A phase-parameterized frank-sequence-based CAZAC waveform for doubly selective channels

Reliable communications over doubly selective channels require waveforms that are robust to both delay and Doppler spreads while maintaining low-complexity reception. Constant-amplitude zero autocorrelation (CAZAC) sequences provide attractive correlation properties and implementation advantages, yet their direct use in doubly selective channels is often suboptimal due to limited design flexibility. In this paper, we propose a phase-parameterized Frank sequence construction that preserves the CAZAC property while introducing an additional phase-parameter vector. Building on this construction, we develop a CAZAC waveform family tailored to doubly selective channels and propose two associated orthogonal modulation schemes. Compared with the fixed-structure Frank-sequence-based construction, the proposed waveform family can provide improved error-rate performance under doubly selective fading. Furthermore, simulation results show that, with linear MMSE reception, the proposed waveform achieves BER performance comparable to two representative high-mobility waveforms, namely, OTFS and AFDM. More importantly, in high-Doppler regimes, when combined with an MMSE-initialized iterative maximum-ratio combining (MRC) receiver, the proposed waveform provides a clear performance gain over OTFS and AFDM, indicating its suitability for high-mobility links.