On the Sensitivity of Noncoherent Capacity to the Channel Model

Details On the Sensitivity of Noncoherent Capacity to the Channel Model On the Sensitivity of Noncoherent Capacity to the Channel Model

2009-05-05

arxiv.org/abs/0905.0619v1

Computer Science

Information Theory

To be presented at IEEE Int. Symp. Inf. Theory 2009, Seoul, Korea

Scientific paper

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the set of harmonics where the power spectral density of the fading process is nonzero determines if capacity grows logarithmically in SNR or slower than logarithmically. An engineering-relevant problem is to characterize the SNR value at which this sensitivity starts to matter. In this paper, we consider the general class of continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. For this class of channels, we show that the noncoherent capacity is close to the AWGN capacity for all SNR values of practical interest, independently of whether the scattering function is compactly supported or not. As a byproduct of our analysis, we obtain an information-theoretic pulse-design criterion for orthogonal frequency-division multiplexing systems.

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