Sampling of communications systems with bandwidth expansion

Many communication systems are {\em bandwidth-expanding}: the transmitted signal occupies a bandwidth larger than the {\em symbol rate}. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. 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. In this work we show that it is possible to get suboptimal performance by sampling close to the {\em symbol rate} of the signal, using well-studied algorithmic components. This work is based on recent results on sampling for some classes of non-bandlimited signals. In the present paper, 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.