Spreading Signals in the Wideband Limit

Abstract— Wideband communications are impossible with signals that are spread over a very large band and are transmitted over multipath channels unknown ahead of time. This work exploits the I-mmse connection to bound the achievable datarate of spreading signals in wideband settings, and to conclude that the achievable data-rate diminishes as the bandwidth increases due to channel uncertainty. The result applies to all spreading modulations, i.e. signals that are evenly spread over the bandwidth available to the communication system, with SNR smaller than log(W/L)/(W/L) and holds for communications over channels where the number of paths L is unbounded by sublinear in the bandwidth W.