5 research outputs found
Optimum sparse subarray design for multitask receivers
The problem of optimum sparse array configuration to maximize the beamformer output signal-to-interference plus noise ratio (MaxSINR) in the presence of multiple sources of interest (SOI) has been recently addressed in the literature. In this paper, we consider a shared aperture system where
optimum sparse subarrays are allocated to individual SOIs and collectively span the entire full array receiver aperture. Each
subarray may have its own antenna type and can comprise a different number of antennas. The optimum joint sparse subarray design for shared aperture based on maximizing the
sum of the subarray beamformer SINRs is considered with and without SINR threshold constraints. We utilize Taylor series approximation and sequential convex programming (SCP) techniques to render the initial non-convex optimization a convex
problem. The simulation results validate the shared aperture design solutions for MaxSINR for both cases where the number of sparse subarray antennas is predefined or left to comstitute an optimization variable
Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching
In this work, we propose a novel strategy of adaptive sparse array beamformer
design, referred to as regularized complementary antenna switching (RCAS), to
swiftly adapt both array configuration and excitation weights in accordance to
the dynamic environment for enhancing interference suppression. In order to
achieve an implementable design of array reconfiguration, the RCAS is conducted
in the framework of regularized antenna switching, whereby the full array
aperture is collectively divided into separate groups and only one antenna in
each group is switched on to connect with the processing channel. A set of
deterministic complementary sparse arrays with good quiescent beampatterns is
first designed by RCAS and full array data is collected by switching among them
while maintaining resilient interference suppression. Subsequently, adaptive
sparse array tailored for the specific environment is calculated and
reconfigured based on the information extracted from the full array data. The
RCAS is devised as an exclusive cardinality-constrained optimization, which is
reformulated by introducing an auxiliary variable combined with a piece-wise
linear function to approximate the -norm function. A regularization
formulation is proposed to solve the problem iteratively and eliminate the
requirement of feasible initial search point. A rigorous theoretical analysis
is conducted, which proves that the proposed algorithm is essentially an
equivalent transformation of the original cardinality-constrained optimization.
Simulation results validate the effectiveness of the proposed RCAS strategy
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Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval
Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims