Sampling of communication systems with bandwidth expansion

Many communication systems are bandwidth-expanding: the transmitted signal occupies a bandwidth larger than the symbol rate. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. discussed by Unser (see Proceedings of the IEEE, vol. 88, no.4, p.569-87, 2000) shows that in order to represent a bandlimited signal, it is necessary to sample at what is popularly referred to as the Shannon or Nyquist rate. However, in many systems, the required sampling rate is very high and expensive to implement. We show that it is possible to get suboptimal performance by sampling close to the symbol rate of the signal, using well-studied algorithmic components. This work is based on previous results on sampling for some classes of non-bandlimited signals. We extend these sampling results to the case when there is noise. In our exposition, we use ultra wideband (UWB) signals as an example of how our framework can be applied.