An Accurate Analysis of the CPFSK System by Considering the Correlation between Discrete Samples in Post-Detection Filtering

Abstract

An analysis method is developed to improve the precision of ordinary discrete integrator model for post-detection filter. The method uses the generalized treatment for correlated complex Gaussian random variables, so that the correlation between discrete samples can be managed. Applying the method to CPFSK receiver shows that the correlation between the direct and the delayed signals may cause more than l dB sensitivity penalty. The analysis also confirms that at large optical bandwidth to data rate ratio the common interferometer demodulation of the CPFSK signal has a worse sensitivity that the dual detection filter receiver. Thus some modification to the interferometer receiver must be done in order to improve its sensitivity.

The Accuracy of the Analysis for non-Gaussian ASE Noise using the Gaussian Approximation - a Rigorous Approach

“…The main analysis procedure is described in [7][8], here only the final formulae are listed. The ASE noise is assumed to be produced by an ideal optical amplifier (the noise figure is 3 dB).…”

“…We will assume that the bandpass filter is described via an equivalent integral time response of duration t 0 (as it was done in [7]), then the autocorrelation function between the noise samples will be:…”

“…The following Bit-Error-Ratio (BER) evaluation will be the same as shown in the appendix of [7]. However, it is much simpler, since if the matrix T in that appendix is given explicitly by (3) and (4) and is already in diagonalized form.…”

“…Third, neither of these two approaches could deal with the arbitrary filter types, only an ideal bandpass filter (described by a finite time type of time response) and an ideal (discrete time) integrator lowpass filter is applicable. sical method to deal with the correlation between complex Gaussian variables [5][6][7]. The principle of their method is also based on the discrete integrator lowpass filter description, however, the correlation between the noise samples could be dealt with by mapping the original covariance matrix into a simpler eigenvalue based representation.…”