Issues related to coherent optical receivers

We have previously shown that the most flexible detection circuit is to use a heterodyne time-domain detector, which is suitable for both test signals and live signals and is not affected by the modulation format.

The device on the left in Figure 1 is such an IQ detector. This diagram clearly illustrates that there are several steps that need to be completed before the incoming bits encoded in the symbol can be identified and further analyzed. The receiver architecture shown here is the recommended design by the Optical Internetworking Forum (OIF) and is able to extract all the information in the signal. Examine the receiver architecture in detail.

Figure 1. OIF proposed integrated intradyne coherent receiver architecture (OIF Implementation Agreement for Integrated Dual-Polarization Coherent Receivers, IA # OIF-DPC-RX-01.2, November 14, 2013)

Significantly reduce impairment

After the optical signal has been converted to digital, it needs to be DSP-ed, which is essential for any coherent optical receiver. Compared with the traditional on/off keying, which has CD and PMD signal distortion effects, using DSP can provide significant advantages. DSP supports algorithmic compensation of CD, PMD and other impairments because coherent detection can provide complete light field information. This means that with composite optical modulation, we no longer have to use PMD compensators or dispersion compensating fibers, nor will we have to worry about the added losses and delays of these modules.

An upstream precorrection step can remove receiver imperfections. These imperfections can include channel imbalance between the four electrical channels, IQ phase angle errors of the IQ mixers, timing offsets between the four ADC channels, and differential imbalance of a normally balanced receiver. Removing these impairments typically requires device characterization over a range of wavelengths as part of instrument calibration.

In addition to these imperfections introduced by the receiver, the DSP must compensate for the attenuation incurred by the signal along the optical path between the transmitter and receiver, including CD and PMD, polarization dependent loss (PDL), polarization rotation or polarization state conversion (PST), and phase noise.

To evaluate the impact of phase noise, the carrier phase can be tracked over time. However, this step is not necessary in a coherent receiver setup.

Carrier Phase Recovery

By introducing a local oscillator, we can track how the signal phase changes relative to the local oscillator phase at different times. However, in reality, there is a frequency difference between the local oscillator and the signal in the heterodyne receiver scenario, resulting in a phase drift that changes linearly with time. This is easy to understand as long as you remember that in a heterodyne receiver, IPhoto is proportional to cos(Δφ + Δω t) ( how to detect a complex modulated optical signal ). Figure 2 shows this "rotated" constellation diagram for QPSK modulation.

Figure 2. The frequency difference between the transmitter laser source and the local oscillator causes the constellation diagram to "rotate".

To prevent ambiguity, the phase must not change faster than π/4 per symbol time, which is half the phase difference between two consecutive symbols. This means that the frequency offset between the local oscillator and the signal must be less than 1/8 of the QPSK symbol clock.

To be able to track the phase, the signal sampling must be performed at time points where the phase value is predictable (e.g., at symbol times). For signals with limited bandwidth, the phase sampling rate is less than the symbol rate. The dark gray line in Figure 3 shows that the phase may not be correctly recovered.

Figure 3. In actual transmission systems, phase recovery is usually impossible due to the low sampling rate, phase noise, and offset.

In these cases, the carrier phase noise and offset must follow very tight limits so that the phase can be recovered. In real transmission systems, this is not usually the case because these tighter specifications do not need to be followed in real line cards performing real-time acquisition.

Figure 4 shows the effect of carrier bandwidth on phase recovery of a DFB laser source. On the left is an example of a high tracking bandwidth. The constellation points in the IQ diagram are artificially narrowed because phase tracking in this case reduces the angular width of the symbol. Lower bandwidths result in more realistic circular symbols. As the bandwidth is further reduced, we reach the limit in the carrier phase diagram and it is no longer possible to track the phase. The phase noise that cannot be eliminated has a significant impact on the symbol angular spread.

Figure 4. This example shows that carrier phase tracking of a DFB laser source depends on the tracking bandwidth.

