advance for the design, significant gain relative to the codes designed without knowledge of channel correlation can be achieved by taking into account the correlation structure while performing the optimization. We demonstrate how to exploit knowledge of transmit and receive correlation in designing the LD codes. Numerical and simulation examples show that knowledge of transmit correlation has a large impact on the optimum performance of the LD codes. Furthermore, additional gain can be achieved from the knowledge of receive correlation.

In this work, we analyze the pairwise error probability (PEP) performance of space-time codes in the presence of transmit fading correlation. Unlike receive correlation, the effect of transmit correlation depends on the specific space-time code used. We show that at low SNR, depending on the code, transmit correlation can either improve or degrade the PEP performance. By analyzing the worst case scenario for asymptotically high or low SNR, we show that, to guarantee robust performance for arbitrary transmit correlation, the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs. Numerical and simulation results are given to corroborate the theoretical analysis.

We derive the exact pairwise error probability (PEP) for space-time coding over quasi-static Rayleigh fading channels in the presence of spatial fading correlation. We show that receive correlation always degrades the PEP for all signal-to-noise ratios (SNRs). We quantify the effect of receive correlation by employing the notion of "majorization". We show that the stronger the receive correlation, the worse the PEP for all SNRs. We show that at low SNR, depending on the codes, transmit correlation can either improve or degrade the PEP performance. We show that to guarantee robust performance for arbitrary transmit correlation, the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs.

In this letter, based on the exact pairwise-error probability, we derive the union bound on the symbol-error probability (SEP) of the differential unitary space-time (DUST) modulation employing group codes. Instead of using the rank-and-determinant or Euclidean distance criteria, we optimize the cyclic group codes such that the union bound on the SEP is minimized for a predetermined scenario, taking into account the number of transmit and receive antennas and the operating signal-to-noise ratio (SNR). Our simulation results show that for a wide range of SNRs, the codes with the minimum union bound for a particular SNR outperform the codes designed based on rank-and-determinant or Euclidean distance criteria.

For asymptotically high SNR, the design criteria of differential unitary space-time (DUST) coding are based on the rank-and-determinant criterion (Hughes, B.L., 2000; Hochwald, B.M. and Sweldens, W., 2000). For a large number of receive antennas or low SNR scenarios, the Euclidean distance criterion is appropriate for differential unitary space-time codes (Wang, J. et al., 2002). In practical systems, with a reasonable number of transmit and receive antennas, the SNR is neither asymptotically high nor asymptotically low. Therefore it is interesting to find what is a good code design criterion at medium range SNR. Based on the exact pairwise error probability, we derive the union bound on the symbol error probability (SEP) of the DUST modulation. Instead of using the rank-and-determinant or Euclidean distance criteria, we optimize the codes such that the union bound on the SEP is minimized for a predetermined scenario taking into account the number of transmit and receive antennas and the operating SNR. Our simulation results show that for a wide range of SNRs, the codes with the minimum union bound for a particular SNR outperform the codes designed based on rank-and-determinant or Euclidean distance criteria.

In this paper, we consider utilizing the space-time codes in the wideband CDMA system. We assume that there are multiple resolvable paths in the frequency selective fading channel. Analytical results show that in addition to spatial diversity, another diversity gain called multipath diversity is achievable. Performance criterion for full space multipath diversity gain is analyzed. We consider both the case that the receiver has the ideal channel state information and the case that there are errors in the channel state information available to the receiver. A RAKE receiver is used in the CDMA system to gain the multipath diversity. We derive the generalized RAKE receiver structure for the space-time block coding (STBC) coded wideband CDMA systems. The simulation results demonstrate the additional gain guaranteed by the multipath diversity.

In this paper, we consider how to design the optimal space-temporal communication systems for multiple access channels with intersymbol interference (ISI) under the assumption that the transmitters know the channel state information (CSI) perfectly. We optimize the spatio-temporal vector coding (STVC) and the space-frequency multiple input multiple output (MIMO) discrete matrix multitone (DMMT) information structure for the multiple access channels such that the total information capacity is maximized. The optimization problem is a convex programming problem and the iterative waterfilling algorithm is employed to find the optimal solution. The simulation results show that a remarkable capacity improvement is achievable by the joint multiuser spatio-temporal optimization.