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