Broad-band fading channels: signal burstiness and capacity

Abstract

Abstract-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.Index Terms-Channel capacity, fading channels, spread spectrum, wide-sense-stationary uncorrelated scattering (WSSUS) fading channels.

Low SNR Capacity of Fading Channels with Peak and Average Power Constraints

“…For low values of peak constraint ρ, the mutual information between the output and the input is well approximated by the leading terms of the Taylor's series expansion. 2 A flat fading channel model in continuous-time comes with the caveat that such a model is questionable when input symbol durations are smaller than the delay spread of the fading process. Still, this model isn't bad for a first-cut approximation of continuous-time channels.…”

“…An average power constraint is imposed at the transmitter. In the low SNR regime, it is known that capacity achieving input signals are bursty [1,2]. To limit this behavior, a hard peak constraint, in addition to the average power constraint, is considered.…”

“…1 This work was supported in part by the National Science Foundation Grant NSF ITR 00-85929, and the Motorola Center for Communication Graduate Fellowship. 2 A continuous time version of the flat fading channel is considered. 2 The channel capacity for M-FSK modulation is calculated in [9].…”

“…2 A continuous time version of the flat fading channel is considered. 2 The channel capacity for M-FSK modulation is calculated in [9]. The input signaling here is bursty in frequency.…”

Performance of single-tone and two-tone frequency-shift keying for ultrawideband

“…Such a scheme is quite different from the wideband spread-spectrum schemes that create signals that mimic white Gaussian noise (WGN), such as would be optimal for infinite bandwidth nonfading channel. Indeed, the use of signals akin to WGN, which we term bandwidth-scaled, with moments that scale inversely with bandwidth, has been shown to yield a vanishing capacity in the limit of infinite bandwidth ( [11], [8], [10]). …”