Sub-Nyquist radar prototype: Hardware and algorithm

Abstract

Traditional radar sensing typically employs matched filtering between the received signal and the shape of the transmitted pulse. Matched filtering (MF) is conventionally carried out digitally, after sampling the received analog signals. Here, principles from classic sampling theory are generally employed, requiring that the received signals be sampled at twice their baseband bandwidth. The resulting sampling rates necessary for correlation-based radar systems become quite high, as growing demands for target distinction capability and spatial resolution stretch the bandwidth of the transmitted pulse. The large amounts of sampled data also necessitate vast memory capacity. In addition, real-time data processing typically results in high power consumption. Recently, new approaches for radar sensing and estimation were introduced, based on the finite rate of innovation (FRI) and Xampling frameworks. Exploiting the parametric nature of radar signals, these techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's estimation capabilities at sufficiently high signal-to-noise ratios (SNRs). Here we present for the first time a design and implementation of an Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demonstrate by real-time analog experiments that our system is able to maintain reasonable recovery capabilities, while sampling radar signals that require sampling at a rate of about 30 MHz at a total rate of 1 MHz.

Cognitive sub-Nyquist hardware prototype of a collocated MIMO radar

“…An ADC can not, however, individually acquire each of the randomly chosen Fourier coefficients. Therefore, sub-Nyquist radar prototype in [15] opted for sampling random disjoint subsets of κ, with each subset containing consecutive Fourier coefficients. The prototype in [15] used four random Fourier coefficient groups, pre-filtered the baseband signal to corresponding four subbands (or Xampling slices), and sampled each subband via separate low-rate ADC.…”

“…The prototype can be configured either as a filled or thinned array, thereby allowing comparison of Nyquist and sub-Nyquist spatial sampling using the same hardware. Our previous work in [15] presented the hardware realization of spectral sub-Nyquist sampling in radar. In [15], a few randomly chosen, narrow subbands of the received signal spectrum are pre-filtered before being sampled by low-rate analog-to-digital converters (ADCs).…”

“…Our previous work in [15] presented the hardware realization of spectral sub-Nyquist sampling in radar. In [15], a few randomly chosen, narrow subbands of the received signal spectrum are pre-filtered before being sampled by low-rate analog-to-digital converters (ADCs). Since this implementation uses a bandpass filter and an ADC for each subband, a similar implementation of spectral sub-Nyquist sampling in each channel of a MIMO receiver would require enormous hardware resources.…”

Compressive Shift Retrieval

“…Since the signal itself is not of interest to the application, we might consider an alternative sampling scheme to directly estimate the shift without first reconstructing the signal. These ideas have in fact been recently explored in the context of radar and ultrasound [13], [14], [15], [16] with continuous time signals and multiple shifts. Here we consider a related problem and ask: What is the minimal information rate to shift retrieval when two related discrete-time signals are under-sampled?…”

“…Furthermore, CSR reduces both the computational load and the number of samples needed in the process. This is of particular interest since recent developments in sampling [17], [18], [19] have shown that Fourier coefficients can be efficiently obtained from space (or time) measurements by the use of an appropriate filter and by subsampling the output. Remarkably, our results also show that in some cases sampling as few as one Fourier coefficient is enough to perfectly recover the true shift.…”