We investigate the transmit beamforming with antenna selection and power combining for multiple antenna systems with practical per-antenna power constraint. We consider that more than one power amplifier (PA) outputs can potentially be combined by using power combiners, such as hybrid combiners, and fed into antennas with stronger channel gains in order to achieve better channel coupling efficiency. The SNR gain of the proposed scheme is analyzed for two different power combining scenarios. For a general number of PAs and transmit antennas, we present an efficient algorithm to find the optimal antenna selection and the power combining vector for multiple-input single-output (MISO) systems, and discuss its extension to general multiple-input multiple-output (MIMO) systems. Numerical results show that the proposed design provides an efficient way to reduce the large SNR loss due to the strong channel imbalance in the MIMO systems.

We study a transmit beamforming for multiple antenna systems under the per-antenna power and the equivalent isotropic radiation power (EIRP) constraints. Finding the optimal beamforming vector maximizing SNR in such case is known to be NP-hard, and its semi-definite programming (SDP) approximation can be still complex due to the large number of the inequality constraints. This work considers a low complexity transmit beamforming technique, called Golay beamforming, based on the structured codebook consisting of the Golay sequences with the bounded EIRP guarantee. We discuss the specific structure and the performance bounds of the Golay beamforming, and propose the weighted Golay beamforming which can further improve the received SNR by using a specific set of the weighted Golay sequences which enjoys the same bounded low EIRP. Numerical results show that the proposed Golay beamforming provides an efficient low complexity solution with the graceful performance degradation under moderate EIRP constraints, and can be further improved by the weighted Golay beamforming.

To evaluate the unitary integrals, such as the well-known Harish–Chandra–Itzykson–Zuber integral, character expansions were developed by Balantekin, where the matrix integrand is a group member; i.e., a square matrix with a nonzero determinant. Recently, this method has been exploited to derive the joint eigenvalue distributions of the Wishart matrices; i.e.,${\bf H}{\bf H}^{\ast}$where${\bf H}$is the complex Gaussian random channel matrix of a multiple-input multiple-output (MIMO) system. The joint eigenvalue distributions are used to calculate the moment generating function of the mutual information (ergodic capacity) of a MIMO channel. In this paper, we show that the previous integration framework presented in the literature is not correct, and results in incorrect joint eigenvalue distributions for the Ricean and full-correlated Rayleigh MIMO channels. We develop a new framework to apply the character expansions for integrations over the unitary group, involving general rectangular complex matrices in the integrand. We derive the correct distribution functions and use them to obtain the capacity of the Ricean and correlated Rayleigh MIMO systems in a unified and straightforward approach. The integration technique proposed in this paper is general enough to be used for other unitary integrals in engineering, mathematics, and physics.

Multiple-input multiple-output (MIMO) channels have been studied from various aspects including the average of the mutual information between the transmitter and receiver (ergodic capacity) when the channel gains are known to the receiver only. A common approach for capacity analysis is to find the moment generating function (MGF) of the mutual information and by direct differentiation, the mean of the mutual information (capacity) is calculated. Recently, character expansions of groups have been used for integration over unitary matrices to obtain the joint eigenvalue distribution of the correlated Wishart matrix i.e. HH* where H is the zero mean full correlated complex Gaussian random MIMO channel matrix. In this paper, we show that the previous attempt for capacity analysis of full correlated MIMO channels is correct for square channel matrices only. We modify the approach from square matrices to rectangular matrices to obtain the correct joint eigenvalue distribution of the correlated Wishart matrix. The result can be used to obtain the MGF and the capacity of full correlated MIMO channels.

