Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and by the discretization of the frequency parameter space. In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most existing approaches in fidelity and tolerance to noise.

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.

In compressed sensing it is generally assumed that the dictionary matrix constitutes a (possibly overcomplete) basis of the signal space. In this paper we consider dictionaries that do not span the signal space, i.e. rank deficient dictionaries. We show that in this case the signal-to-noise ratio (SNR) in the compressed samples can be increased by selecting the rows of the measurement matrix from the column space of the dictionary. As an example application of compressed sensing with a rank deficient dictionary, we present a case study of compressed sensing applied to the Coarse Acquisition (C/A) step in a GPS receiver. Simulations show that for this application the proposed choice of measurement matrix yields an increase in SNR performance of up to 5-10 dB, compared to the conventional choice of a fully random measurement matrix. Furthermore, the compressed sensing based C/A step is compared to a conventional method for GPS C/A.

The technology of Radio Frequency IDentification (RFID) enables many applications that rely on passive, battery-less wireless devices. If a RFID reader needs to gather the ID from multiple tags in its range, then it needs to run an anticollision protocol. Due to errors on the wireless link, a single reader session, which contains one full execution of the anticollision protocol, may not be sufficient to retrieve the ID of all tags. This problem can be mitigated by running multiple, redundant reader sessions and use the statistical relationship between these sessions. On the other hand, each session is time consuming and therefore the number of sessions should be kept minimal. We optimize the process of running multiple reader sessions, by allowing only some of the tags already discovered to reply in subsequent reader sessions. The estimation procedure is integrated with an actual tree-based anticollision protocol, and numerical results show that the reliable tag resolution algorithm attain high speed of protocol execution, while not sacrificing the reliability of the estimators used to assess the probability of missing tags.