MIMO spatial multiplexing systems with limited feedback

Abstract

Abstract-This paper investigates the problem of transmit beamforming in MIMO spatial multiplexing (SM) systems with finite-rate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new design criterion for designing the codebook of beamforming matrices that is based on minimizing the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to an optimum codebook. Under the i.i.d. channel and high SNR assumption, the effect on channel capacity of the finite-bit representation of beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multimode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits. I. INTRODUCTIONThe performance of a multiple-antenna communication system depends on the nature of channel state information (CSI) available at the transmitter and at the receiver. When the transmitter has perfect CSI, a higher capacity link can be achieved in the single user case, and there are other benefits such as lower-complexity receivers and better system throughput in a multiuser environment. However, the assumption that the transmitter has perfect knowledge of multi-dimensional channel could be unrealistic as in many practical systems the channel information is provided to the transmitter through a finite-rate feedback channel. There are several studies dealing with how to feed back the channel information. Some researchers have worked on feedback of channel information in vector forms, for example, for MISO channels [1], [2], [3] and for the principal eigen-mode of MIMO channels [4]. Only recently, feedback of channel information in matrix forms for MIMO channels have begun to be addressed [5], [6], [7]. In this paper, we develop efficient transmit beamforming techniques for MIMO spatial multiplexing (SM) systems with finite-rate feedback.The contributions of the paper are as follows. First, a tractable measure of capacity loss due to finite feedback rate is derived and used to design an optimal codebook of beamforming matrices in the context of a fixed number of spatial channels with equal power allocation. The efficacy of the approach is demonstrated by using it to design quantizers in

Synthesis and implementation of spatial multiplexing blocks for 3GPP-LTE using FPGA

“…The codebook design problems associated with transmit beamforming in MIMO spatial multiplexing systems with fmite-rate feedback is investigated. The effect on the MIMO channel capacity of finite-rate feedback was analyzed for independent and identically distributed channel [2]. Another work on Distributed Antenna Network (DAN-MIMO) uses an expression for the downlink spectral efficiency on spatial multiplexing in a multi-cell environment [3].…”

“…using two maximal length sequence Linear Feedback Shift Registers (LFSR) as c(n) = (Xl (n)+X2 (n))mod2 (2) where Xl and X2 are maximal length sequence. The LFSR for the generation of first maximal length sequence is initialized with Xl (1) = 0, Xl (n) = 1, n=I,2 ... 30.…”