A Study on the Performance of Symbol Dictionary Selection for the Frequency Hopped DFRC Scheme

Increasing pressure on the available spectrum, particularly from wireless communications services, has led to significant research into strategies for coexistence between radar and communications. In this context, Dual-Function Radar-Communications (DFRC) systems have emerged as a potential solution to the spectrum congestion problem. DFRC schemes treat the radar as the primary modality and aim to embed communications symbols into the transmitted waveforms. One such approach is to use the frequency hops in a Frequency-Hopped (FH) Multiple-Input Multiple-Output (MIMO) radar to encode communications symbols. While this scheme allows for higher data rates, embedding the information in the fast time impacts the radar performance. Therefore, the code book selection is an important design consideration that we focus on in this work. We discuss the impact of the selection of the code book on the ambiguity functions of the radar waveforms and elucidate its relation to the probability of having degenerate waveforms. We illustrate these ideas using two code book selections, namely an arbitrary selection and a balanced code book. The results show that balancing the codebook leads to improved radar performance.