Feedback of Channel State Information in Wireless Systems

The problem of sending channel state information from the receiver to the transmitter of a wireless link is investigated in this paper. If the channel state is Gaussian distributed, this problem is equivalent to that of transmission of a Gaussian source over a noisy channel. We focus on a model in which the source outputs are statistically independent and the feedback channel is either AWGN or Rayleigh fading. Due to the strict delay constraints, information theoretic results are hardly applicable to the analysis of such a setting. As a consequence, despite its simplicity, little is known about its fundamental performance limits. Here, two different delay limited digital transmission approaches and a linear analog transmission approach are discussed and compared. If D channel uses per source output are allowed, it is shown that for the AWGN feedback channel delay limited digital approaches can achieve a distortion decay of at least D/2 dB per dB of SNR. This decay rate is 1 for the linear analog approach regardless D. For Rayleigh feedback channels the distortion decay rate is shown to be upper bounded by 1 for digital approaches and is asymptotically 1 for the analog approach. This fact and simplicity are good reasons for the use of analog transmission for feedback purposes over fading channels.