Find the Jones matrix to recover the original polarization state

In order to provide two independent baseband signals (for x-polarization and y-polarization) to the digital demodulator, a step called polarization demultiplexing is required in the DSP. In this step, PMD and PDL must be compensated. It is also necessary to consider that in single-mode fiber (SMF), the polarization state is not maintained during propagation.

As the signal passes through the fiber, the polarization direction gradually changes (Figure 46), so the polarization state (SOP) at the terminal is not only related to the direction of the receiver. If there is a polarization beam splitter in the receiver, we cannot get two independent signals, but only a linear combination of the two polarization signals. Polarization-maintaining fibers can preserve the SOP, but because they have greater attenuation and are more expensive, they are not deployed in data transmission.

Figure 5. Single-mode fiber changes the polarization state of the transmitted light. Therefore, the polarization beam splitter on the receiver side does not provide 2 independent signals, but a linear combination. Here is an example of a dual-polarization QPSK constellation diagram before polarization demultiplexing.

All attenuation effects of all polarized light in a fiber channel can be mathematically described by the Jones matrix. The transmitted signal S is multiplied by the Jones matrix to obtain the received signal R. For an ideal channel with no impairments, the Jones matrix is ​​an identity matrix; the received signal is the same as the originally transmitted signal (see Figure 47). The most common form of the Jones matrix is ​​a complex 2x2 matrix with 8 independent real-time parameters.

Figure 5. Jones matrix of an ideal channel

The Jones matrix must be determined in order to deduce the original signal from the measured received signal. This is difficult to accomplish because we have very little knowledge of the magnitude of the impairments in the channel.

To do this, we usually use so-called "blind algorithms" to approximate the original signal. These estimation methods do not require knowledge of the original signal (except for the modulation format). Here, the received signal is filtered with a series of equalization filters (Figure 6) to obtain the inverse of the Jones matrix. Each filter element models a signal attenuation effect. The algorithm iteratively searches the set of filter variables (α, β, k...) and eventually reaches a converged result, which means that the measured symbols are mapped to the symbols calculated by the algorithm with minimal error.

Figure 6. Equalization filter model for compensating for chromatic dispersion (CD), differential group delay (DGD), polarization dependent loss (PDL), and polarization state transition (PST). (1. J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, H. de Waardt, B. Lankl, and B. Schmauss: “Channel parameter estimation for polarization-diverse coherent receivers,” IEEE Photonics Technology Letters, Vol. 20, No. 10, May 15, 2008)

The disadvantage of this method is that the same polarization channel may be recovered twice. This problem is called the singularity of the algorithm. This method is also very complex because each symbol must be processed individually to calculate the next iteration step.

It is easier to estimate in Stokes space

Using Stokes space makes it easier to estimate. In Stokes space, polarization demultiplexing is a truly blind procedure, since no demodulation is required and no knowledge of the modulation format or carrier frequency is required. In addition, there are no singularity issues in Stokes space.

Stokes space helps to show the polarization condition of an optical signal and is therefore an excellent tool for observing polarization changes in an optical channel. Any polarization state of perfectly polarized light can be depicted by a point in three-dimensional space on the surface of a sphere, with the center of the so-called Poincaré sphere located at the origin of this coordinate system. The radius of the sphere corresponds to the amplitude of the light. Circular polarization can be found along the S3 axis. Linear polarization is found at the equator of the plane spanned by the S1 and S2 axes, and elliptical polarization is found in the middle. In Figure 7, we can see some independent polarization states in green on the sphere.

Figure 7. Poincaré sphere in Stokes space for a polarization multiplexed (PDM) QPSK signal.

Also shown in Figure 7 are the measured x- and y-polarized QPSK signals. There are four possible phase differences between these two signals at the sampling point. Combining the x- and y-signals with these four phase differences gives us the blue point cloud measured in Stokes space. (Using a QPSK signal with only one polarization direction, we can only get one accumulation on the S1 axis.)

The transitions between the four polarization states define a lens-like object in Stokes space (see Figure 8). It follows that any polarization-multiplexed signal of any format can define such a lens.