Fractional Wideband Ambiguity Function for MIMO Radar

We define a new ambiguity function (AF) which involves fractional signal processing and meanwhile incorporates all functions of conventional AFs for the multiple-input multiple-output (MIMO) radar with wideband signals. We term the newly defined AF as the fractional wideband MIMO radar AF, for which we provide explicit derivations and also present explanations and indications. To obtain this, we start from introducing a factor that relates to the fractional signal processing into the matched-filtering exploited by the AF definition, in order to provide a new perspective on evaluating the ambiguity property. We then derive the fractional wideband MIMO radar AF into a simplified version for the case of slow moving targets, and also develop its properties. Moreover, we establish relationships between the newly defined AF and existing ones, and prove that it can serve as a generalized AF form. Simulation results show that the fractional wideband AF gives lower sidelobe levels when the fractional order is properly adopted.