Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

Abstract

Abstract-Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M ) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.Index Terms-Orthogonal Random Beamforming (ORB), beam selection, sparse networks, opportunistic scheduling, Multiuser Diversity (MUD), broadcast channel, feedback quantization.

Random Beamforming in Multi – User MIMO Systems

“…This is because with N T = 4 and α = 1 in this example, the optimal number of beams to achieve d * RBF (1) = 2 is M * RBF (1) = 2 from (45). Since many previous studies have observed that adjusting the number of beams according to the number of users in single-cell RBF can improve the achievable sum rate (see, e.g., [46] [33] [48]), our study here can be considered as a theoretical explanation for such an observation. Fig.…”

“…This important result therefore establishes the optimality of single-cell RBF and motivates further studies on opportunistic communication. Various MIMO-BC transmission schemes with different assumptions on the fading model, feedback scheme, user scheduling, etc., can be shown achieving N T log 2 log K as K → ∞, suggesting that it is a very universal rate scaling law (see, e.g., [30] [33]. More discussions on the large-number-of-users analysis will be given in Section 4.1.2 and 4.2.…”

Beamforming Matrix Transformation for Random Beamforming

“…Random beamforming (RBF) has been widely studied due to its simplicity and lower feedback overhead, even if its performance is poorer than that of other orthogonal beamforming schemes that utilize full channel information [6][8] [9] [10]. In RBF, the base station (BS) transmits a signal modulated by a RBF matrix to users.…”

Exact post-scheduling SINR analysis for orthogonal random beamforming systems

“…To analyse the performance of ORBF systems such as sum-rate, throughput, and average BER, it is necessary to know the statistical distribution of the scheduled user's signal-to-interference-plus-noise ratio (SINR). In the literature [1][2][3][4][5], however, performance analysis has been done with an approximate cumulative distribution function (CDF) of the post-scheduling SINR, which assumes an unrealistic feedback scheme.…”

“…Numerical results: In the literature [1][2][3][4][5], the asymptotic behaviour and the closed form bounds of sum-rate capacity are analysed by the approximate CDF, which is given by…”