Sub-Nyquist Sampled Analog-to-Digital Conversion Based on Photonic Time Stretch and Compressive Sensing With Optical Random Mixing

An approach to realizing wideband analog-to-digital conversion based on the techniques of photonic time stretch (PTS) and compressive sensing (CS) is proposed. In the system, a multitone signal within a wide bandwidth (spectrally sparse) signal is slowed down in the time domain by a photonic time stretcher. The stretched signal is then down-sampled and reconstructed by a random-demodulator-based CS scheme, in which random mixing is realized in an optical domain. Thanks to the techniques of PTS and CS, wideband spectrally sparse signals can be acquired with a sampling rate far below the Nyquist rate of the original signal. The optical random mixing applied in the system has the advantages of lower distortions and larger bandwidth compared to its electrical counterpart. In order to construct a Gaussian measurement matrix with zero mean, balanced detection is applied after the optical mixer. In addition, in order to eliminate the dc component and the even-order harmonics of the stretched signal, we propose to use balanced PTS technique in the system. We demonstrate that a system with a time stretch factor 20 and a compression factor 4 can effectively acquire a spectrally sparse wideband signal, which means a sampling rate as low as 1/80 of the Nyquist rate.