01-03-2017, 03:30 PM
The bit error rate (BER) expressions of 16-phase shifting (PSK) and 16-quadrature amplitude modulation (QAM) are obtained analytically in the presence of a phase error. By averaging over the phase error statistics, the performance penalty can be analyzed analytically as a function of the phase error variance. Phase error variations leading to a signal-to-noise ratio of 1 dB per bit penalty at BER = 10 (-4) have been found 8.7 x 10 (-2) rad (2), 1.2 x 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 admissible phase error variance, the corresponding laser line tolerance can be predicted. We extended the phase-error variance analysis of the decision-maximal carrier-assisted estimation of PSK in PSK M-ary to 16QAM and successfully predicted the laser tolerance in different modulation formats, which coincides with the simulations Of Monte Carlo. Finally, approximate BER expressions are introduced for different modulation formats to allow a rapid estimation of the BER performance depending on the variance of the phase error. In addition, the BER approximations give a lower limit in the laser-wide line requirements in M-ary PSK and 16QAM. It is shown that with respect to laser line tolerance, 16QAM exceeds 16PSK having the same spectral efficiency (SE), and has almost the same performance as 8PSK having lower SE. Therefore, 16-QAM is a promising modulation format for coherent optical communications of high SE.