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This document provides insights into digital communication systems, specifically focusing on the Additive White Gaussian Noise (AWGN) model, signal generation, and vector representations of signals. Illustrative figures depict the synthesizer and analyzer for signal generation, geometric representation of signals, and effects of noise perturbation on signal reception. The content also explores various modulation schemes and their signal constellations including M-ary PSK and QAM, and concepts like rotational and translational invariance. This foundational knowledge supports advanced studies in digital communication.
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ECE 4331, Fall, 2009 Zhu Han Department of Electrical and Computer Engineering Class 18 Oct. 27th, 2007
Figure 5.1 Block diagram of a generic digital communication system.
Figure 5.2 Additive white Gaussian noise (AWGN) model of a channel.
Figure 5.3 (a) Synthesizer for generating the signal si(t). (b) Analyzer for generating the set of signal vectors si.
Figure 5.4 Illustrating the geometric representation of signals for the case when N 2 and M 3.
Figure 5.5 Vector representations of signals s1(t) and s2(t), providing the background picture for providing the Schwarz inequality.
5.3 Conversion of the continuous AWGN channel into a vector channel Figure 5.2 Additive white Gaussian noise (AWGN) model of a channel. Figure 5.3 (a) Synthesizer for generating the signal si(t). (b) Analyzer for generating the set of signal vectors si.
Figure 6.46 Signal constellation for (a) M-ary PSK and (b) corresponding M-ary QAM, for M 16.
Figure 5.7 Illustrating the effect of noise perturbation, depicted in (a), on the location of the received signal point, depicted in (b).
Example of samples of matched filter output for some bandpass modulation schemes
Figure 5.8 Illustrating the partitioning of the observation space into decision regions for the case when N 2 and M 4; it is assumed that the M transmitted symbols are equally likely.
Figure 5.10 Detector part of matched filter receiver; the signal transmission decoder is as shown in Fig. 5.9b.
Figure 5.11 A pair of signal constellations for illustrating the principle of rotational invariance. EE 541/451 Fall 2007
Figure 5.12 A pair of signal constellations for illustrating the principle of translational invariance.
Figure 5.13 Illustrating the union bound. (a) Constellation of four message points. (b) Three constellations with a common message point and one other message point retained from the original constellation.
