Using analytically derived formulae for bit-error rate
Optical communication systems are critical parts of all telecommunications and networks. They consist of transmitters, channels, and receivers for signal transfer. To achieve a high-capacity and cost-effective optical communication, it is imperative to use high-performance receivers. Among the available receivers, Stokes-vector receivers have attracted significant research attention owing to their ability to track random fluctuations in the state of polarization of optical signals using less complex digital signal processors. Unfortunately, they are highly susceptible to inherent branching loss that is often characterized by low sensitivity. Recently, preamplified Stokes-vector receivers have been identified as a promising solution for addressing the branching loss and achieving high sensitivity. However, the bit-error-rate characteristics of Stoke’s vector systems using optically preamplified receivers remain underexplored despite their practical implications.
To this note, Dr. Kazuro Kikuchi from the National Institution for Academic Degrees and Quality Enhancement of Higher Education analyzed bit-error rate characteristics of Stokes-vector modulation-demodulation systems that use optically preamplified receivers. He aimed to theoretically analyze different Stokes-vector modulation formats based on a unified analytic formula and to validate the effectiveness and limits of the Gaussian noise model in analyzing bit-error rate characteristics. The research work is current published in the journal, Optics Express.
In brief, the author first derived a unified analytical formula for the bit-error-rate for the one-dimensional (1D) binary, two-dimensional (2D) quad, and three-dimensional (3D) octal modulation formats based on the assumption that the Stokes vectors are modulated in a binary manner per dimension. Next, the analytical expressions for the bit-error rate were derived after demodulating the three modulation formats using optically preamplified Stokes-vector direction detection receivers. A probability density function of noise in the Stokes-vector direct-detection receiver was used to analyze the estimated receiver sensitivities. Finally, the author conducted a compressive comparison of sensitivities amongst different receivers.
Dr. Kazuro Kikuchi found that the receiver sensitivity could be estimated, independently from the amplifier gain and receiver circuit noise, via the input photon number per bit and input-referred amplifier noise. This way, the effect of the branching loss in the sensitivity measurement could be avoided. The analytical formula enabled a comprehensive comparison of sensitivities of different receivers in the optical communication systems. For example, the sensitivity difference between the Stokes-vector 2D/3D modulation formats and coherent binary phase-shift-keying (BPSK)/quadrature phase-shift-keying (QPSK) was 6dB while that between Stokes-vector 1D modulation format and BPSK was 3dB. Despite the lower sensitivities in some instances, the Stokes-vector system receivers can achieve dispersion compensation in the digital domain. Furthermore, Gaussian approximation was almost valid for 2D and 3D modulation signals, while 1D modulation signals differed significantly from its Gaussian approximation. As such, one-dimensional format exhibited better bit-error rate characteristics than both two- and three-dimensional modulation formats.
In a nutshell, Dr. Kazuro Kikuchi reported an analysis of bit-error rate characteristics of Stokes-vector modulation–demodulation systems using optically preamplified receivers. Most importantly, it is the first to derive a unified analytical formula for bit-error rate of binary, quad, and octal modulation formats for a comprehensive comparison of sensitivities of different receivers used in various optical communication systems. In a statement to Advances in Engineering, Dr. Kikuchi said the proposed formula help overcome some of the inherent challenges associated with most receivers used in the modulation-demodulation systems.
Kikuchi, K. (2020). Sensitivity analysis of optically preamplified Stokes-vector receivers using analytically derived formulae for bit-error rate. Optics Express, 28(18), 26007-26017.