Publications in Scientific Journals:
M. Dörpinghaus, G. Koliander, G. Durisi, E. Riegler, H. Meyr:
"Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels";
IEEE Transactions on Information Theory,
We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, 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 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 symbol 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 oversampling 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.
Fading channels, noncoherent capacity, oversampling
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
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