 # Performance Analysis Models

DOI: 10.4018/978-1-4666-6575-0.ch010
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## Abstract

Modeling and performance analysis are crucial components in the understanding and design of high-speed optical communication systems. The purpose of this chapter is to discuss methods and techniques that can be used in modeling and performance analysis. It provides descriptions of various techniques that can be used to efficiently model and evaluate OTDM-WDM systems. Throughout the chapter, examples are used to demonstrate how the techniques can be applied to model and to evaluate the performance of high-speed optical communication systems.
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## Eye Penalty Estimation

The eye penalty is estimated from the receiver eye diagram, whereby we can use the optical eye diagram or the current eye diagram. The optical eye diagram is drawn based on the received optical signal while the current eye diagram is drawn based on the photodetected current. In order to draw the eye diagram, we plot over P bit periods where P is a small number and every multiple of P bit periods simulated is drawn back over the same axis as shown mathematically below

(10.1) where ED(t) is the eye diagram, U(nPt,(n+1)Pt) refers to the signal from time nPt to time (n+1)Pt and N is the total number of bits. An eye diagram example is shown in Figure 1.

From the figure, the eye penalty is estimated byEye penalty (dB) = 10 log10(Upp_thr / Low_thr) (10.2) where Upp_thr and Low_thr are the upper and lower thresholds of the eye diagrams respectively obtained from the center of the bit period. A closed eye indicates a high presence of noise while an open eye indicates good system performance. The eye penalty gives a rough estimation of the performance of the system by quantifying the relative ‘opening’ of the eye.

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## Amplitude And Timing Jitter

Some methods attempt to calculate the timing or amplitude jitter induced on the system during propagation or at the receiver. There are again many methods to define the amplitude or timing jitters, depending on the normalization criteria. A simple amplitude jitter definition is given byAmplitude jitter (dB) = 10 log10(E[ |U1-E[U1]| ] / E[U1]) (10.3) where E[] is the expected (mean) function and U1 is the amplitude of the 1’s of the signal at the bit period center. In general, amplitude jitter refers to the deviation of the signal pulse amplitude from its mean or stable value. Normally, it is measured at the center of the bit period, which is the time instant used for bit decisions.

A simple timing jitter definition is given byTiming jitter = E[|Maxt[U1]-T| ] (10.4) where Maxt[] is a function that determines the time instant when a signal is maximum within a particular bit period. In general, timing jitter refers to the deviation of the peak of the signal pulse from the actual center of the bit period, which is the time instant used for bit decisions. If the peak deviates from the bit decision instance, the sampled signal will be lower than the peak and, thus, reduces the signal power detected.

The magnitude of the amplitude or timing jitters can be used to estimate the performance of the system. This estimation is useful as the amplitude or timing jitter can often be obtained in closed-form analytical expressions. At the same time, both parameters can be easily measured from signals obtained either through experiments or simulation.

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