Chapter 3: Nonlinear Optical Thresholding Using Two-Photon Absorption
3.5 Simulation Model of a Four-Channel OCDMA System Using TPA Detection
In the previous section it was shown that a TPA-based detector can increase the extinction ratio of an OCDMA signal compared to a standard linear detector, demonstrating the vi- ability of using a TPA-based device as a receiver in an optical system. In this section, a simulation model is generated to examine the overall system performance of a four-channel OCDMA system, based on the experimental results shown in the previous section. In par- ticular, the performance improvement gained through the use of a TPA-based detector is analysed in comparison to the performance of a system using standard detection techniques.
3.5.1 Four-Channel OCDMA Simulation Model
To assess the performance improvement achieved through the use of a TPA-based detector in an OCDMA system quantitively using bit error rate analysis, a simulation model of the TPA detector characterised in Figure 3.10 (a) was generated. From the measured experi- mental data in this figure, the SPA and TPA coefficients, α and β, for the TPA detector were
Figure 3.11: Simulation model of a four-channel OCDMA system employing temporal phase coding and TPA-based detection.
found to be 1.36×10−4m−1and 2.35×10−16m/W assuming an effective area of 9.6 µm2 and a diode length of 600 µm. Using these values and equations (3.3)–(3.5), a TPA de- tector model was created. The nonlinear response of the simulation model is shown in Figure 3.10 (a) by the dashed line. It can be seen that there is excellent agreement between the response of the physical device and the simulation model.
To directly compare the performance of standard linear detection with the TPA model, a simulation model of a four-channel OCDMA system was created using VPI network simu- lation software package. The simulation model is shown in Figure 3.11. A 155 MHz optical pulse train with a pulse width of 2 ps was split into four copies that were each modulated by four separate PRBS signals. These signals were encoded using eight-chip temporal phase codes. The four codes used were eight-chip Walsh codes given as (0, 0, 0, 0, π, π, π, π), (0, π, 0, π, 0, π, 0, π), (0, 0, π, π, 0, 0, π, π) and (0, 0, 0, 0, 0, 0, 0, 0) for encoders one to four respectively. In these codes, 0 represents no phase shift on the given optical chip pulse while π represents a 180◦ phase shift. These codes were chosen due to the minimum amount of interference they generate when passing through a given optical decoder.
The simulation model employs simple slot-level coordination, similar to that described in [19], to prevent optical beat noise between the signals. This slot-level coordination re- sults in each optical signal being delayed by 70 ps with respect to the previous signals. The decoded signal is then either incident on a standard linear detector or the nonlinear TPA model. Throughout all simulation results presented, the phase decoder present corresponds to the optical code used in encoder three. Both detector models pass through a low-pass filter with a bandwidth of 155 MHz. The responsivity of the linear detector was 1 A/W.
An additional EDFA with a gain of 25 dB was used before the TPA model to overcome the inherent inefficiency of the TPA process. The optical power incident on the device is measured before the second EDFA and is shown in Figure 3.11 by the power measurement point. The output electrical signal was then analysed in terms of the generated eye diagrams and the BER measurements as a function of incident power as each additional channel was added to the system.
3.5.1.1 Simulation Results using Standard Detection
Figure 3.12: (a)–(d) Electrical eye diagrams after detection using a standard detector for one, two, three and four transmitting channels respectively (e)–(h) Electrical eye diagrams after detection using a TPA-based detector for one, two, three and four transmitting channels respectively.
