Random Beamforming with Heterogeneous Users and Selective Feedback: Individual Sum Rate and Individual Scaling Laws

This paper investigates three open problems in random beamforming based communication systems: the scheduling policy with heterogeneous users, the closed form sum rate, and the randomness of multiuser diversity with selective feedback. By employing the cumulative distribution function based scheduling policy, we guarantee fairness among users as well as obtain multiuser diversity gain in the heterogeneous scenario. Under this scheduling framework, the individual sum rate, namely the average rate for a given user multiplied by the number of users, is of interest and analyzed under different feedback schemes. Firstly, under the full feedback scheme, we derive the closed form individual sum rate by employing a decomposition of the probability density function of the selected user's signal-to-interference-plus-noise ratio. This technique is employed to further obtain a closed form rate approximation with selective feedback in the spatial dimension. The analysis is also extended to random beamforming in a wideband OFDMA system with additional selective feedback in the spectral dimension wherein only the best beams for the best-L resource blocks are fed back. We utilize extreme value theory to examine the randomness of multiuser diversity incurred by selective feedback. Finally, by leveraging the tail equivalence method, the multiplicative effect of selective feedback and random observations is observed to establish the individual rate scaling.Comment: Submitted in March 2012. To appear in IEEE Transactions on Wireless Communications. Part of this paper builds upon the following letter: Y. Huang and B. D. Rao, "Closed form sum rate of random beamforming", IEEE Commun. Lett., vol. 16, no. 5, pp. 630-633, May 201

MIMO Interference Alignment Over Correlated Channels with Imperfect CSI

Interference alignment (IA), given uncorrelated channel components and perfect channel state information, obtains the maximum degrees of freedom in an interference channel. Little is known, however, about how the sum rate of IA behaves at finite transmit power, with imperfect channel state information, or antenna correlation. This paper provides an approximate closed-form signal-to-interference-plus-noise-ratio (SINR) expression for IA over multiple-input-multiple-output (MIMO) channels with imperfect channel state information and transmit antenna correlation. Assuming linear processing at the transmitters and zero-forcing receivers, random matrix theory tools are utilized to derive an approximation for the post-processing SINR distribution of each stream for each user. Perfect channel knowledge and i.i.d. channel coefficients constitute special cases. This SINR distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate, but also permits a realistic comparison of IA with other transmission techniques. More specifically, IA is compared with spatial multiplexing and beamforming and it is shown that IA may not be optimal for some performance criteria.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Linear Beamforming for the Spatially Correlated MISO broadcast channel

A spatially correlated broadcast setting with M antennas at the base station and M users (each with a single antenna) is considered. We assume that the users have perfect channel information about their links and the base station has only statistical information about each user's link. The base station employs a linear beamforming strategy with one spatial eigen-mode allocated to each user. The goal of this work is to understand the structure of the beamforming vectors that maximize the ergodic sum-rate achieved by treating interference as noise. In the M = 2 case, we first fix the beamforming vectors and compute the ergodic sum-rate in closed-form as a function of the channel statistics. We then show that the optimal beamforming vectors are the dominant generalized eigenvectors of the covariance matrices of the two links. It is difficult to obtain intuition on the structure of the optimal beamforming vectors for M > 2 due to the complicated nature of the sum-rate expression. Nevertheless, in the case of asymptotic M, we show that the optimal beamforming vectors have to satisfy a set of fixed-point equations.Comment: Published in IEEE ISIT 2010, 5 page

Multi-Cell Random Beamforming: Achievable Rate and Degrees of Freedom Region

Random beamforming (RBF) is a practically favourable transmission scheme for multiuser multi-antenna downlink systems since it requires only partial channel state information (CSI) at the transmitter. Under the conventional single-cell setup, RBF is known to achieve the optimal sum-capacity scaling law as the number of users goes to infinity, thanks to the multiuser diversity enabled transmission scheduling that virtually eliminates the intra-cell interference. In this paper, we extend the study of RBF to a more practical multi-cell downlink system with single-antenna receivers subject to the additional inter-cell interference (ICI). First, we consider the case of finite signal-to-noise ratio (SNR) at each receiver. We derive a closed-form expression of the achievable sum-rate with the multi-cell RBF, based upon which we show an asymptotic sum-rate scaling law as the number of users goes to infinity. Next, we consider the high-SNR regime and for tractable analysis assume that the number of users in each cell scales in a certain order with the per-cell SNR. Under this setup, we characterize the achievable degrees of freedom (DoF) for the single-cell case with RBF. Then we extend the analysis to the multi-cell RBF case by characterizing the DoF region. It is shown that the DoF region characterization provides useful guideline on how to design a cooperative multi-cell RBF system to achieve optimal throughput tradeoffs among different cells. Furthermore, our results reveal that the multi-cell RBF scheme achieves the "interference-free DoF" region upper bound for the multi-cell system, provided that the per-cell number of users has a sufficiently large scaling order with the SNR. Our result thus confirms the optimality of multi-cell RBF in this regime even without the complete CSI at the transmitter, as compared to other full-CSI requiring transmission schemes such as interference alignment.Comment: 28 pages, 6 figures, to appear in IEEE Transactions of Signal Processing. This work was presented in part at IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto, Japan, March 25-30, 2012. The authors are with the Department of Electrical and Computer Engineering, National University of Singapore (emails: {hieudn, elezhang, elehht}@nus.edu.sg

Low-Complexity Hybrid Beamforming for Massive MIMO Systems in Frequency-Selective Channels

Hybrid beamforming for frequency-selective channels is a challenging problem as the phase shifters provide the same phase shift to all of the subcarriers. The existing approaches solely rely on the channel's frequency response and the hybrid beamformers maximize the average spectral efficiency over the whole frequency band. Compared to state-of-the-art, we show that substantial sum-rate gains can be achieved, both for rich and sparse scattering channels, by jointly exploiting the frequency and time domain characteristics of the massive multiple-input multiple-output (MIMO) channels. In our proposed approach, the radio frequency (RF) beamformer coherently combines the received symbols in the time domain and, thus, it concentrates signal's power on a specific time sample. As a result, the RF beamformer flattens the frequency response of the "effective" transmission channel and reduces its root mean square delay spread. Then, a baseband combiner mitigates the residual interference in the frequency domain. We present the closed-form expressions of the proposed beamformer and its performance by leveraging the favorable propagation condition of massive MIMO channels and we prove that our proposed scheme can achieve the performance of fully-digital zero-forcing when number of employed phase shifter networks is twice the resolvable multipath components in the time domain.Comment: Accepted to IEEE Acces