通信代写: ES4C4 Optical Communication Systems

(a) (b) (c)

be able to perform an approximate sensitivity calculation for an optically preamplified receiver;

understand the effect of receiver parameters in design issues in optically preamplified receivers;

appreciate recent developments and additional sophistication in optical preamplifier modelling from the literature.

Optical Preamplifier Assignment

SCHOOL OF ENGINEERING

ES4C4 Optical Communication Systems
Optical Preamplifier Assignment Specification

1. Learning Objectives

After completing this work you will:

2. Modelling an Optically Preamplified Receiver

Figure 1 below shows a block diagram of a receiver employing an optical preamplifier. Such a receiver consists of an optical amplifier followed by an optical bandpass filter, to remove much of the amplified spontaneous emission (ASE) noise, and a PIN photodiode based receiver.

Electrical Detection Circuitry

Optical Amplifier

Optional Polariser

Optical Bandpass Filter (OBPF)

pin

photodiode

Figure 1: Optically preamplified receiver

The model here considers the noise arising from the amplification process, the ASE noise. The probability density function of the noise at the receiver is difficult to handle so a Gaussian approximation is used. The moment generating function (mgf) of the signal plus the noise in the model is

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Optical Preamplifier Assignment

 1 mGs

s exp  mM   2  1N0s

(1)

1Ns t  0

where m is the number of photons (which may be m0 in the zero or m1 in the one state) and the other symbols are defined in Table 1 below.

Table 1: Relevant Symbols

Other symbols are defined in the following equations, in terms of those given above. The numbers of photons per bit are given by

m  2r b (2)

1

r 1
m0  2 b (3)

r 1
Employing the Gaussian approximation, for this OOK NRZ system gives a bit error

rate (BER) P defined by eb

where Q is given by

P 1erfcQ eb 2 2

1  0 1 0

(4)

(5)

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Optical Preamplifier Assignment

and 1 (0) is the mean of the signal plus noise distribution for ones (zeros) and 1

(0) is the distribution’s standard deviation for ones (zeros). The power received is

givenbyP 1,0m hfR. sig 1,0 b

3. Tasks

(a) Show that the mean and variance of the distribution (1) may be found from the mgf to be

 m GN mtM 1,0 1,0 02

 2 22m GN 2N2 mtM 1,0 1,00 02

(6) (7)

{HINT: We need to find   0and  2  0  2 ; this is most easily done by considering ln s}

2. (b)  Using any appropriate software (although MATLAB would be a good choice), produce a programme that implements a model based on the Gaussian approximation. The programme should be used to plot the graphs indicated and to estimate the results required in the submission.
3. (c)  Plot a suitable graph of BER against the input signal in dBm for G = 30 dB, r = 108 (easier to substitute in equations than!); nsp  mt  1; Rb = 155 Mbps;

   B = Rb. To obtain the photon wavelength and hence the photon energy energy, take the last two digits of your student code and use it as the second and third decimal places as shown

    = 15 nm

   For example if the last digits of your code are 35, you should use 1535 nm for the wavelength.

4. (d)  Leaving the other parameters unchanged, explore the impact of optical filter bandwidths of 1.55 GHz and 15.5 GHz.
5. (e)  Using M = 10 and leaving the other parameters as they are, investigate the effect of extinction ratios of 10 dB and 20 dB.
6. (f)  Still using M = 10 but reverting to the 108 extinction ratio, determine the effect of amplifier gains of 10 dB and 20 dB.

digits

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Optical Preamplifier Assignment

7. (g)  Demonstrate from (5), (6) and (7) that the quantum efficiency has no effect in this approximation.
8. (h)  Using 30 dB gain and M = 10, include 2 polarisations rather than one.
9. (i)  Again using 30 dB gain, M = 10 and one polarisation, determine the effect of

   nsp 1.5 and nsp  2.5.

10. (j)  Use your graphs and programmes to obtain estimates of the 10-9 sensitivities

    for the various cases above, and hence complete the proforma attached.

4. Submission of Work

The work to be submitted for assessment should consist of:

1. (a)  working to show that the mean and variance may be derived from the mgf, and that the quantum efficiency does not affect the model;
2. (b)  copies of your programmes;
3. (c)  copies of graphs and results;
4. (d)  an Assignment Submission Proforma as attached containing estimates of the values requested obtained from your model;
5. (e)  a one page discussion and summary of your conclusions;
6. (f)  a one page review of developments in optical amplifier modelling that have enhanced the modelling process beyond that considered here (this should refer to relevant literature, factors that are not included above and any developments in amplifiers/communication systems themselves).

Note that a full report is not required, just the items listed above.

DIVISION OF MARKS

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Optical Preamplifier Assignment

Assignment Submission Proforma

Enter below the values obtained using your model.

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