The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding versus Dynamic Range

Abstract

Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in the design of a wideband radio receiver in a noisy environment. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. We then evaluate the performance of a CS-based receiver in two ways: via a theoretical analysis of its expected performance, with a particular emphasis on noise and dynamic range, and via simulations that compare the CS receiver against the performance expected from a conventional implementation. On the one hand, we show that CSbased systems that aim to reduce the number of acquired measurements are somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of subsampling, which parallels the classic noise-folding phenomenon. On the other hand, we demonstrate that since they sample at a lower rate, CS-based systems can potentially attain a significantly larger dynamic range. Hence, we conclude that while a CS-based system has inherent limitations that do impose some restrictions on its potential applications, it also has attributes that make it highly desirable in a number of important practical settings.

Wireless Compressive Sensing for Energy Harvesting Sensor Nodes

“…The MSE performance under bounded noise is studied in the CS literature [3], [15], [16]. Note that there is often a trade-off between the two quantities.…”

Sparsity and Structure in Hyperspectral Imaging : Sensing, Reconstruction, and Target Detection

“…In contrast, by combining random combinations of voxels into a single measurement, compressive systems dramatically reduce the dynamic range over which the measurements that we must quantize can fluctuate. This has been studied in the context of analogto-digital conversion in [37] and is apparent in comparing the first and second columns of Figure 3. For a given bit-depth, this reduced range can allow for reduced quantization error in the compressive case.…”

Compressive Sampling Based Energy Detection of Ultra-Wideband Pulse Position Modulation

“…The C-ED remains a bit away from the C-BEP because the Gaussian measurement matrix does not guarantee (5). Now with regard to the performance of the compressed detectors against the Nyquist-rate detectors, we see that at a compression ratio of , i.e., the sampling rate is only 50% of the Nyquist-rate, the compressed rate detectors offer a reasonably good performance (see [48] for details on the loss incurred due to CS). The C-ED performs better than the reconstructed version, i.e., the R-ED.…”