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

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 CS-based 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

Democracy in action: Quantization, saturation, and compressive sensing

We explore and exploit a heretofore relatively unexplored hallmark of compressive sensing (CS), the fact that certain CS measurement systems are democratic, which means that each measurement carries roughly the same amount of information about the signal being acquired. Using this property, we re-think how to quantize the compressive measurements. In Shannon-Nyquist sampling, we scale down the analog signal amplitude (and therefore increase the quantization error) to avoid the gross saturation errors. In stark contrast, we demonstrate a CS system achieves the best performance when we operate at a significantly nonzero saturation rate. We develop two methods to recover signals from saturated CS measurements. The first directly exploits the democracy property by simply discarding the saturated measurements. The second integrates saturated measurements as constraints into standard linear programming and greedy recovery techniques. Finally, we develop a simple automatic gain control system that uses the saturation rate to optimize the input gain

Regime Change: Sampling Rate vs. Bit-Depth in Compressive Sensing

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement compression (MC) regime, a high SNR favors acquiring fewer measurements with more bits per measurement (as in conventional CS); in the quantization compression (QC) regime, a low SNR favors acquiring more measurements with fewer bits per measurement (as in this thesis). A surprise from our analysis and experiments is that in many practical applications it is better to operate in the QC regime, even acquiring as few as 1 bit per measurement. The above philosophy extends further to practical CS ADC system designs. We propose two new CS architectures, one of which takes advantage of the fact that the sampling and quantization operations are performed by two different hardware components. The former can be employed at high rates with minimal costs while the latter cannot. Thus, we develop a system that discretizes in time, performs CS preconditioning techniques, and then quantizes at a low rate

Stress, Health Risk Behaviors, and Weight Status Among Community College Students

The objective of this study was to describe the relationship between stress, weight-related health risk behaviors (e.g., eating behaviors, physical activity, sedentary behavior, sleep, cigarette smoking and binge drinking), and weight status using cross-sectional data on 2-year community college students enrolled in a randomized controlled weight gain prevention trial. Modified Poisson regression and linear regression were used to examine crude and adjusted cross-sectional associations. Higher stress was associated with higher prevalence of overweight/obesity (crude PR=1.05 [95% CI 1.01, 1.09]), though the relationship was no longer statistically significant after controlling for a wide range of weight-related health risk behaviors (adjusted PR=1.04 [95% CI 1.00, 1.08]). Stress levels were significantly associated with meal skipping and being a current smoker. Future research should investigate the mechanisms through which stress is related to obesity risk and examine the causes of stress among this understudied population to inform the design of appropriate interventions

Adolescent physical activity and screen time: associations with the physical home environment

<p>Abstract</p> <p>Background</p> <p>Previous research on the environment and physical activity has mostly focused on macro-scale environments, such as the neighborhood environment. There has been a paucity of research on the role of micro-scale and proximal environments, such as that of the home which may be particularly relevant for younger adolescents who have more limited independence and mobility. The purpose of this study was to describe associations between the home environment and adolescent physical activity, sedentary time, and screen time.</p> <p>Methods</p> <p>A total of 613 parent-adolescent dyads were included in these analyses from two ongoing cohort studies. Parents completed a Physical Activity and Media Inventory (PAMI) of their home environment. Adolescent participants (49% male, 14.5 ± 1.8 years) self-reported their participation in screen time behaviors and wore an ActiGraph accelerometer for one week to assess active and sedentary time.</p> <p>Results</p> <p>After adjusting for possible confounders, physical activity equipment density in the home was positively associated with accelerometer-measured physical activity (p < 0.01) among both males and females. Most of the PAMI-derived measures of screen media equipment in the home were positively associated with adolescent female's screen time behavior (p ≤ 0.03). In addition, the ratio of activity to media equipment was positively associated with physical activity (p = 0.04) in both males and females and negatively associated with screen time behavior for females (p < 0.01).</p> <p>Conclusions</p> <p>The home environment was associated with physical activity and screen time behavior in adolescents and differential environmental effects for males and females were observed. Additional research is warranted to more comprehensively assess the home environment and to identify obesogenic typologies of families so that early identification of at-risk families can lead to more informed, targeted intervention efforts.</p

Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

Wideband analog signals push contemporary analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the bandlimit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its bandlimit in Hz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations.Comment: 24 pages, 8 figure