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.


Meik Dörpinghaus

Technische Universität Dresden

Günther Koliander

Vienna University of Technology

Giuseppe Durisi

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Erwin Riegler

Swiss Federal Institute of Technology in Zürich (ETH)

Heinrich Meyr

Technische Universität Dresden

RWTH Aachen University

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 60 9 5673-5681 6858069

Areas of Advance

Information and Communication Technology

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