Recovery under Side Constraints

This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using L1-minimization. Furthermore, for constant modulus signals, signals with row-, block- and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning

Distributed UAV Swarm Augmented Wideband Spectrum Sensing Using Nyquist Folding Receiver

Distributed unmanned aerial vehicle (UAV) swarms are formed by multiple UAVs with increased portability, higher levels of sensing capabilities, and more powerful autonomy. These features make them attractive for many recent applica-tions, potentially increasing the shortage of spectrum resources. In this paper, wideband spectrum sensing augmented technology is discussed for distributed UAV swarms to improve the utilization of spectrum. However, the sub-Nyquist sampling applied in existing schemes has high hardware complexity, power consumption, and low recovery efficiency for non-strictly sparse conditions. Thus, the Nyquist folding receiver (NYFR) is considered for the distributed UAV swarms, which can theoretically achieve full-band spectrum detection and reception using a single analog-to-digital converter (ADC) at low speed for all circuit components. There is a focus on the sensing model of two multichannel scenarios for the distributed UAV swarms, one with a complete functional receiver for the UAV swarm with RIS, and another with a decentralized UAV swarm equipped with a complete functional receiver for each UAV element. The key issue is to consider whether the application of RIS technology will bring advantages to spectrum sensing and the data fusion problem of decentralized UAV swarms based on the NYFR architecture. Therefore, the property for multiple pulse reconstruction is analyzed through the Gershgorin circle theorem, especially for very short pulses. Further, the block sparse recovery property is analyzed for wide bandwidth signals. The proposed technology can improve the processing capability for multiple signals and wide bandwidth signals while reducing interference from folded noise and subsampled harmonics. Experiment results show augmented spectrum sensing efficiency under non-strictly sparse conditions

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201