Compressive Parameter Estimation in AWGN

Abstract

Abstract-Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the signal space. In this paper, we establish a framework for estimation of continuous-valued parameters based on compressive measurements on a signal corrupted by additive white Gaussian noise (AWGN). While standard compressed sensing based on naive discretization has been shown to suffer from performance loss due to basis mismatch, we demonstrate that this is not an inherent property of compressive measurements. Our contributions are summarized as follows: (a) We identify the isometries required to preserve fundamental estimation-theoretic quantities such as the Ziv-Zakai bound (ZZB) and the Cramér-Rao bound (CRB). Under such isometries, compressive projections can be interpreted simply as a reduction in "effective SNR." (b) We show that the threshold behavior of the ZZB provides a criterion for determining the minimum number of measurements for "accurate" parameter estimation. (c) We provide detailed computations of the number of measurements needed for the isometries in (a) to hold for the problem of frequency estimation in a mixture of sinusoids. We show via simulations that the design criterion in (b) is accurate for estimating the frequency of a single sinusoid.

Application of Compressive Sensing in Cognitive Radio Communications: A Survey

“…The CS theory can be further extended to address the detection, estimation and classification problems. In this context, the most relevant works are the discussions of compressive parameter estimation in [34], [35], compressive detection in [36], [42], [43] and compressive classification in [36], [43], [46], [47].…”

“…will allow the CR to implement underlay CR techniques such as cognitive beamforming [139], cognitive interference alignment [140], Exclusion Zone (EZ), and power control [141]. Due to the practical constraints in the acquisition hardware, the CS-based approach can be utilized to estimate these parameters compressively, leading to the saving in the hardware resources [34]. In the following, we describe the existing contributions which utilized the CS approach in order to acquire these parameters.…”

A compressive channel estimation technique robust to synchronization impairments

“…Nr for our analysis; off grid extensions can be made using [3] [8]. We test our algorithm using off-grid parameters in the simulations.…”

“…Having obtainedĜ using Algorithm 1, we now need to split it into a matrix and a vector, corresponding to C and p respectively, as G = C ⊚ p. This decomposition is performed using singular value decomposition (svd) ofĜ (3) , the mode 3 unfolding ofĜ. In other words,p and vec C are the left and right singular vectors corresponding to the maximum singular value ofĜ (3) . The final step of unfolding the tensor along mode 3 followed by the SVD is inspired by [12].…”

Localization of Cooperative WSN using Distributed PSO with Optimum References

“…Cooperative localization method improves positioning accuracy [5], but increases the computational complexity, network traffic and delay. Some of the positional information may also be destructive as some devices have poor estimates [6].…”