Cognitive waveform design with desired spectrum-autocorrelation properties

This paper proposes a novel cognitive waveform design methodology aimed at shaping a specified spectrum and achieving good autocorrelation properties in terms of the spectrum band notch and local autocorrelation peak sidelobe level (A-PSL). To this end, the Pareto optimization framework is introduced that minimizes the lp-norm of multi-objective functions both encompassing the stopband energy and local A-PSL. In addition, along with energy and peak-to-average power ratio constraints to ensure hardware compatibility, the out-of-band (OOB) spectrum energy and the rest autocorrelation sidelobe level are restricted to resist the OOB strong interference (also prevent spectrum leakage) and enhance multiple target detectability, respectively. To tackle the resultant nonconvex nonsmooth (in general NP-hard) design problem, an iterative majorization minimization proximal method of multipliers (MM-PMM) algorithm is developed along with each iteration involving multiple subproblems which are solved through a majorization method or closed-form solutions. In particular, resorting to Wiener-Khintchine theorem, the developed algorithm is efficiently implemented via the fast fourier transform and element-wise arithmetic. Extensive numerical examples highlight that the synthesized waveform shares the desired spectrum-autocorrelation properties and is capable of enhancing the weak target detection and anti-jamming performance in comparison with some counterparts.