Phase Retrieval-Based Coherent Receivers: Signal Design and Degrees of Freedom

Abstract

Kramers-Kronig (KK) detection exploits properties of minimum-phase, single-sideband signals to recover the phase of a signal from its intensity. It offers many of the benefits of standard coherent detection, while not requiring a local oscillator, quadrature hybrid, or balanced photodiodes. Adding a carrier to a transmitted signal to render it minimum-phase, however, causes a power penalty for KK detection relative to standard coherent detection. We study the mutual information (MI) achieved by KK detection and the impact of signal and system design parameters, including excess bandwidth, carrier-to-signal power ratio, modulation order, probabilistic shaping, and chromatic dispersion, making comparisons to standard coherent detection and standard direct detection. We study the effective degrees of freedom for KK detection, confirming that it tends towards unity at high signal-to-noise ratio (SNR), supporting the classification of KK detection as coherent detection. At low SNR, however, KK detection is outperformed by standard direct detection in terms of MI per symbol. This study focuses on the fundamental performance of the detection methods under comparison, by numerically approximating ideal continuous-time signals and signal processing operations. The results and conclusions reported here will be constrained, in practice, by limitations of practical implementation, including those addressed in the Discussion section.