Combining Channel Output Feedback and CSI Feedback for MIMO Wireless Systems

The use of channel output feedback to improve the reliability of fading channels has received scant attention in the literature. In most work on feedback for fading channels, only channel state information (CSI) feedback has been exploited for coding at the transmitter. In this work, the design of a coding scheme for multiple-input multiple-output (MIMO) fading systems with channel output and channel state feedback at the transmitter is considered. Under the assumption of additive white Gaussian noise and an independent and identically distributed fading process, a simple linear coding strategy that achieves any rate up to capacity is proposed. The framework assumes perfect CSI at the transmitter and receiver. This simple linear processing scheme can provide a doubly exponential probability of error decay with blocklength for all rates less than capacity. Remarkably, this encoding scheme actually consists of two separate encoding blocks: one that adapts to the current CSI and one that adapts to the previous channel output feedback. This scheme is extended to the case when the CSI is quantized at the receiver and conveyed to the transmitter over a limited rate feedback channel; for multiple-input single-output (MISO) fading systems it is shown the doubly exponential probability of error decay is achieved as the blocklength increases.