Systematic approach in designing wavelet packet modulation-orthogonal frequency division multiplexing radar signal by applying the criterion of least-squares

In recent years, wavelet packet modulation-orthogonal frequency division multiplexing (WPM-OFDM) signals have been introduced for radar applications. These signals have some significant properties such as inherent high range resolution, high resistance of radar system against jamming reception and improved target detection performance in contrast with common traditional signals. However, there is no systematic method for designing WPM-OFDM signals to be used in radar applications. In the present study, the authors have started solving the problem of designing a WPM-OFDM radar signal under a criterion of minimising the least-squares error between designed and desired ambiguity functions. A thumbtack shape is assumed to be the ideal shape of the ambiguity function. In the following, an iterative algorithm is introduced to allocate a proper phase to the desired ambiguity function for obtaining better results. In this study, it is shown that this algorithm can reduce side-lobes, throughout the entire plane of the ambiguity function; therefore using the mentioned algorithm leads to having a desired signal for a radar application. Consequently, by extending the presented method, a pair of WPM-OFDM signals is simultaneously designed which obtain their cross ambiguity function to approximate a desired one under the criterion of least-squares.