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Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the optimality of Gaussian signalling, an optimal transmit covariance matrix is known for some special cases only and the general case remains an open problem. An iterative custom-made algorithm to find a globally-optimal transmit covariance matrix in the general case is developed in this paper, with guaranteed convergence to a global optimum. While the original optimization problem is not convex and hence difficult to solve, its minimax reformulation can be solved via the convex optimization tools, which is exploited here. The proposed algorithm is based on the barrier method extended to deal with a minimax problem at hand. Its convergence to a global optimum is proved for the general case (degraded or not) and a bound for the optimality gap is given for each step of the barrier method. The performance of the algorithm is demonstrated via numerical examples. In particular, 20 to 40 Newton steps are already sufficient to solve the sufficient optimality conditions with very high precision (up to the machine precision level), even for large systems. Even fewer steps are required if the secrecy capacity is the only quantity of interest. The algorithm can be significantly simplified for the degraded channel case and can also be adopted to include the per-antenna power constraints (instead or in addition to the total power constraint). It also solves the dual problem of minimizing the total power subject to the secrecy rate constraint. [ABSTRACT FROM PUBLISHER]

Parameter estimation of multiple sinusoids is one of the fundamental problems of signal processing having numerous application areas, including wireless communications and array signal processing. This article proposes an iterative, fast, and efficient algorithm to estimate the frequencies and amplitudes of multiple sinusoids in noisy environments. The proposed approach interpolates on the q-shifted DFT coefficients of multiple sinusoids. We theoretically demonstrate that the performance of the proposed algorithm depends on DFT-shift, number of iterations and minimum DFT frequency separation parameters. Further, mean square error of the proposed algorithm achieves the Cramér-Rao lower bound when these parameters are selected appropriately. We also propose solid bounds regarding how these parameters can be selected for optimum overall performance. The total computational cost of the proposed algorithm is in the order of O(K N log N), where K is the number of sinusoidal components and N is the signal length. We provide comprehensive numerical simulations that confirm the correctness of our theoretical deductions. [ABSTRACT FROM AUTHOR]