Multirate Synchronous Sampling of Sparse Multiband Signals

Abstract

Recent advances in optical systems make them ideal for undersampling multiband signals that have high bandwidths. In this paper we propose a new scheme for reconstructing multiband sparse signals using a small number of sampling channels. The scheme, which we call synchronous multirate sampling (SMRS), entails gathering samples synchronously at few different rates whose sum is significantly lower than the Nyquist sampling rate. The signals are reconstructed by solving a system of linear equations. We have demonstrated an accurate and robust reconstruction of signals using a small number of sampling channels that operate at relatively high rates. Sampling at higher rates increases the signal to noise ratio in samples. The SMRS scheme enables a significant reduction in the number of channels required when the sampling rate increases. We have demonstrated, using only three sampling channels, an accurate sampling and reconstruction of 4 real signals (8 bands). The matrices that are used to reconstruct the signals in the SMRS scheme also have low condition numbers. This indicates that the SMRS scheme is robust to noise in signals. The success of the SMRS scheme relies on the assumption that the sampled signals are sparse. As a result most of the sampled spectrum may be unaliased in at least one of the sampling channels. This is in contrast to multicoset sampling schemes in which an alias in one channel is equivalent to an alias in all channels. We have demonstrated that the SMRS scheme obtains similar performance using 3 sampling channels and a total sampling rate 8 times the Landau rate to an implementation of a multicoset sampling scheme that uses 6 sampling channels with a total sampling rate of 13 times the Landau rate.

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

“…Though this may be an interesting task for experts, it contradicts the basic goal of our design-that is, using standard and available devices. In [15] a nonconventional ADC is designed by means of high-rate optical devices. The hybrid optic-electronic system introduces a front-end whose bandwidth reaches the wideband regime, at the expense and size of an optical system.…”

“…3. Calculating the coefficients in this setting gives (15) Evaluating the integral we have (16) where , and thus (17) Let be the discrete Fourier transform matrix (DFT) whose th column is (18) with , and let be the matrix with columns -a reordered column subset of . Note that for is unitary.…”

Efficient Recovery of Sub-Nyquist Sampled Sparse Multi-Band Signals Using Reconfigurable Multi-Channel Analysis and Modulated Synthesis Filter Banks

“…Thus, at any given time frame, the users can be allocated either the granularity bands {6-9, 14, 15, 22, 23} or the bands {6, 7, 14, 15, 22-25}. For the above two possible combination of band locations (two modes), we used the subNyquist sampling points, m = 0, 3,5,14,16,19,21,30, which ensures that D in (11) is an invertible matrix. The sampling instants were determined using the method in [29].…”

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

“…The same authors proposed later [6] a set of TI-ADCs working synchronously (i.e., with τ i = 0, i = 0, . .…”

“…Different sampling patterns to operate different TI-ADC architectures have been reported, e.g., in [5,6,7,8]. All these works assume that the wideband signal is multiband sparse (i.e., only a small number of frequency subbands are occupied) and that the locations of the occupied subbands are not known a priori.…”