Receive antenna selection in diversely polarized MIMO transmissions with convex optimization

Abstract

In this paper, we present a low complexity approach to receive antenna selection for capacity maximization, based on the theory of convex optimization. By relaxing the antenna selection variables from discrete to continuous, we arrive at a convex optimization problem. We show via extensive Monte-Carlo simulations that the proposed algorithm provides performance very close to that of the optimal selection based on an exhaustive search. We consecutively optimize not only the selection of the best antennas but also the angular orientation of individual antenna elements in the array for a so-called true polarization diversity system. Dual- and triple-polarized antenna structures are a very good solution for realizing compact devices and also robust against many imperfections as compared to spatially separated antenna structures. Effectively we extend our work from two dimensional antenna structures to three dimensions. We model such polarized antenna systems and then apply convex optimization theory for selecting the best possible antennas in terms of capacity maximization. Channel parameters like transmit and receive correlations, and cross-polarization discrimination ($\text{XPD}$) are taken into consideration while modeling polarized systems. We compare our results with the Spatially Separated (SP) MIMO with and without selection by performing extensive Monte Carlo simulations. We found that by using a convex optimization algorithm, the performance of multiple polarized systems can be significantly enhanced. For certain channel conditions we observe that triple polarized systems increase the performance significantly compared to dual-polarized and spatially separated systems. We observed that applying selection at the receiver only boosts the performance in Non-Line of Sight (NLOS) channels compared to Line of Sight (LOS) channels.

Introduction

Multiple-Input Multiple-Output (MIMO) systems have received increased attention because they significantly improve wireless link performance through capacity and diversity gains [1]. A major limiting factor in the deployment of MIMO systems is the cost of multiple analog chains (such as low noise amplifiers, mixers and analog-to-digital converters) at the receiver end. Antenna selection at the transmitter/receiver is a powerful technique that reduces the number of analog chains required, yet preserving the diversity benefits obtained from the full MIMO system. With antenna selection, a limited number of transmit/receive chains are dynamically multiplexed between several transmit/receive antennas. MIMO antenna selection techniques have thus been extensively studied, and there are several antenna selection criteria. For full-diversity space–time codes, a subset of available antennas can be selected to maximize the channel norm [2]. For spatial-multiplexing systems, antennas can be selected to minimize the error ratios [3]. A useful tutorial paper on antenna selection can be found in [4]. Various selection algorithms applied to MIMO OFDM systems can be found in [5]. An exhaustive search based on maximum output SNR is proposed in [6], when the system uses linear receivers. Since an exhaustive search is computationally expensive for large MIMO systems, several sub-optimal algorithms with lower complexity are derived at the expense of performance. A selection algorithm based on accurate approximation of the conditional error probability of quasi-static MIMO systems is derived in [7]. In [8], the authors formulate the receive antenna selection problem as a combinatorial optimization problem and relax it to a convex optimization problem. They employ an interior point algorithm, i.e., a barrier method, to solve a relaxed convex problem. However, they treat only the case of capacity maximization. An alternative approach to receive antenna selection for capacity maximization that offers near optimal performance at a complexity significantly lower than the schemes in [9] but marginally greater than the schemes in [10] is described in [11]. In [12], [13] a new approach to antenna selection is proposed, based on the minimization of the union bound, which is the sum of the all Pairwise Error Probabilities (PEPs). Our approach is based on formulating the selection problem as a combinatorial optimization problem and relaxing it to obtain a problem with a concave objective function and convex constraints. We follow the lines of [8], [11], and extend it to systems with both spatial and angular correlation, so-called True Polarization Diversity (TPD) [14], [15], [16] arrays. We optimize the performance of systems with such arrays of antennas which are both spatially separated and also inclined at a certain angle. A model for combined spatial and angular correlation functions is also given in [17], but we adhere to the work from Valenzuela [14], [15], [16]. We apply a simple norm based antenna selection method to a polarization diverse array. Application of receive antenna selection on a polarized array can be found in [18], [19]. We proceed to apply optimization now to the system of arrays with Dual-Polarized (DP) and Triple-Polarized (TP) antenna structures. Application of receive antenna selection on a polarized array can be found in [18], [19]. We first model the DP and TP systems with respect to many channel characteristics, e.g., $K$-factor, channel correlations and cross-polarization discrimination (XPD). A good investigation on the modeling of DP MIMO channels is in [20]. In [21] the author models TP systems and presents the performance in terms of outage probabilities. We then compare the results with the Spatially Separated–Single-Polarized (SS–SP) systems with the same channel characteristics. We extend our DP and TP systems to Spatially-Separated Dual-Polarized (SS–DP) and Triple-Polarized (SS–TP) systems. These systems are a combination of both spatial and polarization domains. The remainder of this paper is organized as follows: Section 2 details the generic model and the structure of polarization diverse arrays. We also describe the correlation models for both spatial and angular arrays in this section. We proceed forward to describe the channel model for three dimensional antenna structures in 3. In Section 4, the performance metric to optimize with receive antenna selection is outlined with details. A description of the performance as an optimization problem is presented in 5 for 2D and 3D structures. Important simulation results for polarization diverse systems and triple-polarized systems and comparison with the performance of Uniform Linear Arrays (ULA) are discussed in Section 6. We conclude our work in Section 7.