A theory for the signal-to-noise ratio (SNR) of optical direct-detection receivers employing return-to-zero (RZ) coding (and possibly optical preamplification) is developed. The results are valid for both signal-independent noise limited and signal-dependent noise limited receivers, as well as for arbitrary optical pulse shapes and receive filter characteristics. Even if the same receiver bandwidth is used, RZ coding is seen to perform better than nonreturn-to-zero (NRZ) coding. Asymptotic expressions for the SNR in case of very high and very low receiver bandwidths show that the full sensitivity enhancement potential of RZ coding is exhausted at fairly moderate duty cycles. A realistic example taking into account intersymbol interference (ISI) shows that a receiver sensitivity gain (compared to NRZ coding) of, e.g., 3.2 dB can be obtained in a signal-independent noise limited receiver with a bandwidth of 80% of the data rate, using a duty cycle of three.
Peter J. Winzer and Andras Kalmar, "Sensitivity Enhancement of Optical Receivers by Impulsive Coding," J. Lightwave Technol. 17, 171- (1999)