Compressive Sensing for Spread Spectrum Receivers

With the advent of ubiquitous computing there are two design parameters of wireless communication devices that become very important power: efficiency and production cost. Compressive sensing enables the receiver in such devices to sample below the Shannon-Nyquist sampling rate, which may lead to a decrease in the two design parameters. This paper investigates the use of Compressive Sensing (CS) in a general Code Division Multiple Access (CDMA) receiver. We show that when using spread spectrum codes in the signal domain, the CS measurement matrix may be simplified. This measurement scheme, named Compressive Spread Spectrum (CSS), allows for a simple, effective receiver design. Furthermore, we numerically evaluate the proposed receiver in terms of bit error rate under different signal to noise ratio conditions and compare it with other receiver structures. These numerical experiments show that though the bit error rate performance is degraded by the subsampling in the CS-enabled receivers, this may be remedied by including quantization in the receiver model. We also study the computational complexity of the proposed receiver design under different sparsity and measurement ratios. Our work shows that it is possible to subsample a CDMA signal using CSS and that in one example the CSS receiver outperforms the classical receiver.Comment: 11 pages, 11 figures, 1 table, accepted for publication in IEEE Transactions on Wireless Communication

Measurement Matrix Design for Compressive Sensing Based MIMO Radar

In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to a fusion center, where an L1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits the target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with many fewer measurements. The measurement matrix is vital for CS recovery performance. This paper considers the design of measurement matrices that achieve an optimality criterion that depends on the coherence of the sensing matrix (CSM) and/or signal-to-interference ratio (SIR). The first approach minimizes a performance penalty that is a linear combination of CSM and the inverse SIR. The second one imposes a structure on the measurement matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve SIR, while maintaining CSM comparable to that of the Gaussian random measurement matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM

Convolutional Sparse Support Estimator Network (CSEN) From energy efficient support estimation to learning-aided Compressive Sensing

Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy methods or optimization techniques. Indeed, a vast majority of them use sparse signal recovery techniques to obtain support sets instead of directly mapping the non-zero locations from denser measurements (e.g., Compressively Sensed Measurements). This study proposes a novel approach for learning such a mapping from a training set. To accomplish this objective, the Convolutional Support Estimator Networks (CSENs), each with a compact configuration, are designed. The proposed CSEN can be a crucial tool for the following scenarios: (i) Real-time and low-cost support estimation can be applied in any mobile and low-power edge device for anomaly localization, simultaneous face recognition, etc. (ii) CSEN's output can directly be used as "prior information" which improves the performance of sparse signal recovery algorithms. The results over the benchmark datasets show that state-of-the-art performance levels can be achieved by the proposed approach with a significantly reduced computational complexity

A Compressive Phase-Locked Loop

We develop a new method for tracking narrowband signals acquired through compressive sensing, called the compressive sensing phase-locked loop (CS-PLL). The CS-PLL enables one to track oscillating signals in very large bandwidths using a small number of measurements. Not only does the CS-PLL potentially operate below the Nyquist rate, it can extract phase and frequency information without the computational complexity normally associated with compressive sensing signal re-construction. The CS-PLL has a wide variety of applications, including but not limited to communications, phase tracking, robust control, sensing, and FM demodulation. In particular we emphasize the advantages of using this system in wideband surveillence systems. Our design modifies classical PLL designs to operate with CS-based sampling systems. Performance results are shown for PLLs operating on both real and complex data. In addition to explaining general performance tradeoffs, implementations using several different CS sampling systems are explored