The Information-Theoretic Cost of Learning Fading Channels

Abstract: Recent results in communication theory suggest that significant throughput gains in wireless fading networks can be achieved by exploiting network coordination (e.g., CoMP, network MIMO, and interference alignment), provided that each node in the network has perfect channel knowledge. In practice, however, the channels are not known a priori and must be estimated. Lack of a priori channel knowledge determines a penalty on the throughput compared to the case where perfect channel knowledge is available. In this thesis, we take a fresh look at the problem of learning fading channels. We characterize the cost of learning fading channels in an information-theoretic way by determining the maximal achievable rate over point-to-point fading channels under the assumption that neither the transmitter nor the receiver have a priori channel knowledge. Paper A and Paper B characterizes the capacity of fading channels in the high signal-to-noise ratio (SNR) regime. Specifically, in paper A, we establish an upper bound on the capacity pre-log (i.e., the asymptotic ratio between capacity and the logarithm of SNR as SNR goes to infinity) of Rayleigh-fading correlated block-fading single-input multiple-output (SIMO) channels. The upper bound matches the lower bound reported in Riegler et al. (2011), and, hence, yields a complete characterization of the SIMO capacity pre-log, provided that the channel covariance matrix satisfies a mild technical condition. In Paper B, we characterize the capacity of Rayleigh-fading constant block-fading multiple-input multiple-output (MIMO) channels in the high SNR regime, and provide the input distribution that achieves capacity up to a term that vanishes as SNR grows large. The insights gained from the high-SNR analysis allows us to obtain tight bounds on the maximal achievable rate $R^'(n,epsilon)$ for a given blocklength $n$ and block error probability $epsilon$ at finite SNR. Specifically, in Paper C, we establish upper and lower bounds on $R^'(n,epsilon)$ for a single-antenna Rayleigh-fading constant block-fading channel. Our results show that for a given block-length and error probability, $R^'(n, epsilon)$ is not monotonic in the channel coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel. Finally, in Paper D, we consider the special case when the fading channel does not vary over the transmission of each codeword (quasi-static fading channels). We characterize the channel dispersion in the SIMO setting, and provide tight bounds on $R^'(n,epsilon)$ together with an easy-to-compute approximation.