On the Unique Optimality of Chirp Coding in Communications
Abstract
Chirp coding and modulation is widely recognised as an effective approach for transmitting information through noisy and dynamically varying communication channels. However, whether chirp signalling is uniquely optimal relative to alternative modulation schemes under comparable channel and power constraints remains an important theoretical question. This paper develops a mathematical framework to investigate the optimality of chirp-based signalling in noise-dominated environments. Drawing on information theory, functional analysis, and time–frequency analysis, we examine the performance of chirp modulation with respect to information-theoretic efficiency, robustness to Doppler-induced frequency shifts, and resilience to multi-path and multiple-scattering propagation. Analytical comparisons with conventional modulation schemes are used to establish the conditions under which chirp signalling provides superior signal distinguishability, noise resilience, and propagation robustness. The analysis indicates that chirp-based waveforms possess a distinctive combination of time–frequency characteristics that enables them to maintain reliable signal separation under challenging channel conditions. Under the assumptions and channel models considered, the results suggest that chirp modulation can achieve simultaneous optimality across multiple performance dimensions, providing a stronger theoretical basis for its use than conventional modulation approaches. The results therefore…
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