We aim to enhance the end-to-end rate of a general dual-hop relay network with multiple channels and finite modulation formats, by jointly optimizing channel pairing, power allocation, and integer bit loading. Such an optimization problem has both a discrete feasible region, due to the combinatoric nature of channel pairing, and a discrete objective, due to the bit loading requirement. For this type of mixed-integer programming problems, the Lagrange dual method generally is inapplicable, due to the non-zero duality gap. However, by exploring the structure of our problem, we are able to bound the gap to within one bit, allowing the extraction of an exact optimal integer solution. We further present complexity reduction techniques, and demonstrate that the proposed solution only requires a computational complexity that is polynomial in the number of channels, realizing efficient implementation in practical systems. Through numerical experiments, we show that the jointly optimal solution can significantly outperform common sub-optimal alternatives.

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation, to maximize the weighted sum-rate, in a single-relay cooperative system with multiple channels and multiple users. Common relaying strategies are considered, and transmission power constraints are imposed on both individual transmitters and the aggregate over all transmitters. The joint optimization problem naturally leads to a mixed-integer program. Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users. We further demonstrate through numerical experiments that the jointly optimal solution can significantly improve system performance over its suboptimal alternatives.

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation in a single-relay multiple-access system. The optimization objective is to maximize the weighted sum-rate under total and individual power constraints on the transmitters. By observing the special structure of a three-dimensional assignment problem derived from the original problem, we propose a polynomial-time algorithm based on continuity relaxation and dual minimization. The proposed method is shown to be optimal for all relaying strategies that give a concave rate function in terms of power constraints.

Receive antenna selection for unitary space-time modulation (USTM) over semi-correlated Ricean fading channels is analyzed (this work generalizes that of Ma and Tepedelenlio-glu for the independent and identically distributed (i.i.d.) Rayleigh fading case). The antenna selection rule is that the receive antennas with the largest signal powers are chosen. For single antenna selection, we derive the maximum likelihood decoding for the correlated Ricean case. We also derive the Chernoff bound on the pairwise error probability for the high signal to- noise ratio (SNR) region and obtain the coding gain and diversity order. Our results show that even when there are transmitter side correlations and a line of sight component, receive antenna selection with USTM preserves the full diversity order if the USTM constellation is of full rank. We also give an approximation to the distribution function of a quadratic form of non-zero mean complex Gaussian variates (from Nabar et al.) at the high SNR region. Based on this approximation, a closed-form expression for the coding gain is also obtained and compared with that of the i.i.d. Rayleigh case. We also analyze the case of multiple receive antenna selection and derive the coding gain and diversity order. We show that USTM constellations, which have been proposed for the i.i.d. Rayleigh channel, can be used with the correlated Ricean channel as well.

In this paper, we study power allocation (PA) in a single-relay OFDM system with limited feedback. We propose a PA scheme that uses a codebook of quantized PA vectors designed offline and known to the source, relay, and destination. The destination, which has full knowledge of channel side information (CSI), chooses one of the codebook vectors and conveys back to the source and relay. With the limited amount of available feedback, the design of an appropriate codebook is central to PA, which varies depending on the destination's strategy to choose the optimal PA vector. Assuming high received SNR on either link in the relay path, we first derive the optimal PA solutions as the function of channel realizations with two design criteria, maximizing capacity and minimizing error rate. It is found that when there is high received SNR in either the relay path or the direct path, the optimal solutions for both criteria reduce to simple forms. For maximizing capacity, the available power should be equally allocated to each OFDM subcarrier shared by the source and relay; while for minimum error rate, the available power should be allocated such that the received SNRs for all subcarriers at the destination are the same. The findings lead us to the sub-optimal solutions with great complexity reduction. We then present an adaptation of Lloyd's algorithm to construct a codebook to quantize the optimal PA vectors subject to the amount of feedback. Simulations show that a mild to negligible performance loss can be achieved with only a few bits of feedback at different SNR values.

In [1], antenna selection for multiple antenna systems that employ unitary space-time (ST) signaling has been studied under the assumption of an independent Rayleigh fading channel. In this paper, the performance of such a system is investigated for spatially correlated-fading channels. The channel state information (CSI) is not known at the receiver nor at the transmitter. Antenna selection is thus performed at the receiver based on the instantaneous received signal power. By deriving the Chernoff bound on the pairwise error probability (PEP), we quantify the effects of channel correlation on the diversity order and coding gain at high signal-to-noise ratio (SNR). Analytical results indicate that the full diversity order is preserved in such a channel as long as the unitary signals are full rank. However, spatial correlations result in a loss of the coding gain.

There has been considerable research on the design of space-time block codes (STBCs) that guarantee full diversity without sacrificing the data rate. The main challenge is to maximize the coding gain by maximizing the determinant criterion. It is shown that the most of previous STBCs with full rate and full diversity order (FRFD) (e.g. threaded algebraic space-time (TAST) codes) are constructed via a unitary generator matrix. However, the unitary matrix has been represented using only a small number parameters to enable algebraic code design. In this paper, for a 2 times 2 STBC, we use a more general unitary matrix with a large number of parameters for STBC design. We obtain an upper bound on the coding gain and show that the maximum coding gain is attainable only with PAM signaling. Since optimum parameters for the case of QAM signaling is analytically intractable, we search using the genetic algorithm (GA) method. We also use the union bound criterion for code parameter search by GA. Our simulation results show that with both criteria, the optimum code for QAM signaling is the Golden code. The proposed code significantly outperforms other existing STBCs with the gains about 2 dB at a symbol error rate of 10 for BPSK and 4-PAM. The proposed code performs identically to the Golden code for QAM.

Because of their orthogonality properties, unitary matrices are an important class of matrices that are used in mathematics, physics, control, communications and others. In multiple-input multiple-output (MIMO) communication systems, there are two main applications that use unitary matrices: differential space-time modulation (DUSTM) and precoding. DUSTM is used when the channel state information (CSI) is not available for both transmitter and receiver, while unitary precoding is used when complete or partial CSI is available for both sides. For DUSTM and limited feedback MIMO systems, a codebook of unitary matrices should be designed. Conventionally, design parameters are optimized based on a cost function depending on the application. This optimization is time consuming when the system dimension and/or codebook size are increased. In this paper, we propose to relax the design parameters to be real rather than integer and use a genetic algorithm to find the optimal solution based on the related cost function. This approach provides better codes than the codes extracted from exhaustive search over integer parameters. The code extraction is rapid even when the system dimensions are large

In this paper, we propose an extended class of unitary signal constellations for differential unitary space-time modulation (DUSTM). We also derive an approximation of the upper bound on the symbol error probability (SEP) as a general criterion to find the optimum codes. This criterion is valid for both group or non-group constellations. For asymptotically high or low signal-to-noise ratio (SNR), signal-constellation parameters are usually determined based on the rank-and-determinant (diversity product) or the Euclidean distance (diversity sum) criterion. Since both these criterion are SNR-independent, the search results are not necessarily optimum parameters in medium to low SNRs. Thus instead of using diversity sum or product, we search for the constellation parameters to minimize the union-bound based criterion, taking into account the number of receive antenna and the operation SNR. Simulation results show that the constellations optimized for the union-bound based criterion outperform the previous codes resulting from rank-and- determinant (diversity product) or Euclidean distance (diversity sum).