Mixed-order and higher-order ambiguity functions

Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. In general, objects cannot be completely separated by their distance or relative velocity, thus order and direction estimations are needed to estimate the number of objects and their direction of arrival. In this paper we start with the antenna array ambiguity function of single objects known from literature and generalize it to multiple objects. Therewith we develop criterions to evaluate the order estimation capabilities of an antenna array and its unique direction estimation of multiple objects. It is shown that some arrays are much more suitable than others for estimating the number of objects. Arrays which can be used to estimate the direction of a single object ambiguity-free are not always able to estimate the direction of two objects uniquely. The proposed criterions can be used to optimize automotive radar antenna arrays to be non-ambiguous up to multiple objects to handle complicated traffic situations correctly.