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This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments. In many practical scenarios, the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace. We address the particularly troublesome cases of low interference-to-noise ratio (INR), relatively rapid interference motion, and correlated noise across the receiving array. A polynomial-based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time, mitigate interference subspace estimation errors, and improve canceler performance. The application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution. Here even weak residual interference after cancelation may obscure a signal of interest, so very deep beampattern nulls are required. Performance for conventional subspace projection (SP) is compared with polynomial-augmented SP using simulated and real experimental data, showing null-depth improvement of 6 to 30 dB. [ABSTRACT FROM PUBLISHER]