Performance of Orthogonal Beamforming for SDMA with Limited Feedback

On the multi-antenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to CSI inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser-interference-limited regime, the throughput of PU2RC is shown to scale logarithmically with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and also linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.Comment: 27 pages; to appear in IEEE Transactions on Vehicular Technolog

How much does transmit correlation affect the sum-rate scaling of MIMO Gaussian broadcast channels?

This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO Gaussian broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n + M log P/M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n → ∞. When the channel exhibits some spatial correlation with a covariance matrix R (non-singular with tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n + M log P/M + log det(R) + o(1). We further show that the sum-rate of various beamforming schemes achieves M log log n + M log P/M + M log c + o(1) where c ≤ 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in and more generally, for random beamforming with preceding in which beams are pre-multiplied by a fixed matrix. Simulation results are presented at the end of the paper

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling

On the capacity of MIMO broadcast channels with partial side information

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=αlogn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness

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