1. Introduction

The optical signal to noise ratio (OSNR) of a quaternary phase shift keyed (QPSK) signal is a useful parameter to assess system performance. It can be employed as a performance monitor for optical transmission networks and provide important information to optimise digital signal processing (DSP) algorithms in coherent optical networks. Traditionally OSNR has been measured using an optical spectrum analyser (OSA), however with the development of coherent optical technologies, a digital optical receiver is capable of measuring the full optical field and can therefore be used to perform monitoring functions alongside its traditional data recovery role. Previously other authors have used signal histograms [1, 2], tap delay sampling [3] and even neural networks [4] to monitor system performance using coherent optical receivers. We propose a technique to estimate the OSNR of an equalised polarisation division multiplexed QPSK signal based on the radial moments of the complex signal constellation. Figure 1 illustrates the main optical components, DSP processes and signal constellations in a PDM-QPSK system [5,6]. The signal used to estimate the OSNR is taken from just after the constant modulus (CMA) adaptive equaliser, before the carrier phase recovery stage. This is the earliest point in the digital signal processing chain where any signal variations are caused by noise and not linear distortions.

 

Fig. 1 Outline of a PDM-QPSK transmission link.

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2. Theory

Consider a linear transmission link limited by amplified spontaneous emission (ASE) then for the signal taken just after the CMA adaptive equaliser the likelihood of receiving a complex signal point, z, for an actual constellation point, Re^jθ, with Gaussian noise variance, σ², made up of ASE noise, ${\sigma }_{ASE}^2$ and receiver noise, ${\sigma }_{Rx}^2$ such that ${\sigma }^2={\sigma }_{ASE}^2+{\sigma }_{Rx}^2$, is given by the bivariate normal distribution,

Initially the carrier phase θ is unknown and so we treat this as a uniformly distributed random nuisance variable and remove it by integration [7]. Hence by substitution of r = |z|, we can write the likelihood as a univariate distribution of r,

The estimation of the parameters, R and σ of this distribution has been addressed in many fields using maximum likelihood estimation and the moments of the radial distribution with fixed point analysis [10–12]. We propose to estimate the parameters from the moments of the squared radial distribution, r². From the Rician distribution we have

For comparison the parameters, R and σ of the distribution in Eq. (2) were also estimated by maximising the log likelihood [7, 10]

For an ideal matched signal recovery from a noiseless detector where the optical noise is limited by ASE the optical signal to noise ratio, OSNR_dB, is given by [5]

3. Simulation

To demonstrate the accuracy of the technique a 112 Gb.s⁻¹ PDM-QPSK transmission simulation was carried out for various levels of additive white Gaussian noise to emulate different OSNRs. In our simulation four shifted PRBS of length 2¹⁵ – 1 were shaped using a root raised cosine filter before ideally modulating a carrier with a 1 MHz Lorentzian linewidth. The optical signal was transmitted through 10 km of standard single mode fibre before being received by an idealised coherent optical receiver with a local oscillator frequency offset of 10 MHz and zero linewidth. The received signal was equalised using a CMA adapted 17 tap FIR filter. The OSNR was calculated for the combined polarisation signals as a single data set, a total of 20000 data points, using Eqs. (4), (5) and (6). Figure 2 shows the estimated OSNR and the simulated OSNR, in 0.1 nm noise bandwidth for both the maximum likelihood and radial moments based techniques. The results show that the maximum likelihood and radial moments based techniques agree and both offer a bias free estimate of the OSNR over a wide range of OSNR.

 

Fig. 2 112 Gb.s⁻¹ simulation, estimated OSNR vs simulated OSNR for the two Rician distribution parameter estimation techniques.

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The estimation of the parameters of the Rician distribution from the radial moments is affected by the number of samples used. Table 1 shows the bias (estimated OSNR_dB - simulated OSNR_dB) and standard deviation of the estimated OSNR_dB for a various number of samples. In a digital optical coherent receiver the data is likely to be processed in parallel with a bus width > 100 such that by estimating the OSNR across this bus width the bias will be less than 0.1 dB.

