# Cognitive Frequency-Hopping Waveform Design for Dual-Function MIMO Radar-Communications System
###### Abstract
The works of [21; 22; 23; 24; 25; 26] indicated a possibility of employing the radar-communications integration concept to solve the lack of radio frequency (RF) spectrum. Efficient utilization of shared bandwidth between wireless communications and radar can be achieved by using dynamic frequency allocation. For example, using dynamic frequency allocation is a way to make shared bandwidth between wireless communications and radar possess more efficient utilization. The work of [23] proposed a novel dual-function radar-communications (DFRC) strategy to embed quadrature amplitude modulation (QAM) based communication information in the radar waveforms by exploiting sidelobe control and waveform diversity. In [27; 28], the authors proposed a novel distributed DFRC MIMO system capable of simultaneously performing radar and communication tasks. The distributed DFRC MIMO system performs both objectives by optimizing the power allocation of the different transmitters in the DFRC system. The proposed strategy can serve multiple communication receivers located in the vicinity of the distributed DFRC MIMO system. Numerous recent studies [29; 30; 31] considered that the developing concept of DFRC is secondary to the main radar task. Communication source embedding into the illumination of MIMO radar system is realized using waveform diversity, sidelobe control, or the time-modulated array technique, which was studied in [30]. [PERSON] and [PERSON] presented a signaling strategy for communication source embedding into the illumination of FH-based MIMO radar system [32]. The main principle behind the signaling strategy is to embed phase modulation (PM)-based symbols by using phase rotating the FH pulses. The phase shift is implemented to each transmit FH waveform of the MIMO radar system. The PM-based symbol embedding does not influence the function of the MIMO radar system, which uses the FH waveforms. The investigation on cognitive radar waveform optimization has received a lot of interest [33; 34; 35]. To further enhance the performance of the TIR estimation in a time-varying target scene, the transmittedsignal parameters should be constantly adjusted. Then, updated knowledge about the time-varying target scene is employed to allocate fundamental resources like transmitted signal parameters in a cognitive mode [34]. A new strategy for optimizing the waveforms of a cognitive radar was presented in [34]. The aim is to enhance the performance of target estimation by minimizing the mean-square error (MSE) of the estimates of target scattering coefficients (TSC) based on Kalman filtering and then minimizing MI between the radar target echoes at successive time instants. However, there is also an increase in the computational load due to the Kalman filtering step in the waveform optimization. Such a cognitive radar system cannot be used in real applications to address the environmental sensing issues. To improve the performance of the target parameters estimation and classification, the pioneering study by Bell in [36] developed an information-theoretic method for the radar waveforms optimization. The authors in [37; 38; 39] extended the information-theoretic method by maximizing the MI between the target response and the target-scattering signals as a waveform design criterion in the MIMO radar system. The work of [40] proposed an innovative method to designing the transmit signal of cognitive MIMO radar system, which combines the signal optimization and selection processes. The works of [41; 42; 43; 44] present a signaling scheme for information embedding into the illumination of the radar using FH pulses. An FH-based joint radar-communication system enables implementing a primary radar operation and a secondary communication function simultaneously. Then, the authors consider the problem of radar codes optimization under a peak-to-average-power ratio (PAR) and an energy constraint. However, a time-variant radar scenario is not considered.