Capacity of Underspread WSSUS Fading Channels in the Wideband Regime

We characterize the infinite bandwidth capacity behavior of the general class of underspread wide-sense stationary uncorrelated scattering (WSSUS) time-frequency selective Rayleigh fading channels. In particular, we propose a signaling scheme, termed time-frequency pulse position modulation (TF-PPM), which is shown to achieve AWGN channel capacity in the infinite bandwidth limit. As a trivial consequence of this result, the infinite bandwidth capacity of WSSUS underspread fading channels, irrespectively of the scattering function, equals the AWGN channel's infinite bandwidth capacity. The wideband slope achieved by TF-PPM is found to be zero, irrespectively of the channel's scattering function, even in the presence of perfect receive channel state information. Our proof techniques use the fact that underspread fading channels have a highly structured set of eigenfunctions and a property of orthogonal signaling schemes first presented in Butman and Klass, Jet Propulsion Lab.., Tech. Rep., 1973