This paper investigates the problem of localization of co-channel transmitters or primary users (PUs) using an array mounted on a moving aerial platform. As a practical alternative for a sensor network to pursue the localization task, the proposed Phase Interferometric Source Localization (PISL) technique utilizes a moving sensor that measures phase difference between two antennas mounted on the platform. Due to the sparse nature of PUs’ distribution in the region, we model the localization task as a simple basis-pursuit denoising framework and introduce a reconstruction method using a sparse recovery algorithm to discover locations of unknown PUs based on the phase difference measurements. We show that the ratio of distance between two antennas to the carrier-frequency wavelength is the critical parameter making the localization feasible. We also propose a scheme for sensor motion design in order to maximize the number of detectable PUs based on mutual coherence property. Since the motion optimization problem is very hard to address we develop a simple geometric relaxation to address the problem. The simulation results show that PISL can precisely recover the map of PUs with only few measurements and also reveal that sensor motion path can have determinate effect on the localization accuracy. PISL performance is compared with an state-of-the-art technique that utilizes adaptive beamforming and results show the superiority of PISL results in localization accuracy.

We propose a novel technique for finding representatives from a large, unsupervised dataset. The approach is based on the concept of self-rank, defined as the minimum number of samples needed to reconstruct all samples with an accuracy proportional to the rank-$K$ approximation. Our proposed algorithm enjoys linear complexity w.r.t. the size of original dataset and simultaneously it provides an adaptive upper bound for approximation ratio. These favorable characteristics result in filling a historical gap between practical and theoretical methods in finding representatives.

In this paper, a framework for localization of multiple co-channel transmitters using phase difference measurements between two antennas mounted on sensors of a sensor network is proposed. To pursue localization, we equip each sensor with two antennas and we use temporal cross-correlations between the received signals of the {two} antennas to extract the phase differences between each antenna pairs, named as phase interferometry measurements (PIMs), provoked by each {transmitters} using tensor decomposition. We calculate Cramer-Rao lower bound of error of localization using PIMs. Our simulation results show that highly accurate estimations can be achieved using PIMs. We also compare the accuracy of our proposed technique with a sensor network that exploits highly directional linear array antennas and show that {our} proposed technique can perform similar to a network that employs very large antenna arrays.

Finding a small subset of data whose linear combination spans other data points, also called column subset selection problem (CSSP), is an important open problem in computer science with many applications in computer vision and deep learning. There are some studies that solve CSSP in a polynomial time complexity w.r.t. the size of the original dataset. A simple and efficient selection algorithm with a linear complexity order, referred to as spectrum pursuit (SP), is proposed that pursuits spectral components of the dataset using available sample points. The proposed non-greedy algorithm aims to iteratively find K data samples whose span is close to that of the first K spectral components of entire data. SP has no parameter to be fine tuned and this desirable property makes it problem-independent. The simplicity of SP enables us to extend the underlying linear model to more complex models such as nonlinear manifolds and graph-based models. The nonlinear extension of SP is introduced as kernel-SP (KSP). The superiority of the proposed algorithms is demonstrated in a wide range of applications.