# Cognitive Frequency-Hopping Waveform Design for Dual-Function MIMO Radar-Communications System
###### Abstract  
A frequency-hopping (FH)-based dual-function multiple-input multiple-output (MIMO) radar communications system enables implementation of a primary radar operation and a secondary communication function simultaneously. The set of transmit waveforms employed to perform the MIMO radar task is generated using FH codes. For each transmit antenna, the communication operation can be realized by embedding one phase symbol during each FH interval. However, as the radar channel is time-variant, it is necessary for a successive waveform optimization scheme to continually obtain target feature information. This research work aims at enhancing the target detection and feature estimation performance by maximizing the mutual information (MI) between the target response and the target returns, and then minimizing the MI between successive target-scattering signals. The two-step cognitive waveform design strategy is based upon continuous learning from the radar scene. The dynamic information about the target feature is utilized to design FH codes. Simulation results show an improvement in target response extraction, target detection probability and delay-Doppler resolution as the number of iterations increases, while still maintaining high data rate with low bit error rates between the proposed system nodes. m 20202  
works [12; 13; 14; 15] designed the transmit waveform directly instead of just the covariance matrix. The work of [13] considered prior knowledge of the target impulse response (TIR) and utilized the information to select the transmit waveforms which optimize the mutual information (MI) between the target echoes and the TIR. The work of [15] investigated the problem of the spectrally compatible waveform design for MIMO radar in the presence of multiple targets and signal-dependent interference. A new method was proposed to deal with a more general problem, i.e., designing a spectrally compatible waveform for multiple targets, by minimizing the waveform energy of the overlayed space-frequency bands. The waveform optimization which employs prior knowledge of TIR is also implemented in the single-input multiple-output (SIMO) radar system [16]. The work of [17] derived MIMO radar ambiguity functions. [PERSON] and [PERSON] discussed some properties of the MIMO radar ambiguity function, which provide several ideas for MIMO waveform optimization [17]. The frequency-hopping (FH) sequences presented in [18] were used in MIMO radar configuration [19; 20]. The FH orthogonal transmit waveforms discussed in [18] are initially considered for multiuser radar system. Furthermore, [18] employed the FH codes to minimize the peaks in the cross correlation functions of the transmit waveforms as much as possible. However, in the multiuser radar scenario, each operator activates its individual system. This is different from the MIMO radar system where the receiver antennas can cooperate to resolve the target responses. The FH sequences, which were designed by [PERSON] and [PERSON], optimized the MIMO ambiguity function. Based on their characteristics of being easily produced and modulus constant, FH codes are considered a good choice for the MIMO radar waveforms. A new scheme for optimizing the MIMO radar waveforms was provided in [19]. The scheme makes the energy of the MIMO ambiguity function spread in the range and angular dimensions evenly, as well as decreases the sidelobes in the MIMO radar ambiguity function. The work of [19] also designed optimal FH waveforms, which had separate FH codes and amplitudes, for a collocated MIMO radar system. The joint design problem can be solved by using game theory, provided by [20]. The authors considered the two objective functions, corresponding to FH codes and amplitudes separately, as two interacting players. By this concept, the joint optimization scheme obtained better integrated code and amplitude matrices that can improve performance much better than separate designs.