Oversampling increases the pre-log of noncoherent Rayleigh fading channels

Journal article, 2014

We analyze the capacity of a continuous-time, time- selective, Rayleigh block-fading channel in the high signal-to-noise ratio regime. The fading process is assumed stationary within each block and to change independently from block to block; further- more, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete- time channel grows logarithmically with the signal-to noise ratio (SNR), with a capacity pre-log equal to 1 − Q/N . Here, N is the number of symbols transmitted within one fading block, and Q is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that sym- bol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversam- pling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as 1 − 1/N . Since the capacity pre-log corresponding to symbol-rate sampling is 1−Q/N , our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.