A Novel Joint Radar and Communications Technique based on Frequency Permutations

This paper presents a new waveform that is suitable for simultaneous data transmission and radar sensing. The approach considers a classical random stepped frequency radar waveform that is suitable for the emerging automotive radar application. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. More specifically, we propose a new Lehmer code based signaling model that modulates data based on the selection of the permutation. Considering maximum likelihood detection, the union bound on the communication block error probability is derived for baseband communication both in an additive white Gaussian noise (AWGN) channel and Rayleigh fading channel. Using the Hungarian Algorithm, an efficient implementation method for the communications receiver is also presented. From the radar perspective, we derive the ambiguity function, which is a key analytical tool in radar waveform design, and characterize the behavior of the Lehmer code based random stepped frequency radar waveform. Numerical examples are used to illustrate the performance of the proposed waveform.