Constant-modulus sequence set with low peak sidelobe level is a necessity for enhancing the performance of modern active sensing systems like Multiple Input Multiple Output (MIMO) RADARs. In this paper, we consider the problem of designing a constant-modulus sequence set by minimizing the peak side-lobe level, which can be cast as a non-convex minimax problem, and propose a Majorization-Minimization technique based iterative monotonic algorithm named as the PSL minimizer. The iterative steps of our algorithm are computationally not very demanding and they can be efficiently implemented via Fast Fourier Transform (FFT) operations. We also establish the convergence of our proposed algorithm and discuss the computational and space complexities of the algorithm. Finally, through numerical simulations, we illustrate the performance of our method with the state-of-the-art methods. To highlight the potential of our approach, we evaluate the performance of the sequence set designed via our approach in the context of probing sequence set design for MIMO RADAR angle-range imaging application and show results exhibiting good performance of our method when compared with other commonly used sequence set design approaches.
Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a nonnegative matrix into a product of two nonnegative matrices which gives some meaningful interpretation of the data. Thus, nonnegative matrix factorization has an edge over the other decomposition techniques. In this paper, we propose two novel iterative algorithms based on Majorization Minimization (MM)-in which we formulate a novel upper bound and minimize it to get a closed form solution at every iteration. Since the algorithms are based on MM, it is ensured that the proposed methods will be monotonic. The proposed algorithms differ in the updating approach of the two nonnegative matrices. The first algorithm-Iterative Nonnegative Matrix Factorization (INOM) sequentially updates the two nonnegative matrices while the second algorithm-Parallel Iterative Nonnegative Matrix Factorization (PARINOM) parallely updates them. We also prove that the proposed algorithms converge to the stationary point of the problem. Simulations were conducted to compare the proposed methods with the existing ones and was found that the proposed algorithms performs better than the existing ones in terms of computational speed and convergence.
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