Table 1. OSNR Bias and Standard Deviation as a Function of Estimation Block Length

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The alternative would be to maintain a rolling estimate of the expected radial moments.

4. Experimental results

In order to show the method under experimental conditions a back to back transmission experiment was performed. A laser source was externally modulated using an IQ modulator to generate a 28 GBaud QPSK signal. The signal was subsequently divided, delayed and recombined with a polarising beam splitter to produce a 112 Gb.s⁻¹ PDM-QPSK signal. The signal was noise loaded with ASE noise before being detected with a coherent optical receiver with balanced detection. The combined linewidth of the transmitter laser and local oscillator was < 1MHz. The signal was sampled using a 50 GSa.s⁻¹ real time scope before off line DSP was carried out using MATLAB®. The OSNR was then calculated using Eqs. (4) and (6). The actual OSNR was measured using an OSA for comparison. Figure 3 shows the estimated OSNR vs the OSA measured OSNR both for a 0.1 nm reference bandwidth.

 

Fig. 3 112 Gb.s⁻¹ experimental results before and after calibration correction.

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5. Discussion

The uncorrected results of Fig. 3 show a deviation between the OSNR estimated from the coherent optical receiver and the OSNR measured using the OSA. This is because the SNR is degraded from the ideal case through additional receiver noise caused by electrical noise, ADC noise and noise due to the imperfect matching of the adaptive FIR filter. The estimated SNR is given by

The receiver noise term, $2{\sigma }_{Rx}^2/R^2$ was obtained through calibration at the operating conditions. A useful calibration point would be the OSNR at the FEC BER limit as there is a sharp increase in the BER of the output data at this point, as illustrated in Fig. 4, allowing a precise determination of the OSNR and a known expected SNR (and hence OSNR).

 

Fig. 4 Illustration of the post-FEC BER edge for a super FEC code using two interleaved extended BCH(1020,988) codes [13].

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In this case to perform the calibration we used one coherent receiver estimated SNR and its corresponding OSA measured OSNR and calculated the receiver noise term by inversion of Eq. (8). The additional receiver noise estimated from this single calibration point, taken at the lowest OSNR, was found to be $10{\text{log}}_{10}\left(2{\sigma }_{Rx}^2/R^2\right)=-19.5\text{dB}$. This receiver noise will lead to a Q-factor ceiling of 19.5 dB for a noise free optical input giving a system BER floor of 2 × 10⁻²¹. Figure 3 shows the corrected and uncorrected OSNR estimates from the coherent receiver and the OSNR measured using the OSA. It can be seen that the single point calibration brings the estimated OSNR closer to the OSA measured OSNR. Figure 5 shows the difference between the coherent receiver estimated OSNR and the OSA measured OSNR after calibration vs the OSA measured OSNR and shows that the coherent receiver estimated OSNR was within 0.5 dB of the OSA measured OSNR.

 

Fig. 5 112 Gb.s⁻¹ experimental results after calibration correction.

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The technique, based on the radial moments, described here provides an accurate estimate of the SNR of the equalised signal. It estimates the SNR based on the amplitude noise alone and is unaffected by phase noise. The effect of non-linear transmission has not been assessed in this work however it is anticipated that by performing a statistical test on the equalised signal noise distribution the presence of non-linear interference may be established.

6. Conclusion

We have proposed a method to estimate the OSNR from an equalised PDM-QPSK signal. The technique has applications for OSNR monitoring in transmission systems and uses signals available within the optical coherent receiver and requires no additional hardware. Using simulation we have compared the technique with the more computationally complex maximum likelihood estimation and shown that the technique gives a bias free estimate of the OSNR over a wide range of OSNR. We have also shown the effect of block length on the estimation of OSNR and that for a typical parallel bus width used in digital coherent receivers a block length > 100 gives a small bias of <0.1 dB. We have shown that with a single point calibration the technique works well with real experimental data giving an OSNR to within 0.5 dB and have suggested the use of the FEC BER limit as a precise calibration point.