From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Abstract

Abstract-Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.

Photonic compressive sensing enabled data efficient time stretch optical coherence tomography

“…Figure 2 shows the single tone signal convoluted with time stretched MLL Gaussian pulses. As the number of measurements required linearly dependent on sparse tones, the number of measurements required are higher in this case 17 .…”

Compressive power spectral density estimation

“…Lastly, this estimation technique can, in principle, be extended to other CS sampling structures. In particular, the modulated wideband converter [4] operates on the same principles as the MC sampler and results in nearly the same Fourier description. Thus, despite the differences in the systems' sampling mechanisms, it should be possible to develop a similar estimator for the modulated wideband converter.…”

“…A number of compressed sensing (CS) structures have been proposed for sub-Nyquist sampling of continuous-time signals [1][2][3][4]. 1 All of these systems extend CS theory and serve as viable mechanisms to "compressively" acquire these types of signals.…”

CR Technology and Activation Plan for White Space Utilization

“…이러한 문제를 기술적으로 해결하 [19,20] . 압축 센싱 이론은 신호처리분야 전 반에 활용 가능한 일반적인 이론으로 이를 스펙트럼 센싱에 적용하기 위한 선행 연구들이 진행되었다 [16,21] . [13] .…”