This paper presents a significant modification to the Random Demodulator (RD)of Tropp et al. for sub-Nyquist sampling of frequency-sparse signals. Themodification, termed constrained random demodulator, involves replacing therandom waveform, essential to the operation of the RD, with a constrainedrandom waveform that has limits on its switching rate because fast switchingwaveforms may be hard to generate cleanly. The result is a relaxation on thehardware requirements with a slight, but manageable, decrease in the recoveryguarantees. The paper also establishes the importance of properly choosing thestatistics of the constrained random waveform. If the power spectrum of therandom waveform matches the distribution on the tones of the input signal(i.e., the distribution is proportional to the power spectrum), then recoveryof the input signal tones is improved. The theoretical guarantees provided inthe paper are validated through extensive numerical simulations and phasetransition plots.
展开▼
