Fractional Ambiguity Function for the Generalized Wideband MIMO Radar

Abstract

In this article, we define an ambiguity function (AF) for the generalized wideband multiple-input multiple-output (MIMO) radar, wherein the AF combines the signal processing in the fractional Fourier domain with all the functions of conventional AFs. We name it as the fractional AF for the wideband MIMO radar. In order to obtain the AF, we start from introducing the fractional order that relates to fractional signal processing into the matched-filter exploited by the AF, based on which we then derive the explicit expression of the AF. We provide explanations and implications of the fractional AF, and also derive its simplifications in terms of the case of slow-moving targets in far field. Moreover, we derive corresponding properties for the fractional AF, and meanwhile, we conduct analysis on the computational complexity of the AF. On the basis of the AF definition as well as its simplifications, we establish relationships of our proposed fractional AF to conventional AF forms. We show that our defined fractional AF can serve as a generalized AF form since conventional AFs are special cases of it. Our simulations show that the proper selection of fractional-orders can enable low sidelobe levels of the fractional AF for wideband MIMO radar.