With the increase in demand for spectral resources and bandwidth constraints, efficient solutions for the coexistence of radar and communication systems are needed. Simultaneously, the development of multifunctional radio frequency (RF) systems with less hardware have received considerable attention. Most previous work on coexistence has focused on hardware design and mitigation of interference between radar and communication systems. This work proposes, a novel method for controlling a chaotic trajectory, which allows for the coexistence of both radar and communication systems. Binary information can be encoded in a chaotic state by adjusting its trajectory. In this approach, a state variable is selected to control the trajectory and generate a controlled chaos-based frequency modulated (CCBFM) waveform for joint radar-communication system signal transmission. We also design a communication receiver to decode the information and a radar receiver that extracts the signature of the target are designed accordingly. The performance of the controlled chaotic communication system is assessed in terms of the bit error ratio (BER). The analysis of the communication system shows that the CCBFM receiver performs reasonably well compared to a half-sine pulse frequency modulated (HSPFM) receiver. Analysis of the radar system performance is assessed using the entropy of the target's signature. The use of a CCBFM waveform leads to accurate target detection and classification for a signal-to-noise ratio as low as −30 dB. These analyses demonstrate that a CCBFM waveform can be successfully used for joint radar-communication systems in a shared spectrum. INDEX TERMS Controlled chaos, chaotic systems, joint radar-communication systems, Lorenz oscillator, radar imaging. Research (ONR) launched an Advanced Multifunction RF Systems (AMRFS) program [3] to develop a single system that performs multiple operations such as sensing, communication, electronic warfare, etc. Numerous studies have been dedicated to integrating radar and communication subsystems into a single system [4]-[8]. In spite of advances, the challenge of designing a singlewaveform transmission approach for joint radar and communication (RadCom) system remains [9]. The use of a single waveform for both radar sensing and communication data transmission is desirable to avoid multiple expensive RF transmitters [4]. A dual-function system that adopts this fixed signal approach would, of course, require a trade-off between its radar and communication performance [10]. For instance,

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In this article, we propose the utilization of chaos-based frequency modulated (CBFM) waveforms for joint monostatic and bistatic radar-communication systems. Short-duration pulses generated via chaotic oscillators are used for wideband radar imaging, while information is embedded in the pulses using chaos shift keying (CSK). A self-synchronization technique for chaotic systems decodes the information at the communication receiver and reconstructs the transmitted waveform at the bistatic radar receiver. Using a nonlinear detection scheme, we show that the CBFM waveforms closely follow the theoretical bit-error rate (BER) associated with bipolar phase-shift keying (BPSK). We utilize the same nonlinear detection scheme to optimize the target detection at the bistatic radar receiver. The ambiguity function for both the monostatic and bistatic cases resembles a thumbtack ambiguity function with a pseudo-random sidelobe distribution. Furthermore, we characterize the high-resolution imaging capability of the CBFM waveforms in the presence of noise and considering a complex target.

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We propose a scheme for bistatic radar that uses a chaotic system to generate a wideband FM signal that is reconstructed at the receiver via a conventional phase lock loop. The setup for the bistatic radar includes a 3 state variable drive oscillator at the transmitter and a response oscillator at the receiver. The challenge is in synchronizing the response oscillator of the radar receiver utilizing a scaled version of the transmitted signal s r (t, x) = αs t (t, x) where x is one of three driver oscillator state variables and α is the scaling factor that accounts for antenna gain, system losses, and space propagation. For FM, we also assume that the instantaneous frequency of the received signal, x s , is a scaled version of the Lorenz variable x. Since this additional scaling factor may not be known a priori, the response oscillator must be able to accept the scaled version of x as an input. Thus, to achieve synchronization we utilize a generalized projective synchronization technique that introduces a controller term -μe where μ is a control factor and e is the difference between the response state variable x s and a scaled x. Since demodulation of s r (t) is required to reconstruct the chaotic state variable x, the phase lock loop imposes a limit on the minimum error e. We verify through simulations that, once synchronization is achieved, the short-time correlation of x and x s is high and that the self-noise in the correlation is negligible over long periods of time.