Zadoff-Chu Sequences for Chirp-Domain Communication: Diversity-Complexity Tradeoffs in Doubly Dispersive Channels

Orthogonal frequency-division multiplexing (OFDM) combats multipath-induced time dispersion by dividing the channel into narrowband sub-channels. However, when the channel also exhibits frequency dispersion due to mobility (Doppler effect), these sub-channels lose orthogonality and cause inter-carrier interference that degrades the reliability performance of the communication system. We investigate Zadoff-Chu (ZC) sequences for chirp-domain communication to improve reliability in time-frequency dispersive channels. We show that ZC sequences are the only constant-amplitude zero-autocorrelation (CAZAC) sequences that transform a doubly dispersive channel into a singly dispersive channel that is either pure time or frequency dispersion. This transformation is controlled by the ZC root, which provides a geometric projection from the delay-Doppler domain onto a one-dimensional chirp-domain axis with a closed-form design rule. Because the transformed channel is singly dispersive, the receiver equalizes a one-dimensional convolutional channel rather than a two-dimensional delay-Doppler channel and can reuse trellis-based detectors that generate the soft information that coded systems require. Then, we present ZC-based modulations, derive the effective channel after transformation, and analyze diversity, which reveals an underlying trade-off between diversity and receiver complexity. When evaluated at a vehicle speed of 540 km/h and a carrier frequency of 4 GHz, ZC-based modulations demonstrate performance comparable to affine frequency division multiplexing (AFDM) and orthogonal time-frequency space (OTFS), with gains of about 5 dB over orthogonal chirp division multiplexing (OCDM) and 10 dB over OFDM.