Broad-band fading channels: Signal burstiness and capacity

Médard and Gallager recently showed that very large bandwidths on certain fading channels cannot be effectively used by direct sequence or related spread-spectrum systems. This paper complements the work of Médard and Gallager. First, it is shown that a key information-theoretic inequality of Médard and Gallager can be directly derived using the theory of capacity per unit cost, for a certain fourth-order cost function, called fourthegy. This provides insight into the tightness of the bound. Secondly, the bound is explored for a wide-sense-stationary uncorrelated scattering (WSSUS) fading channel, which entails mathematically defining such a channel. In this context, the fourthegy can be expressed using the ambiguity function of the input signal. Finally, numerical data and conclusions are presented for direct-sequence type input signals.