Multirate Synchronous Sampling of Sparse Multiband Signals

Recent advances in electro-optical systems make them ideal for undersampling multiband signals with very high carrier frequencies. In this paper, we propose a new scheme for sampling and reconstructing of a multiband sparse signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The locations of the signal bands are not known a priori. The scheme, which we call synchronous multirate sampling (SMRS), entails gathering samples synchronously at few different rates whose sum is significantly lower than the Nyquist sampling rate. The signals are reconstructed by finding a solution of an underdetermined system of linear equations by applying a pursuit algorithm and assuming that the solution is composed of a minimum number of bands. The empirical reconstruction success rate is higher than obtained using previously published multicoset scheme when the number of sampling channels is small and the conditions for a perfect reconstruction in the multicoset scheme are not fulfilled. The practical sampling system which is simulated in our work consists of three sampling channels. Our simulation results show that a very high empirical success rate is obtained when the total sampling rate is five times higher than the total signal support of a complex signal with four bands. By comparison, a multicoset sampling scheme obtains a very high empirical success rate with a total sampling rate which is three times higher than the total signal support. However, the multicoset scheme requires 14 channels.