A Low-PAPR, Synchronization-Robust Non-Coherent Grassmannian Modulation for Optical Communications

Non-coherent Grassmannian (unitary space-time) signaling detects on the received subspace, which is invariant to a branch-side (polarization or mode-coupling) rotation and to a phase that is constant over the coherence block.

It therefore needs no carrier-phase or polarization recovery within the block and is robust to phase noise when the per-block phase drift is small, while a multi-branch (polarization or spatial) front end harvests diversity without channel estimation or pilots.

However, the Grassmannian-constellation literature usually assumes a distortion-free, linear channel and transmitter and already-acquired symbol timing.

This paper closes both gaps while reusing off-the-shelf Grassmannian packings.

First, we impose a constant-modulus (low peak-to-average-power-ratio, PAPR) constraint on the constellation and quantify the PAPR/chordal-distance trade-off: a constant-modulus design lowers the 0.1% PAPR from 6.1 dB (unconstrained) to 3.6 dB -- 1.6 dB below 16-QAM (5.2 dB) -- easing the optical modulator linear range and the fiber Kerr-nonlinearity penalty, at a ~1.8 dB cost in high-SNR coding gain.

Second, we derive a phase-blind subspace timing-error detector (TED) that exploits the invariance of the GLRT projection energy to the unknown carrier phase, plus a feedforward acquisition metric, supplying clock recovery without prior carrier or polarization recovery.

The TED yields a clean S-curve with a stable lock point for roll-offs down to beta=0.1.

Under block fading the proposed estimator attains genie-timing SER within a fraction of a dB and recovers full diversity, whereas an uncorrected 0.35-symbol timing offset floors the error rate near 0.4.

Results use a symbol-rate block-fading abstraction; full fiber, modulator, and phase-noise modeling is future work.

The scheme combines low PAPR with the diversity and phase-recovery-free operation of non-coherent reception.