Joint eigenvalue distribution of the noncentral complex Wishart matrix, i.e. HH* where H is the nonzero-mean complex Gaussian random channel matrix of a multiple-input multiple-output (MIMO) system, is required for the analysis of Ricean MIMO channels from different aspects, including the average of mutual information between the transmitter and the receiver (ergodic capacity), when the channel gains are known to the receiver only. Previous works rely on the available results in mathematics for the joint eigenvalue distribution, obtained by integration over unitary matrices using classic integration methods. In this paper, we present a powerful integration method over unitary matrices which exploits the representation theory and characters of groups. The method was originally proposed for square matrices. We modify the approach from square matrices to rectangular matrices to solve a more general integral over unitary matrices and obtain the joint eigenvalue distribution of the noncentral Wishart matrix. Our result is the generalization of the previous classical integral over unitary matrices so that the result is not restricted to diagonal and/or real matrices, particularly.

Multiple-input multiple-output (MIMO) systems achieve significant diversity and array gains by using transmit beamforming. When complete channel state information (CSI) is not available at the transmitter, a common set of beamformers (codebook) is used by both the transmitter and the receiver. For each channel realization, the best beamformer is selected at the receiver and its index is sent back to the transmitter via a limited feedback channel. In this paper, a codebook design method using the genetic algorithm is proposed, which reduces the design complexity and achieves large minimum-distance codebooks. Exploiting the specific structure of these beamformers, an order and bound algorithm is proposed to reduce the beamformer selection complexity at the receiver side. The exact bit error rate (BER) of the optimal beamforming in finite-series expression is used to facilitate the BER analysis of limited feedback beamforming. By employing a geometrical approach, an approximate BER of limited feedback beamforming is derived when the codebook size is relatively large (high resolution analysis). The simulation results show that the approximate BER is comparatively tight even for small size codebooks.

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.

Despite primary space-time coding where the channel state information (CSI) is available at the receiver only, the capacity and performance of multiple-input multiple-output (MIMO) systems can be increased significantly when a complete or partial CSI is available at the transmitter. Recently, limited feedback methods including antenna subset selection and unitary preceding have been proposed for orthogonal space-time codes where a partial knowledge of the channel is available at the transmitter via an error-free, zero-delay feedback channel. In this paper, we propose a general structure matrix rather than a unitary one for precoding. By maximizing the signal-to-noise ratio (SNR) per received symbol, we find the optimal precoder for general space-time codes with rate⩽1 symbol per channel use. The performance of the optimal scheme is analytically evaluated. Next, we extend the result for limited feedback systems. Simulation results show that the proposed precoder outperforms the previous work.

In recent investigations, several methods for limited feedback multiple-input multiple-output (MIMO) systems have been proposed. Antenna selection at the transmitter and(or) receiver side is one of the approaches to minimize the average probability of error by using a limited bits of feedback information. In this paper, by using a novel approach, we calculate the optimal signal-to-noise ratio (SNR) for each received symbol for a general space-time block code. We propose an antenna selection method at the transmitter to maximize the average SNR for each symbol. Since we propose the optimal selection, our antenna selection method outperforms antenna selection methods available in the literature for space-time codes with rate⪕ 1 symbol per channel use, derived either based on SNR or capacity maximization. The proposed selection performs better than unitary precoding schemes (even optimal precoding) for systems with small number of transmitter and receiver antennas (particularly for mobile systems), although precoding techniques exploit more bits of feedback information and computational complexity than the proposed method.

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

Preceding is a well-known method to reach the promised performance and capacity of multiple-input multiple-output (MIMO) systems. Recent investigations, when the transmitter has the channel-state information (CSI), have revealed several preceding techniques. Minimum distance based precoders outperform precoders based on other criteria such as maximizing signal-to-noise ratio (SNR), minimizing the mean square error and maximizing the minimum singular value of the equivalent channel. On the other hand, when the CSI is not available at the transmitter, one resorts to limited feedback precoding methods. Previously, unitary matrices for precoding have been derived from subspace packing in the Grassmann manifold. In this paper, we use the same set of unitary matrices and enhance them by defining the precoder matrix to have a general form not unitary only. We extract the precoding parameters by applying the minimum-distance approach. Although in this case the number of feedback parameters is increased, the performance results are accordingly impressive. The optimality of quantization of feedback parameters is also presented.