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The topic of sequence design has received considerable attention due to its wide applications in active sensing. One important desired property for the design sequence is the spectral shape. In this paper, the sequence design problem is formulated by minimizing the regularized spectral level ratio subject to a peak-to-average power ratio constraint. Then, two algorithms are proposed by combining both the Dinkelbach's algorithm and the majorization–minimzation (MM) method organically. Specifically, by using the Dinkelbach's algorithm, the challenging fractional programming problem can be handled by solving a series of subproblems, which are further solved via the MM method. The numerical experiments verify the effectiveness of the optimization metric and demonstrate the performance of the proposed algorithms compared with the benchmark.
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