Limited Feedback Multiple-input Multiple-output Research Articles

A Diversity Guarantee and SNR Performance for Unitary Limited Feedback MIMO Systems

A multiple-input multiple-output (MIMO) wireless channel formed by antenna arrays at the transmitter and at the receiver offers high capacity and significant diversity. Linear precoding may be used, along with spatial multiplexing (SM) or space-time block coding (STBC), to realize these gains with low-complexity receivers. In the absence of perfect channel knowledge at the transmitter, the precoding matrices may be quantized at the receiver and informed to the transmitter using a feedback channel, constituting a limited feedback system. This can possibly lead to a performance degradation, both in terms of diversity and array gain, due to the mismatch between the quantized precoder and the downlink channel. In this paper, it is proven that if the feedback per channel realization is greater than a threshold, then there is no loss of diversity due to quantization. The threshold is completely determined by the number of transmit antennas and the number of transmitted symbol streams. This result applies to both SM and STBC with unitary precoding and confirms some conjectures made about antenna subset selection with linear receivers. A closed form characterization of the loss in SNR (transmit array gain) due to precoder quantization is presented that applies to a precoded orthogonal STBC system and generalizes earlier results for single-stream beamforming.

Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques. In the absence of full channel knowledge at the transmitter, the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low-rate feedback channel. In the literature, quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution, commonly the uncorrelated Rayleigh distribution. When the channel is not uncorrelated Rayleigh, however, these quantization strategies result in a degradation of the receive signal-to-noise ratio (SNR). In this paper, switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution. The codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel. The convergence properties of the codebook selection algorithm are studied assuming a block-stationary model for the channel. In the case of a nonstationary channel, it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in SNR. Simulation results show that in the case of correlated channels, the SNR performance of the link can be significantly improved by adaptation, compared with nonadaptive quantization strategies designed for uncorrelated Rayleigh-fading channels

Duplex distortion models for limited feedback MIMO communication

The use of limited feedback in multiple-input multiple-output (MIMO) wireless communications has grown in interest over the last few years. Research has shown that feedback can be used to increase achievable data rates and add resilience against fading. Most of the work to this point, however, has ignored the data rate overhead associated with feedback. Models that do not consider feedback overhead are valid in wireless systems with ever present control channels, but they fail to capture the data rate cost of feedback when control channels are not present. In this paper, we present a new system model, called a duplex model, that captures the true loss (or cost) of feedback. A new distortion function for use with codebook design follows from the duplex system model. This system model is used to derive bounds on the amount of feedback needed under different antenna, signal-to-noise ratio, and bandwidth assumptions. Simulation results show the necessity of taking feedback into account.