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

Minimum Codebook Size to achieve Maximal Diversity Order for RVQ based MIMO Systems

Multiple antenna systems provide both capacity and diversity gains relatively to single antenna based networks. These gains rely heavily on the availability of channel state information. In this manuscript we assume that the receiver has accurate channel information, which is quantized and fed back to the transmitter. Sufficient conditions for the feedback rate are provided that guarantee no loss of diversity due to channel quantization. Considering a K × M MIMO system, we show that to achieve a diversity of D = M – K + 1 which is the maximum allowable, a feedback channel with rate of log2(1 + D) bits per channel use is enough

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