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Optical Fiber Communication chapter7


CHAPTER 7 OPTICAL RECEIVER OPRATION

Having discussed the characteristics and operation of photodetectors in the previous chapter, we now turn our attention to the optical receiver. An optical receiver consists of a photodetector, an amplifier, and signal-processing circuitry. It has the task of first converting the optical energy emerging from the end of a fiber into an electric signal, and then amplifying this signal to a large enough level so that it can be processed by the electronics following the receiver amplifier. In these processes, various noises and distortions will unavoidably be introduced, which can lead to errors in the interpretation of the received signal. As we saw in the previous chapter, the current generated by the photodetector is generally very weak and is adversely affected by the random noises associated with the photodetection process.
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When this electric signal output from the photodiode is amplified, additional noises arising from the amplifier electronics will further corrupt the signal. Noise considerations are thus important in the design of optical receivers, since the noise sources operating in the receiver generally set the lowest limit for the signals that can be processed. In designing a receiver, it is desirable to predict its performance based on mathematical models of the various receiver stages. These models must take into account the noises and distortions added to the signal by the components in each stage, and they must show the designer which components to choose so that the desired performance criteria of the receiver are met. The most meaningful criterion for measuring the performance of a digital communication system is the average error probability. In an analog system the fidelity criterion is usually specified in terms of a peak signal-to-rms-noise ratio.
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The calculation of the error probability for adigital optical communication receiver differs from that of conventional electric systems. This is because of the discrete quantum nature of the optical signal and also because of the probabilistic character of the gain process 。 when an avalanche photodiode is used. Various authors have used different numerical methods to derive approximate predictions for receiver performance. In carrying out these predictions, a tradeoff results between simplicity of the analysis and accuracy of the approximation. General reviews and concepts of optical receiver designs are given in Refs.9-18 In this chapter, we first present an overview of the fundamental operational characteristics of the various stage of an optical receiver. This consists of tracing the path of a digital signal through the receiver and showing what happens at each step along the way. Section 7.2 then outlines the fundamental probability methods for determining the biterror rate or probability of error of a digital receiver based on
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signal-to-noise considerations. The mathematical details for this are given in Sec.7.3. These derivations and Sec.7.4 on receiver preamplifiers encompass advanced material that can be skipped without loss of continuity, these sections are designated by a star. The final discussion in Sec.7.5 addresses analog receivers, which play an important part in many applications, such as extensions of microwave and satellite links, DATV, and video transmission systems.

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7 OPTICAL RECEIVER OPRATION

Signal path though an optical date link

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7.1 FUNDASMENTAL

RECEIVER OPERATION

The design of an optical receiver is much more complicated than that of an optical transmitter because the receiver must first detect weak, distorted signals and then make decisions on what type of data was sent based on an amplified version of this distorted signal. To get an appreciation of the function of the optical receiver, we first examine what happens to a signal as it is sent through the optical data link shown in Fig.7-1. Since most fiber optic systems use a two-level binary digital signal, we shall analyze receiver performance by using this signal form first. Analog receivers are discussed in Sec.7.5.

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7.1.1

Digital Signal Transmission. .

A typical digital fiber transmission link is shown in Fig.7-1. The transmitted signal is a two-level binary data stream consisting of either a 0 or a 1 in a time slot of duration Tb. This time slot is referred to as a bit period. Electrically, there are many ways of sending a given digital message. One of the simplest(but not necessarily the most efficient) techniques for sending binary data is amplitudeshift keying, wherein a voltage level is switched between two values, which are amplitude V relative to the zero voltage level when a binary 1 occurs and a zerovoltage-level space when a binary 0 occurs. Depending on the coding scheme to be used, a 1 may or may not fill the time slot Tb. For simplicity, here we assume that when a 1 is sent, a voltage pulse of duration Tb occurs, whereas for a 0 the voltage remains at its zero level. A discussion of more efficient transmission codes is given in Chapter.8. The function of the optical transmitter is to convert the electric signal to an optical signal. As shown in Chapter.4.,an electric current I(t) can be used to modulate directly an optical
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7.1.1

Digital Signal Transmission.

source(either an LED or a laser diode) to produce an optical output power P(t). thus, in the optical signal emerging from the transmitter, a 1 is represented by a pulse of optical power (light) of duration Tb, whereas a 0 is the absence of any light. The optical signal that gets coupled from the light source to the fiber becomes attenuated and distorted as it propagates along the fiber waveguide. Upon reaching the receiver, either a pin or an avalanche photodiode converts the optical signal back to an electrical format. After the electric signal produced by the photodetector is amplified and filtered, a decision circuit compares the signal in each time slot with a certain reference voltage known as the threshold level. If the received signal level is greater than the threshold level, a 1 is said to have been received. If the voltage is below the threshold level, a 0 is assumed to have been received.
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7.1.2 Receiver Configuration

