M.Sc Thesis

M.Sc StudentFleyer Michael
SubjectBlind Reconstruction of Sparse Multi-Band Signals Using
Synchronous Multi-Rate Optical Sampling
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Moshe Horowitz


Recent advances in electro-optical systems make them ideal for undersampling multiband signals with very high carrier frequencies. In this research, we propose and demonstrate experimentally a new scheme for sampling and reconstruction of several bandwidth limited signals when the signal bands locations are not known apriori. 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. Signals are reconstructed by finding a solution of an underdetermined system of linear equations.

The empirical reconstruction success rate is higher than obtained using the multi-coset sampling scheme when the number of the sampling channels is small and conditions for a perfect reconstruction in the multi-coset scheme are not fulfilled. The practical sampling system which is simulated in our work consists of only 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. Synchronous sampling has significant advantages as compared to the asynchronous sampling scheme that has been previously demonstrated. In particular, synchronous sampling gives higher reconstruction success rate since synchronization between channels enables to resolve aliasing that occurs in all sampling channels. We have demonstrated experimentally the SMRS scheme in optical system for undersampling several bandwidth-limited signals with carrier frequencies that are not known apriori and can be located within a broad frequency region 0-20 GHz. This is, for the best of our knowledge, the first optical system that is capable of undersampling and reconstructing signals with unknown carrier frequencies that are overlapped by other signals in all channels. The system is based on undersampling synchronously using three optical channels operating at different sampling rates. To use our reconstruction algorithm the system was accurately calibrated.

Blind reconstruction was demonstrated for thee different time-overlapping signals with bandwidth of about 200 MHz each. We could successfully reconstruct signals even in cases when they overlapped at the baseband in all three sampling channels. The dynamic range of the optical system and the jitter of the optical pulsed sources are experimentally characterized.