Frequency Permutations for Joint Radar and Communications

Abstract

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood (ML) detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise (AWGN) channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel model is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function (AF) and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds (CRLBs) on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed. Numerical examples are used to highlight the accuracy of the analysis and to illustrate the performance of the proposed waveform.

Combined Radar and Communications with Phase-Modulated Frequency Permutations

“…We first consider the classical stepped frequency radar waveform and modulate data using PSK. Next, we extend the work in [22] by incorporating phase modulation into the random stepped frequency permutation waveform. This allows us to use both phase and frequency to modulate data and as a result transmit more data between nodes.…”

“…This allows us to use both phase and frequency to modulate data and as a result transmit more data between nodes. We provide an analysis of both the communication and radar performances and make comparison with the waveform in [22].…”

“…The finite bandwidth 𝐵 is introduced since 𝜔 2 and ω2 do not converge when 𝑠 𝑝 (𝑡) is a perfect rectangular pulse. The approximation in ( 19) is derived by neglecting small high order terms in the integrals which vanish when 𝐵𝑇 → ∞ [22]. The detailed derivations of 𝐽 11 , 𝐽 22 and 𝐽 12 are given in Appendices C, D and E, respectively.…”

“…In the linear stepped frequency radar waveform considered in (10), the frequency was linearly changed according to (2). Motivated by [22], we proceed to change the order of frequency tones on top of the phase modulation, such that the randomisation in the frequency tones can be used to send more data.…”

“…As is analysed in [22], the overall structure of the AF resulting from the random stepped frequency permutation based waveform has a narrow main-lobe and small side-lobes. When phase modulation is introduced, these good radar properties will not be affected much.…”