Q factor in numerical simulations of DPSK with optical delay demodulation

Abstract— A simple model is used to estimate the Q factor in numerical simulations of differential phase shift keying (DPSK) with optical delay demodulation and balanced detection. It is found that an alternative definition of Q is needed for DPSK in order to have a more accurate prediction of the bit error ratio (BER). Index Terms— DPSK, BER, optical communication. I. I NTRODUCTION IFFERENTIAL PHASE SHIFT KEYING (DPSK) was studied in the early days of optical fiber communications [1-4]. Recently, direct-detection (no local oscillator) DPSK has attracted much attention for applications in high bit-rate wavelength-division-multiplexed (WDM) systems, and studies were carried out both numerically [5-7] and experimentally [8-10]. Using DPSK, a transmission distance of 4,000 km at 42.7 Gb/s bit-rate has been demonstrated [10]. It is well-known that in a linear channel DPSK has a receiver sensitivity advantage over on-off keying (OOK) by approximately 3 dB with optical delay demodulation and balanced detection [11-14]. However, to our knowledge, such benefit of balanced detection has not been properly taken into account in DPSK numerical simulations published so far. For example, it was reported in [5] that “at the level of the practical optical-signal-to-noise (OSNR) regime, balanced detection gives only marginal improvement”, which seems to contradict the results of earlier theoretical and experimental studies of DPSK. We note that one challenge in numerical simulations is to provide a reliable estimate of the BER. To save the computation time, a typical simulation program uses only hundreds of bits, and therefore, the BER is usually not counted directly but estimated by evaluating the statistical fluctuation in the received signal. In simulations of OOK, such fluctuation is often characterized by a Q factor defined as