Analysis of compressive sensing with optical mixing using a spatial light modulator.

Compressive sensing (CS) in a photonic link has a high potential for acquisition of wideband sparse signals. In CS it is necessary to mix the input sparse signal with a pseudorandom sequence prior to subsampling. A pulse shaper with a spatial light modulator (SLM) can be used in photonic CS as an optical mixer to improve the speed of mixing. In this approach, the sparse signal is modulated on a chirped optical pulse and the pseudorandom sequence is recorded on the SLM within the pulse shaper. The optical mixing in the frequency domain is realized based on the principle of frequency-to-time mapping. In this paper, we investigate the performance and limitations of photonic CS with an SLM in detail. A theoretical model to describe optical mixing based on frequency-to-time mapping is presented. We point out that there is an upper limit on the length of the pseudorandom sequence recorded on the SLM that can be mixed with the sparse signal due to the condition of the far-field approximation of the frequency-to-time mapping. Since the length of the pseudorandom sequence is one of the major factors that affect the signal recovery performance in CS, this limitation should be fully considered in the system design of the CS with optical mixing in the frequency domain. We present numerical and experimental results to verify the theoretical findings. Discussion on the performance improvement is also presented.