In some cases, an optical amplifier is placed ahead of the photodiode to boost the optical signal level before photodetection. This is done so that the signal-to-noise ratio degradation caused by thermal noise in the receiver electronics can be suppressed. Compared with other front-end devices, such as avalanche photodiodes or optical heterodyne detectors, an optical preamplifier provides a larger gain factor and a broader bandwidth. However, this process also introduces additional noise to the optical signal. 7.1.2 Receiver Configuration a schematic diagram of a typical optical receiver is shown in Fig.7-4. The three basic stages of the receiver are a photodetector, an amplifier, and an equalizer. The photodetector can be either an avalanche photodiode with a mean gain M or a pin photodiode for which M=1. The photodiode has a quantum efficiency η and a capacitance Cd. The detector bias resistor has a resistance Rb which generates a thermal noise current (t).
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7.1.2 Receiver Configuration

The amplifier has an input impedance represented by the parallel combination of a resistance Ra and a shunt capacitance Ca. Voltages appearing across this impedance cause current to flow in the amplifier output. This amplifying function is represented by the voltagecontrolled current source which is characterized by a transconductance (given in amperes/volt, or siemens). There are two amplifier noise sources. The input noise current source (t) arises from the thermal noise of the amplifier input resistance Ra, whereas the noise voltage source (t) represents the thermal noise of the amplifier channel. These noise sources are assumed to be gaussian in statistics, flat in spectrum(which characterizes white noise), and uncorrelated (statistically independent). They are thus completely described by their noise spectral densities and (see App.E). The equalizer that follows the amplifier is normally a linear frequencyshaping filter that is used to mitigate the effects of signal distortion and intersymbol interference. Ideally, it accepts the combined frequency
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7.1.2 Receiver Configuration

response of the transmitter, the transmission medium, and the receiver, and transforms it into a signal response that is suitable for the following signal-processing electronics. In some cases, the equalizer may be used only to correct for the electric frequency response of the photodetector and the amplifier.

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7.1.2 Receiver Configuration

To account for the fact that the rectangular digital pulses that were sent out by the transmitter arrive rounded and distorted at the receiver, the binary digital pulse train incident on the photodetector can be described by

Here, P(t)is the received optical power, Tb is the bit period, is an amplitude parameter representing the nth message digit, and (t) is the received pulse shape, which is positive for all t. For binary data the parameter can take on the two values, and ,corresponding to a binary 1 and 0, respectively. If we let the nonnegative photodiode input pulse (t) be normalized to have unit area

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7.1.2 Receiver Configuration

Then represents the energy in the nth pulse. The mean output current from the photodiode at time t resulting from the pulse train given in Eq.(7-4) is (neglecting dc components arising from dark noise currents)

Where R0=ηq/hν is the photodiode reponsivity as given in Eq.(6-6). This current is then amplified and filtered to produce a mean voltage at the output of the equalizer.

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7.2 DIGITAL RECEIVER PERFORMANCE

7.2 DIGITAL RECEIVER PERFORMANCE In a digital receiver the amplified and filtered signal emerging from the equalizer is compared with a threshold level once per time slot to determine whether or not a pulse is present at the photodetector in that time slot. Ideally, the output signal (t) would always exceed the threshold voltage when a 1 is present and would be less than the threshold when no pulse (a 0) was sent. In actual systems, deviations from the average value of (t) are caused by various noises, interference from adjacent pulses, and conditions wherein the light source is not completely extinguished during a zero pulse.

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7.2.1 Probability of Error

In practice, there are several standard ways of measuring the rate of error occurrences in a digital data stream. One common approach is to divide the number Ne of errors occurring over a certain time interval t by the number Nt of pulses (ones and zeros) transmitted during this interval. This is called either the error rate or the bit-error rate, which is commonly abbreviated BER. Thus, we have Where B=1/Tb is the bit rate (i.e., the pulse transmission rate). The error rate is expressed by a number, such as ,for example, which states that, on the average, one error occurs for every billion pulses sent. Typical error rates for optical fiber telecommunication systems range from to . This error rate depends on the signal-to-noise ratio at the receiver(the ratio of signal power to noise power). The system error rate requirements and the receiver noise levels thus set a lower limit on the optical signal power level that is required at the photodetector.
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7.2.1 Probability of Error

To compute the bit-error rate at the receiver, we have to know the probability distribution of the signal at the equalizer output. Knowing the signal probability distribution at this point is important because it is here that the decision is made as to whether a 0 or a 1 is sent. The shapes of two signal probability distributions re shown in Fig.7-5. there are

Which is the probability that the equalizer output voltage is less than v when a logical 1 pulse is sent, and

Which is the probability that the output voltage exceeds v when a logical 0 is transmitted. Note that the different shapes of the two probability distributions in Fig.7-5 indicate that the noise power for a logical 0 is usually not the same as that for a logical 1. this occurs in optical systems because of signal distortion from transmission
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7.2.1 Probability of Error

impairments (e.g., dispersion, optical amplifier noise, and distortion from nonlinear effects) and from noise and ISI contributions at the receiver. The functions p(y) and p(y) are the conditional probability distribution functions; that is, p(y)is the probability that the output voltage is y, given that an x was transmitted.

