Digital Communications 2

5Multi-carrier Modulations

5.1. Introduction

As already mentioned in Chapter 4, the channel may generate distortions on the received symbols. The channel is frequency-selective if its frequency response is uncorrelated on the considered bandwidth [PRO 08, GOL 05]. The coherence band B_c is defined as the frequency band on which two frequency components of the channel can be assumed uncorrelated.

The frequency-selectivity of a channel is equivalently characterized by one of the following definitions: either the maximum delay of the channel’s impulse response T_m is large compared to the symbol period T, or the channel’s coherence band is small compared to its bandwidth B. If the channel is frequency-selective, it generates inter-symbol interference at the receiver. On the contrary, we assume that a channel is non-frequency-selective with an almost flat frequency response in its bandwidth if B ≤ 0.1B_c.

The maximum delay of the channel’s impulse response and the channel’s coherence band are related as follows:

An example of frequency-selective channel is given in Figure 5.1. It represents the modulus of the frequency response of channel g_c with impulse response:

in baseband and with bandwidth B = 1 MHz. This channel is frequency-selective, since its maximum delay T_m = 6 × T_s = 6 μ ...