Spectral Estimation Based On Spatial And Temporal Compressed Sampling

Spectral analysis and sensing,which consider the problem of determining the spectral content of a signal from a finite set of measurements,has been of a growing interest in signal processing and wireless communications.For example,wideband spectrum sensing is a key functionality in Cognitive Radio(CR),which aims to identify the frequency locations of a number of narrowband transmissions that spread over a wide frequency band.To perform wideband spectrum sensing,a conventional receiver requires to sample the received signal at a Nyquist rate,which may be infeasible if the spectrum under monitoring is very wide,say,reaches several GHz.Also,spectral analysis in the spatial domain is of great importance in locating the radiating sources using a phased array.To have a higher spatial resolution in direction of arrival(DoA)estimation and to resolve more sources,the number of antennas in the receiver should be increased.In a radar or communication system,the hardware cost and power consumption could become prohibitively high if a large number of antennas are deployed.In this thesis,to overcome the hardware limitations mentioned above,the problem of spectral analysis and sensing based on temporal and spatial compressed sampling is investigated.The main contributions of this thesis are listed below:1)The line spectral estimation problem based on super-resolution compressed sensing is considered,and is formulated as a sparse signal recovery problem with an unknown parametric dictionary.The log-sum sparsity-encouraging penalty function is introduced,and an iterative reweighted method is proposed which jointly estimates the sparse signals and the unknown parameters associated with the true dictionary.A simple yet effective scheme is developed for adaptively updating the regularization parameter that controls the tradeoff between the sparsity of the solution and the data fitting error.Theoretical analysis is conducted to justify the proposed method.Simulation results show that the proposed algorithm achieves super resolution and outperforms other state-of-the-art methods in many cases of practical interest.2)Super-resolution line spectral estimation problem with the prior knowledge of the frequency distribution is concerned.To exploit the prior knowledge,a weighting function designed according to the frequency distribution is introduced.The prior information can be harnessed through minimizing the corresponding weighted log-sum penalty function.An iterative reweighted algorithm is proposed to solve this optimization problem.Simulation results show that the proposed algorithm outperforms other methods both in noiseless and noisy case.3)The problem of joint wideband spectrum sensing and DoA estimation in a temporal sub-Nyquist sampling framework is studied.Specifically,the objective is to estimate the carrier frequencies and the DoAs associated with the narrow-band sources,as well as reconstruct the power spectra of these narrow-band signals.A new phased-array-based sub-Nyquist sampling architecture with flexible time delays is proposed,where a uniform linear array(ULA)is employed and the received signal at each antenna is delayed by a flexible amount of time and then sampled by a low-rate analog–digital converter(ADC).Based on the collected sub-Nyquist samples,we calculate a set of cross-correlation matrices with different time lags,and develop a tensor decomposition-based method for joint DoA,carrier frequency,and power spectrum recovery.Conditions for perfect recovery of the associated parameters and the power spectrum are analyzed.Simulation results show that our proposed method presents a clear performance advantage over existing methods,and achieves an estimation accuracy close to the associated Cramér-Rao bound(CRB)using only a small number of data samples.4)Wideband DoA estimation with sparse linear array(SLA)is concerned.We rely on the assumption that the power spectrum of the wideband sources is the same up to a scaling factor,which could in theory allow us to resolve not only more sources than the number of antennas but also more sources than the number of degrees of freedom(DoF)of the difference co-array of the SLA.We resort to the Jacobi-Anger approximation to transform the co-array response matrices of all frequency bins into a single virtual ULA response matrix.Based on the obtained model,two super-resolution DoA estimation approaches based on atomic norm minimization(ANM)are proposed,one with and one without prior knowledge of the power spectrum.Simulation results show that our proposed methods outperform the state of the art and are indeed capable of resolving more sources than the number of DoF of the difference co-array.