On Envelope Detection of Noisy Phase Signals with Asymptotically Small Linewidths

Abstract

The impact of laser's phase noise on heterodyne and homodyne linewidth communications, as well as on direct detection systems with optical amplification is governed by intractable statistics induced by the phase sample path. Here we derive analytic asymptotic bounds on the underlying distribution inherited by the squared envelope of noisy phase signals. The approach taken invokes standard results from the theory of Large-Deviations and yields straightforward, closed-form expressions. This fundamental problem has many applications in linewidth communications, such as the determination of the BER floor in heterodyne ASK systems, which is hereby illustrated. The asymptotic theory predicts an IF bandwidth increase with the square root of the linewidth-to-bit ratio for a specified floor level. A comparison with the numerical solution of the underlying Fokker-Planck equation reveals a good agreement even at significant (non-asymptotic) laser's linewidths.