Unstable basis function for joint radar-communication systems

Abstract

• A combined radar and communications system using basis functions derived from an unstable second-order system is described. • Using unstable systems with different frequencies allows for the creation of a set of orthogonal basis functions. • Both communications and radar signals may be decoded with linear analog circuits, leading to simple inexpensive receivers. • The radar properties are not sensitive to the encoded communications method. • Because of simplicity and low cost, the system could be used in applications where it was necessary to piggyback a radar signal on a communications signal. In this paper, we develop a joint radar-communication waveform based on the unstable basis function. Basis functions of a chaotic waveform are uncertain, vary continuously and hence the use of a traditional matched filter is not practical. Corron et al. [1,2] demonstrated a chaotic circuit for which an analytic matched filter could be constructed, solving the signal detection problem. The Corron circuit produced a narrow band signal, which is not optimal for spread spectrum communications and radar applications. In this paper, we adapt Corron’s concept of a chaotic signal composed of a linear combination of basis functions and show how the basis functions are used to design joint radar-communications systems that still have simple analytic matched filters. The form of the matched filter makes it useful for both the radar and communications systems where it is necessary to minimize weight or power consumption.