Channel Output Feedback Based Design of a Coding Scheme for MISO Fading Channels

The design of beamformers using limited channel state feedback at the transmitter for multiple-input single-output (MISO) fading channels has been extensively studied in the literature. It has been established that the limited feedback of channel state can lead to significant capacity enhancement. In this paper, it is demonstrated that the use of channel output feedback in addition to limited channel state feedback can result in better reliability in addition to the closed-loop capacity improvement. In particular, a capacity achieving linear coding scheme for an independent and identically distributed Rayleigh fading process is proposed that has a probability of error decaying double exponentially. The proposed coding scheme highlights the separation between channel state adaption and channel output adaption. The scheme can be viewed as an extension of the Schalkwijk-Kailath-Butman scheme and the scheme proposed in [1] to MISO fading channels with limited state feedback. Finally, simulations are presented to exhibit the doubly exponential decay of the scheme.