Transmit Antenna Selection for Multi-user MIMO Precoding Systems with Limited Feedback

Manar Mohaisen
2011 Journal of information and communication convergence engineering  
Transmit antenna selection techniques are prominent since they exploit the spatial selectivity at the transmitter side. In the literature, antenna selection techniques assume full knowledge of the channel state information (CSI). In this paper, we consider that the CSI is not perfectly known at the transmitter; however, a quantized version of the channel coefficients is fed back by the users. We employ the non-uniform Lloyd-Max quantization algorithm which takes into consideration the
more » ... on of the channel coefficients. Simulation results show that the degradation in the BER of the system with imperfect CSI at the transmitter is tolerable, especially when the transmit diversity order is high. Index Terms-Multi-user MIMO system, transmit antenna selection, imperfect channel state information, nonuniform quantization, Lloyd-Max quantizer. I.INTRODUCTION IN recent broadband communication standards, multiuser multiple-input multiple-output (MU-MIMO) systems have been considered as a means for increasing the system throughput [1]- [2] .In MU-MIMO systems, multiple users are assigned the same time and frequency resources, while the spatial resources can be either shared or orthogonally assigned. In the downlink MU-MIMO system, the base station (BS) has a pre-knowledge of the users' data and the fed back channel state information (CSI) from the users. As such, data can be precoded so that inter-user interference (IUI) can be cancelled, or highly reduced. Optimally, each user receives his data without experiencing the existence of other users. Dirty paper coding (DPC) is the optimal precoding scheme for downlink MU-MIMO systems [3] . The main idea behind DPC is that it considers the MIMO channel to be a white paper that includes some dirt, i.e., interference. Since the location of the dirt is well-known, the BS only writes on the clean parts of the paper. Therefore, the reader, i.e., the mobile station (MS) receiver, can clearly distinguish between the dirt and the useful writing. Several practical precoding techniques have been proposed in the literature, including linear precoding techniques [4], Tomlison-Harashimaprecoding [5], [6], and vector perturbation techniquescombined with linear precoders[7]-[10]. Linear zero-forcing precoding(ZFP) can be seen as a beamforming algorithm, where the beamforming weights are the rows of the pseudo-inverse of the channel matrix, while in the minimum-mean square error precoder (MMSEP) the channel matrix is regularized so that a tradeoff between noise amplification and IUI is achieved. On the other hand, THP and VP techniques linearly perturb the data vector such that the required transmit power is reduced. Combining these techniques with linear precoders is interesting in future communication systems such as long-term evolution (LTE) and LTE-advanced (LTE-A). This is because BS is supposed to have a large number of transmit antennas, e.g., up to 8 antennas in LTE-A system, and to communicate simultaneously with several users [11] . Due to its simplicity, we will restrict our discussions in the sequel on the ZFP, unless otherwise mentioned. Transmit antenna selection improves the system performance by exploiting the spatial diversity at the transmitter side. Therefore, when the number of antennas at the BS is larger than the number of radio frequency (RF) chains, the subset of antennas that achieve the best conditions can be selected and connected to the available RF chains. In the literature, several antenna selection techniques have been proposed for different scenarios. In [12], [13], various antenna selection techniques have been proposed for single user MIMO systems, and in [14] , [15] , authors proposed efficient antenna selection algorithms for the MU-MIMO case. Since the evaluation of the antenna selection is out of the scope of this paper, we will consider the optimum algorithm for the ZFP. For more computationally efficient algorithms, readers can refer to [15] and references therein. The aforementioned references consider perfect channel state information at the transmitter (PCSIT), which is in general not practical, due to mobility, noise, and errors in the channel estimation. In this paper, we investigate transmit antenna selection in MU-MIMO systems with ZFP, when only a quantized version of the channel, a.k.a. limited feedback, is available at the transmitter. In the sequel, this will be referred to as imperfect CSIT (ICSIT). In this paper, the quantization of the channel coefficients is performed using the nonuniform Lloyd-Max iterative quantizer which takes into consideration the probability density function (pdf) of the
doi:10.6109/jicce.2011.9.2.193 fatcat:xtp7kqfuo5cgxea4emhcmsqfti