Yu Changyuan, Zhang Shaoliang, Kam Pooi Yuen, Chen Jian
Department of Electrical & Computer Engineering, National University of Singapore, 117576 Singapore.
Opt Express. 2010 Jun 7;18(12):12088-103. doi: 10.1364/OE.18.012088.
The bit-error rate (BER) expressions of 16- phase-shift keying (PSK) and 16- quadrature amplitude modulation (QAM) are analytically obtained in the presence of a phase error. By averaging over the statistics of the phase error, the performance penalty can be analytically examined as a function of the phase error variance. The phase error variances leading to a 1-dB signal-to-noise ratio per bit penalty at BER=10(-4) have been found to be 8.7 x 10(-2) rad(2), 1.2 x 10(-2) rad(2), 2.4 x 10(-3) rad(2), 6.0 x 10(-4) rad(2) and 2.3 x 10(-3) rad(2) for binary, quadrature, 8-, and 16-PSK and 16QAM, respectively. With the knowledge of the allowable phase error variance, the corresponding laser linewidth tolerance can be predicted. We extend the phase error variance analysis of decision-aided maximum likelihood carrier phase estimation in M-ary PSK to 16QAM, and successfully predict the laser linewidth tolerance in different modulation formats, which agrees well with the Monte Carlo simulations. Finally, approximate BER expressions for different modulation formats are introduced to allow a quick estimation of the BER performance as a function of the phase error variance. Further, the BER approximations give a lower bound on the laser linewidth requirements in M-ary PSK and 16QAM. It is shown that as far as laser linewidth tolerance is concerned, 16QAM outperforms 16PSK which has the same spectral efficiency (SE), and has nearly the same performance as 8PSK which has lower SE. Thus, 16-QAM is a promising modulation format for high SE coherent optical communications.
在存在相位误差的情况下，通过解析得到了16相移键控（PSK）和16正交幅度调制（QAM）的误码率（BER）表达式。通过对相位误差的统计进行平均，可以解析地研究性能损失作为相位误差方差的函数。已发现，对于二进制、四进制、8相和16相PSK以及16QAM，在误码率为10^(-4)时导致每比特1dB信噪比损失的相位误差方差分别为8.7×10^(-2)rad²、1.2×10^(-2)rad²、2.4×10^(-3)rad²、6.0×10^(-4)rad²和2.3×10^(-3)rad²。根据允许的相位误差方差，可以预测相应的激光线宽容限。我们将多进制PSK中判决辅助最大似然载波相位估计的相位误差方差分析扩展到16QAM，并成功预测了不同调制格式下的激光线宽容限，这与蒙特卡罗模拟结果吻合良好。最后，引入了不同调制格式的近似误码率表达式，以便快速估计误码率性能作为相位误差方差的函数。此外，误码率近似值给出了多进制PSK和16QAM中激光线宽要求的下限。结果表明，就激光线宽容限而言，16QAM优于具有相同频谱效率（SE）的16PSK，并且与具有较低SE的8PSK性能几乎相同。因此，16 - QAM是一种有前途的用于高SE相干光通信的调制格式。
