Digital Communications 2

4Synchronization and Equalization

4.1. Introduction

In Chapter 3, we studied the performances of digital modulations in the ideal additive white Gaussian channel case with perfect synchronization between transmitter and receiver. Yet, these two assumptions are unrealistic in most transmission systems, which may introduce distortions, phase and frequency shifts, as well as delays.

The receiver must then correct these issues in order to perform signal detection. This chapter aims at detailing the operations performed at the receiver in order to apply detection as optimally as possible, in spite of the inter-symbol interference introduced by distortion and asynchronicity. The chapter is divided into separate sections: synchronization and equalization.

Section 4.2 presents the different techniques implemented at the receiver so that it can acquire synchronicity parameters and estimate the channel. These techniques are either data-aided, which means that the transmitter sends some training sequence already known by the receiver, of blind. This chapter studies statistical methods for the estimation of the frequency shift and time delay. Cramer–Rao’s bound is then introduced. It measures the relevance of each estimator. The specific case of synchronization in multi-carrier orthogonal frequency division multiple access (OFDM) systems is not detailed in this chapter, but in section 5.3.6.

Once synchronization parameters have been acquired by the receiver, equalization is performed before ...