  In this study, we propose index modulation (IM) with circularly-shifted
chirps (CSCs) (CSC-IM) for dual-function radar and communication (DFRC)
systems. The proposed scheme encodes the information bits with the CSC indices
and the phase-shift keying (PSK) symbols. It allows the receiver to exploit the
frequency selectivity naturally in fading channels by combining IM and wideband
CSCs. It also leverages the fact that a CSC is a constant-envelope signal to
achieve a controllable peak-to-mean envelope power ratio (PMEPR). For radar
functionality, CSC-IM maintains the good autocorrelation (AC) properties of a
chirp by ensuring that the transmitted CSCs are separated apart sufficiently in
the time domain through index separation (IS). We investigate the impact of IS
on spectral efficiency (SE) and obtain the corresponding mapping functions. For
theoretical results, we derive the union bound (UB) of the block error rate
(BLER) for arbitrary chirps and the Cramer-Rao lower bounds (CRLBs) for the
range and reflection coefficients for the matched filter (MF)-based estimation.
We also prove that complementary sequences (CSs) can be constructed through
CSCs by linearly combining the Fourier series of CSCs. Finally, through
comprehensive comparisons, we demonstrate the efficacy of the proposed scheme
for DFRC scenarios.