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7.2.1 Probability of Error

If the threshold voltage is then the error probability Pe is defined as

The weighting factors a and b are determined by the a priori distribution of the data. That is ,a and b are the probabilities that either a 1 or a 0 occurs, respectively. For unbiased data with equal probability of 1 and 0 occurrences, a=b=0.5. the problem to be solved now is to select the decision threshold at that point where Pe is minimum. To calculate the error probability we require a knowledge of the meansquare noise voltage <> which is superimposed on the signal voltage at the decision time. The statistics of the output voltage at the sampling

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7.2.1 Probability of Error

time are very complicated, so that an exact calculation is rather tedious to perform. A number of different approximations have therefore been used to calculate the performance of a binary optical fiber receiver. In applying these approximations, we have to make a tradeoff between computational simplicity and accuracy of the results. The simplest method is based on a gaussian approximation. In this method, it is assumed that, when the sequence of optical input pulses is known, the equalizer output voltage (t) is a gaussian random variable. Thus, to calculate the error probability, we need only to know the mean and standard deviation of (t). other approximations that have been investigated are more involved and will not be discussed here. Thus, let us assume that a signal s (which can be either a noise disturbance or a desired information-bearing signal) has a gaussian probability distribution function with a mean value m. if we sample the signal voltage level s(t)at any arbitrary time t1, the probability that the measured sample s(t1) falls in the range s to s+ds is given by
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7.2.1 Probability of Error

Where f(s) is the probability density function, is the noise variance, and its square root σ is the standard deviation, which is a measure of the width of the probability distribution. By examining Eq.(7-19) we can see that the quantity 2σ measures the full width of the probability distribution at the point where the amplitude is 1/e of the maximum. We can now use the probability density function to determine the probability of error for a data stream in which the 1 pulses are all of amplitude V. As shown in Fig.7-6,the mean and variance of the gaussian output for a 1 pulse are and , respectively, whereas for a 0 pulse they are and ,respectively. Let us first consider the case of a 0 pulse being sent, so that no pulse is present at the decoding time. The probability of error in this case is the probability that the noise will exceed the threshold voltage and . Using Eqs.(7-17) and (7-19),we have
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7.2.1 Probability of Error

Where the subscript 0 denotes the presence of a 0 bit. Similarly, we can find the probability of error that a transmitted 1 is misinterpreted as a 0 by the decoder electronics following the equalizer. This probability of error is the likelihood that the sampled signal-plusnoise pulse falls below . From Eqs.(7-16) and (7-19), this is simply given by

Where the subscript 1 denotes the presence of a 1 bit. If we assume that the probabilities of 0 and 1 pulses are equally likely, then, using Eqs.(7-20) and (7-21), the bit-error rate (BER) or the error probability Pe given by Eq.(7-18) becomes

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7.2.1 Probability of Error

The approximation is obtained from the asymptotic expansion of erf(x),. Here, the parameter Q is defined as and

Is the error function, which is tabulated in various mathematical handbooks. The factor Q is widely used to specify receiver performance, since it is related to the signal-to-noise ratio required to achieve a specific bit-error rate. In particular, it takes into account that in optical fiber systems the variances in the noise powers generally are different for received logical 0 and 1 pulse. Figure 7-7shows how the BER varies with Q. The approximation for Pe given in Eq.(7-22) and shown by the dashed line in Fig.7-7 is accurate to 1 percent for Q=3 and improves as Q increases. A commonly quoted Q value is 6,since this 22 corresponds to a BER=10-9.

7.2.2 The Quantum Limit

Let us consider the special case when and =0, so that . Then, from Eq.(7-23) we have that the threshold voltage =V/2, so that Q=V/2σ. Since σ is usually called the peak signal-to-rms-noise ratio. In this case, Eq.(722) becomes

In designing an optical system, it is useful to know what the fundamental physical bounds are on the system performance. Let us see what this bound is for the photodetection process. Suppose we have an ideal photodetector which has unity quantum efficiency and which produces no dark current; that is, no electron-hole pairs are generated in the absence of an optical pulse. Given this condition, it is possible to find the minimum received optical power required for a specific bit-error-rate performance in a digital system. This minimum received power level is known as the quantum limit, since all system parameters are assumed ideal and the performance is limited only by the photodetection statistics.
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7.2.2 The Quantum Limit

Assume that an optical pulse of energy E falls on the photodetector in a time interval τ. This can only be interpreted by the receiver as a 0 pulse if no electron-hole pairs are generated with the pulse present. From Eq.(7-2) the probability that n=0 electrons are emitted in a time interval τ is Where the average number of electron-hole pairs. N? , is given by Eq.(711). Thus, for a given error probability Pr(0), we can find the minimum energy E required at a specific wavelength λ.

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