A statistical approach to the optimization of the radar ambiguity function and the chaos-based waveform design.

• Statistical approach for radar ambiguity function optimization is proposed. • A code defining the waveform and resulting from a random variable with an appropriate distribution allows a good ambiguity function. • The chaotic codes generated by the skew tent map have almost the desired statistical properties. • The ambiguity function allowed by theses chaotic codes still present high side lobe peaks for time delays close to zero. • This drawback is avoided by down-sampling the considered chaotic sequences. In this paper we adopt a statistical approach to optimize the ambiguity function of a radar system. By considering the codes defining the transmitted waveform as realizations of a random variable we firstly show that a suitable distribution of the random variable allows to obtain good codes. Secondly we show that using the chaotic skew tent map it is possible to generate deterministic codes having the desired statistical properties. This allows to obtain an optimized global ambiguity function of the radar system. The advantage of using chaos-based sequences is that they can be easily generated in any length and number. We further improve their performance by introducing down sampling. It appears that the proposed sequences have performance quite similar to those of the sequences of the literature computationally optimized. [ABSTRACT FROM AUTHOR]