A Compact Formulation for the ℓ2,1\ell_{2,1} Mixed-Norm Minimization Problem

Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of- arrival estimation. Recently, this problem has been address using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixed-norm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work we derive an equivalent, compact reformulation of the $\ell_{2,1}$ mixed-norm minimization problem which provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the $\ell_{2,1}$ mixed-norm minimization and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method

Sensor Array Signal Processing via Eigenanalysis of Matrix Pencils Composed of Data Derived from Translationally Invariant Subarrays

An algorithm is developed for estimating characteristic parameters associated with a scene of radiating sources given the data derived from a pair of translationally invariant arrays, the X and Y arrays, which are displaced relative to one another. The algorithm is referred to as PR O—E SPRIT and is predicated on invoking two recent mathematical developments: (1) the SVD based solution to the Procrustes problem of optimally approximating an invariant subspace rotation and (2) the Total Least Squares method for perturbing each of the two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same. For uniform linear array scenarios, the use of forward-backward averaging (FBAVG) in conjunction with PR O—E S PR IT is shown to effect a substantial reduction in the computational burden, a significant improvement in performance, a simple scheme for estimating the number of sources and source decorrelation. These gains may be attributed to FBAVG’s judicious exploitation of the diagonal invariance operator relating the Direction of Arrival matrix of the Y array to that associated with the X array. Similar gains may be achieved in the case where the X and Y arrays are either not linear or not uniformly spaced through the use of pseudo-forward-backward averaging (PFBAVG). However, the use of PFBAVG does not effect source decorrelation and reduces the maximum number of resolvable sources by a factor of two. Simulation studies and the results of applying PR O—E S PR IT to real data demonstrate the excellent performance of the method

Efficient method of estimating Direction of Arrival (DOA) in communications systems.

Masters Degree. University of KwaZulu- Natal, Durban.In wireless communications systems, estimation of Direction of Arrival (DOA) has been used both for military and commercial purposes. The signal whose DOA is being estimated, could be a signal that has been reflected from a moving or stationary object, or a signal that has been generated from unwanted or illegal transmitter. When combined with estimating time of arrival, it is also possible to pinpoint the location of a target in space. Localization in space can also be achieved by estimating DOA using two receiving nodes with capability of estimating DOA. The beamforming pattern in smart antenna system is adjusted to emphasize the desired signal and to minimize the interference signal. Therefore, DOA estimation algorithms are critical for estimating the Angle of Arrival (AOA) and beamforming in smart antennas. This dissertation investigates the performance, angular accuracy and resolution of the Minimum Variance Distortionless Response (MVDR), Multiple Signal Classification (MUSIC) and our proposed method Advanced Multiple Signal Classification (A-MUSIC) as DOA algorithms on both Non-Uniform Array (NLA) and Uniform Linear Array (ULA). DOA is critical in antenna design for emphasizing the desired signal and minimizing interference. The scarcity of radio spectrum has fuelled the migration of communication networks to higher frequencies. This has resulted into radio propagation challenges due to the adverse environmental elements otherwise unexperienced at lower frequencies. In rainfall-impacted environments, DOA estimation is greatly affected by signal attenuation and scattering at the higher frequencies. Therefore, new DOA algorithms cognisant of these factors need to be developed and the performance of the existing algorithms quantified. This work investigates the performance of the Conventional Minimum Variance Distortion-less Look (MVDL), Subspace DOA Estimation Methods of Multiple Signal Classification (MUSIC) and the developed hybrid DOA algorithm on a weather impacted wireless channel. The performance of the proposed Advanced-MUSIC (A-MUSIC) algorithm is compared to the conventional DOA estimation algorithms of Minimum Variance Distortionless Response (MVDR) and the Multiple Signal Classification (MUSIC) algorithms for both NLA and ULA antenna arrays. The developed simulation results show that A-MUSIC shows superior performance compared to the two other algorithms in terms of Signal Noise Ratio (SNR) and the number of antenna elements. The results show performance degradation in a rainfall impacted communication network with the developed algorithm showing better performance degradation

Compact Formulations for Sparse Reconstruction in Fully and Partly Calibrated Sensor Arrays

Sensor array processing is a classical field of signal processing which offers various applications in practice, such as direction of arrival estimation or signal reconstruction, as well as a rich theory, including numerous estimation methods and statistical bounds on the achievable estimation performance. A comparably new field in signal processing is given by sparse signal reconstruction (SSR), which has attracted remarkable interest in the research community during the last years and similarly offers plentiful fields of application. This thesis considers the application of SSR in fully calibrated sensor arrays as well as in partly calibrated sensor arrays. The main contributions are a novel SSR method for application in partly calibrated arrays as well as compact formulations for the SSR problem, where special emphasis is given on exploiting specific structure in the signals as well as in the array topologies

3-D Beamspace ML Based Bearing Estimator Incorporating Frequency Diversity and Interference Cancellation

The problem of low-angle radar tracking utilizing an array of antennas is considered. In the low-angle environment, echoes return from a low flying target via a specular path as well as a direct path. The problem is compounded by the fact that the two signals arrive within a beamwidth of each other and are usually fully correlated, or coherent. In addition, the SNR at each antenna element is typically low and only a small number of data samples, or snapshots, is available for processing due to the rapid movement of the target. Theoretical studies indicates that the Maximum Likelihood (ML) method is the only reliable estimation procedure in this type of scenario. However, the classical ML estimator involves a multi-dimensional search over a multi-modal surface and is consequently computationally burdensome. In order to facilitate real time processing, we here propose the idea of beamspace domain processing in which the element space snapshot vectors are first operated on by a reduced Butler matrix composed of three orthogonal beamforming weight vectors facilitating a simple, closed-form Beamspace Domain ML (BDML) estimator for the direct and specular path angles. The computational simplicity of the method arises from the fact that the respective beams associated with the three columns of the reduced Butler matrix have all but three nulls in common. The performance of the BDML estimator is enhanced by incorporating the estimation of the complex reflection coefficient and the bisector angle, respectively, for the symmetric and nonsymmetric multipath cases. To minimize the probability of track breaking, the use of frequency diversity is incorporated. The concept of coherent signal subspace processing is invoked as a means for retaining the computational simplicity of single frequency operation. With proper selection of the auxiliary frequencies, it is shown that perfect focusing may be achieved without iterating. In order to combat the effects of strong interfering sources, a novel scheme is presented for adaptively forming the three beams which retains the feature of common nulls

A pre-filtering maximum likelihood approach to multiple source direction estimation.

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