Figure 3.12 (a)–(d) shows the eye diagrams for decoder three using a linear detector for four different cases; only one channel present (a), two channels (b), three channels (c), and when all four channels (d) are present. The multiple eye levels clearly seen in the two, three and four-channel cases can be explained due to the interference from the incorrectly de- coded channels. As these channels pass through the decoder, the phase nature of the codes results in constructive and destructive interference occurring in the signal. This results in each channel having a different average power after passing through the decoder, which is subsequently detected by the linear detector. Thus, examining the eye diagram generated for two channels in Figure 3.12 (b), four different levels are present. These levels are (0, 0), (0, 1), (1, 0) and (1, 1), where (x, y) corresponds to the data bit transmitted by the desired channel and the interfering channel respectively. This eye diagram highlights the problem associated with using a linear detector with a bandwidth equal to the data rate of the desired
Figure 3.13: BER plot as a function of received average power for a standard linear detector used in a four-channel OCDMA simulation model.
signal. Since the detector integrates the entire incident energy over the bit period, addi- tional levels are introduced when interfering channels are transmitting. If both the desired and unwanted signal possessed the same average power when incident on the detector, then the eye levels (0,1) and (1,0) would merge together in the centre of the eye due to the detec- tors inability to differentiate between the two signals, thus making correct detection of the desired signal impossible. This problem is further exacerbated with the addition of further channels, resulting in the eye diagram closing quite severely. Again, it should be noted that in this simulation model each channel has a different average power after passing through the decoder and as a result a small portion of the eye opening remains, albeit with a large amount of noise present.
Figure 3.13 shows the simulated bit-error rate plot as a function of incident average power for decoder 3 using a linear detector. As shown, error-free performance, corresponding to a BER of 1×10−9, using a linear detector can only be achieved for systems having at most two channels. Even for the two-channel case, incident average optical power falling on the linear detector must be of the order of –8 dBm in order to ensure error-free performance. This results in a power penalty of 18 dB when the system increases the number of channels from one to two. The two other cases presented containing three and four-channel systems are unable to achieve error-free performance, with a four-channel system having an error floor at a BER of 1×10−2. This error floor is due to the increased levels of MAI generated by the unwanted optical signals falling on the detector. The level of MAI noise increases proportionally with the number of users within the network, limiting overall system perfor- mance. From the results presented in Figure 3.13 it is obvious that when a linear detector is
employed in this particular system, the maximum number of users is limited to two. There- fore, if the number of channels is to be increased, some form of nonlinear thresholding is required.
3.5.1.2 Simulation Results using a TPA-Based Detector
As previously mentioned, in order to allow more channels to transmit data across the net- work, some form of noise suppression is required to reduce the impact of MAI on the overall performance. In this section, the results measured for the four-channel OCDMA system using the model of a TPA-based detector are discussed. These results allow a direct comparison in performance between the two different detection schemes.
Figure 3.12 (e)–(h) show the eye diagrams for the same four transmission scenarios dis- cussed in section 3.5.1.1. As was the case for the linear detector results, the addition of in- terfering channels results in multiple eye levels being present in the eye diagram. However, the eye openings when using the TPA-based detector are significantly improved when com- pared to the corresponding eye diagrams for a linear detector. This is due to the TPA-based detectors nonlinear response that suppresses the amount of MAI that is being generated by the improperly decoded optical signals incident on the detector, thus improving overall sys- tem performance. The amount of improvement gained is clearly demonstrated by the BER plots for the TPA-based detector shown in Figure 3.14.
Figure 3.14 shows the simulated BER plots obtained for the TPA-based detector. It can be clearly seen that the performance of the TPA detector differs greatly from the performance of the linear detector shown in Figure 3.13. The performance improvement gained through the TPA-based detector allows a BER of 1×10−9 to be achieved in all four transmitting scenarios. For a one channel system, error-free performance can be achieved when the in- cident average power is around -13 dBm. When a second transmitting channel is added to the OCDMA system, a power penalty of approximately 3 dB is incurred. The addition of a third channel incurs a further penalty of ∼8 dB, while the addition of the fourth channel incurs a further 3 dB penalty. As a result, there is an overall power penalty of 14 dB when the number of channels is varied from a single channel to a four-channel system. While 14 dB is a significant power penalty, the benefit of such an increase in the incident power is that error-free performance can be achieved with four-channels transmitting data simul- taneously using TPA detection. Again this is in comparison to the same situation for linear detection using higher incident optical powers, where error rates of only 1×10−2 could be achieved with four channel operation.
Figure 3.14: BER plot as a function of received average power for a TPA-based detector used in a four-channel OCDMA simulation model.