Structured random measurements in signal processing

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements.Comment: 22 pages, 2 figure

Secrecy Rate of the Cooperative RSMA-Aided UAV Downlink Relying on Optimal Relay Selection

The Cooperative Rate-Splitting (CRS) scheme, proposed evolves from conventional Rate Splitting (RS) and relies on forwarding a portion of the RS message by the relaying users. In terms of secrecy enhancement, it has been shown that CRS outperforms its non-cooperative counterpart for a two-user Multiple Input Single Output (MISO) Broadcast Channel (BC). Given the massive connectivity requirement of 6G, we have generalized the existing secure two-user CRS framework to the multi-user framework, where the highest-security users must be selected as the relay nodes. This paper addresses the problem of maximizing the Worst-Case Secrecy Rate (WCSR) in a UAV-aided downlink network where a multi-antenna UAV Base-Station (UAV-BS) serves a group of users in the presence of an external eavesdropper (Eve). We consider a practical scenario in which only imperfect channel state information of Eve is available at the UAV-BS. Accordingly, we conceive a robust and secure resource allocation algorithm, which maximizes the WCSR by jointly optimizing both the Secure Relaying User Selection (SRUS) and the network parameter allocation problem, including the RS transmit precoders, message splitting variables, time slot sharing and power allocation. To circumvent the resultant non-convexity owing to the discrete variables imposed by SRUS, we propose a two-stage algorithm where the SRUS and network parameter allocation are accomplished in two consecutive stages. With regard to the SRUS, we study both centralized and distributed protocols. On the other hand, for jointly optimizing the network parameter allocation we resort to the Sequential Parametric Convex Approximation (SPCA) algorithm. Our numerical results show that the proposed solution significantly outperforms the existing benchmarks for a wide range of network loads in terms of the WCSR.Comment: arXiv admin note: text overlap with arXiv:1910.07843 by other author