Optimizing FECAF in MTSFM Waveforms Using Conjugate Gradient Descent With Efficient Line Search for Radar and Sonar Applications

Optimizing waveforms in radar and sonar systems is crucial for enhancing spectral efficiency and target detection capabilities, yet this process often faces challenges like computational complexity and convergence issues. This research introduces a novel method that leverages the frequency-domain exponential cross ambiguity function (FECAF) within multi-tone sinusoidal frequency modulated (MTSFM) waveforms, combined with the Conjugate Gradient Method with Efficient Line Search (CGM-ELS) for optimization. The optimization of MTSFM waveforms is achieved by combining the generalized integrated sidelobe level (GISL) and peak-to-mean power envelope ratio (PMEPR) metrics. The GISL metric controls the main lobe and sidelobe structure of the waveform's autocorrelation function (ACF), quantifying unwanted energy in sidelobes to find an optimal compromise. PMEPR ensures efficient operation of radar or sonar transmitters by minimizing energy variations in the waveform's envelope, which is crucial for peak power-limited systems. To optimize these metrics, the CGM-ELS algorithm is employed, ensuring efficient convergence through iterative adjustment of waveform parameters based on gradient information and penalty functions. The proposed method transforms the optimization problem into an unconstrained format, reducing computational complexity and improving convergence rates. Experimental results have shown significant enhancements in computational efficiency and convergence rate, demonstrating the effectiveness of the CGM-ELS algorithm in synthesizing waveforms with optimal ambiguity function characteristics for radar and sonar applications.