LIST OF FIGURES
Figure 1.1 Basic Components of Transmission System …..………...……1 Figure 1.2 Functional block diagram of a communication system ………..…..2 Figure 1.3 Illustration of channel distortion: (a) the input signal spectrum, (b) the
Channel frequency response, (c) the channel output ………..…6 Figure 1.4 Illustration of (a) white noise, (b) its autocorrelation, and
(c) its power spectrum ………...9 Figure 1.5 (a) A pink noise signal and (b) its magnitude spectrum ………...…..11 Figure 1.6 (a) A brown noise signal and (b) its magnitude spectrum ………..11 Figure 1.7 Time and frequency sketches of: (a) an ideal impulse, (b) and (c) short
duration pulses ……….………...12 Figure 1.8 Illustration of variations of the impulse response of a non-linear system with the increasing amplitude of the impulse ………...13 Figure 1.9 (a) A scratch pulse and music from a gramophone record………...14 Figure 1.10 Pulse shaping with the pulse shaping filter. In this example, the resulting pulse shape is a so-called raised cosine pulse ………...18 Figure 1.11 The spectrum of the base band signal. The spectrum is symmetric around f=0, if and only if the symbols are real …...………...………...19 Figure 1.12 System Adaptation ………....20 Figure 1.13 A transmitted sequence of data {d (t)}, propagating through a time-variant channel, yields a received sampled sequence {y (t)} .………...21 Figure 2.1 The structure of equalizer ……….…………..….……...18 Figure 2.2 The Structure of a Decision Feedback Equalizer ………...…21 Figure 2.3 The Structure of an Indirect Adaptive Equalizer …………...………….……25 Figure 2.4 Neural Decision Feedback Equalizer………..31 Figure 2.5 The Structure of an Indirect Adaptive Equalizer …….…………..……...35 Figure 2.6 Data transmission over a no ideal band limited linear AWGN channel. The blocks inside the dotted rectangle are modeled by the MATLAB function ……...…..…36 Figure 2.7 Filter Pulse Shapes and Channel Impulse Response ………..36 Figure 2.8 FIR Equalizer with 2L+1 Taps and Detection Delay ...………..…37
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Figure 2.9 The FIR Filter …………...……….……...40
Figure 2.10 System Adaptation……….41
Figure 2.11 A transmitted sequence of data {d(t)}, propagating through a time-variant channel, yields a received sampled sequence {y(t)}………..42
Figure 2.12 Structure of neural equalization system……….43
Figure 3.1 Biological Neuron ………...45
Figure 3.2 Artificial Neuron (Perception) ………....46
Figure 3.3 Multi-layer Perception ………....47
Figure 3.4 Back Propagation Network ………..…...50
Figure 3.5 Model of Neural Structure ………..…51
Figure 3.6 Artificial Neuron ………...52
Figure 3.7 Sigmoid Activation Function ………..………52
Figure 3.8 An Input Layer Neuron ………..….53
Figure 3.9 A hidden Layer Neuron ………..53
Figure 3.10 A output Layer Neuron ……….54
Figure 4.1 Three-tap channel model symbol points seen in a two-dimensional observation space ………..60
Figure 4.2 (a) Structure of LMS equalizer system,(b) Simulation LMS Linear Equalizer………61
Figure 4.3 Output for LMS equalizer ………...63
Figure 4.4 Structure of neural equalization system …………..………...65
Figure 4.5 Output of adaptive equalization system ………...67
Figure 4.6 Simulation of Adaptive equalization using LMS ………...…68
Figure 4.7 The outputs of simulation for RLS and LMS……….….69
Figure 4.8 Neural network structures………...70
Figure 4.9 Performance of NN (solid line) and LMS (dashed line) equalizers for channel …...………..…...73
Figure 4.10 Error plot………....74
Figure 4.11 Channel states: (a) noise free, ( b) with noise, (c) after equalization (after 500 learning iterations), (d) after equalization (after 1000 learning iterations)…...………….74
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