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8

Performance Analysis

8.1 Introduction

In Chapter 4, various types of digital modulation schemes such as PSK, OOK, and FSK were introduced and
in Chapter 5, different receiver architectures such as direct detection, homodyne, and heterodyne detections
were discussed. In this chapter, the performances of these modulation schemes with the different receiver
architectures are investigated. Firstly, the concept of a matched filter is introduced in Section 8.2. In practice,
optical matched filters are rarely used in optical communication systems due to the difficulties involved in
fabricating such a matched filter. Nevertheless, the performance is optimum when the matched filters are
used, and the expressions for the error probability developed in this Chapter using the matched filters provide
a lower bound on the achievable BER.

8.2 Optimum Binary Receiver for Coherent Systems
In this section, we consider the generalized model for the optimum binary receivers (See Fig. 8.1) and later, we
apply this model to various detection schemes. Let x (t) and x (t) be the real optical signals used to transmit
1 2
bits ‘1’ and ‘0’, respectively:
{
x (t) when the message = ‘1’
1
x(t)= (8.1)
x (t) when the message = ‘0’.
0
Here, x (t), j = 0, 1 are arbitrary pulses of duration ≤T , where T is the bit interval. We assume that the
j b b
channel can be modeled as an additive white Gaussian noise (AWGN) channel, which means that the power
spectral density of the noise is constant and the probability distribution of the noise process is Gaussian. The
output of the channel may be written as
y(t)= x(t)+ n(t), (8.2)
where n(t) is the noise added by the channel and
= N ∕2 (8.3)
n
0
is the power spectral density of n(t). Let the Fourier transform of x (t) be
j
̃ x ()= [x (t)], j = 0, 1. (8.4)
j
j
The channel output is passed through a filter. The purpose of this filter is to alter the ratio of the signal power
and noise power so that the best performance can be attained. The filter multiplies the signal spectrum by

Fiber Optic Communications: Fundamentals and Applications, First Edition. Shiva Kumar and M. Jamal Deen.
© 2014 John Wiley & Sons, Ltd. Published 2014 by John Wiley & Sons, Ltd.