Multiple frequencies estimation from compressive phase-only data: algorithm and application

In the article, the issue of multiple frequencies estimation from compressive phase-only data is addressed. A phase-only frequency receiver scheme based on compressive sensing technique is presented first. Then, we propose two reconstruction algorithms: one is convex; and the other is hybrid, which is based on robust optimisation and iterative hard threshold. With these methods, multiple frequencies estimation is accomplished by reconstructing the Fourier transform of the complex-valued time signal and finding peaks in the frequency domain. Simulation experiments illustrate its advantages both with noiseless and additive white Gaussian noise(AWGN) cases. Finally, the effects of phase quantisation errors (it would happen in a phase-to-digital converter) on the reconstruction algorithms are discussed.