CCS

Multiamplitude Signal Transmission

In the preceding section, we treated the transmission of digital information by use of
binary signal waveforms. Thus, each signal waveform conveyed 1 bit of information.
In this section, we use signal waveforms that take on multiple amplitude levels. Thus,
we can transmit multiple bits per signal waveform.

Signal Waveforms with Four Amplitude Levels

Optimum Receiver for the AWGN Channel

Signal Correlator

The Detector

The detector observes the correlator output r and decides which of the four PAM signals
was transmitted in the signal interval.

Because the received signal amplitude Ai can take the values ± d, ± 3d, as illustrated
in the signal constellation in Figure 5.24, the optimum amplitude detector compares
the correlator output r with the four possible transmitted amplitude levels and
selects the amplitude level that is closest in Euclidean distance to r. Thus, the optimum
amplitude detector computes the distances

Matlab Coding,

 1 % MATLAB script 2 
 3 echo on
 4 clear;
 5 SNRindB1=0:1:12;
 6 SNRindB2=0:0.1:12;
 7 for i=1:length(SNRindB1),
 8     % simulated error rate
 9     smld_err_prb(i)=smldPe58(SNRindB1(i));
10     echo off;
11 end;
12 echo on;
13 for i=1:length(SNRindB2),
14     % signal-to-noise ratio
15     SNR_per_bit=exp(SNRindB2(i)*log(10)/10);
16     % theoretical error rate
17     theo_err_prb(i)=(3/2)*Qfunct(sqrt((4/5)*SNR_per_bit));
18     echo off;
19 end;
20 echo on;
21 % Plotting commands follow.
22 semilogy(SNRindB1,smld_err_prb,'*');
23 hold
24 semilogy(SNRindB2,theo_err_prb);
25 xlabel('SNR')
26 
27 
28 function [p]=smldPe58(snr_in_dB)
29 % [p]=smldPe58(snr_in_dB)
30 %        SMLDPE58  simulates the probability of error for the given
31 %           snr_in_dB, signal to noise ratio in dB.
32 d=1;
33 SNR=exp(snr_in_dB*log(10)/10);           % signal to noise ratio per bit
34 sgma=sqrt((5*d^2)/(4*SNR));           % sigma, standard deviation of noise
35 N=10000;                    % number of symbols being simulated

36 % Generation of the quaternary data source follows.
37 for i=1:N,
38   temp=rand;                         % a uniform random variable over (0,1)
39   if (temp<0.25),
40     dsource(i)=0;                   % With probability 1/4, source output is "00."
41   elseif (temp<0.5),
42     dsource(i)=1;                   % With probability 1/4, source output is "01."
43   elseif (temp<0.75),
44     dsource(i)=2;                   % With probability 1/4, source output is "10."
45   else
46     dsource(i)=3;                  % With probability 1/4, source output is "11."
47   end
48 end;

49 % detection, and probability of error calculation
50 numoferr=0;
51 for i=1:N,
52   % the matched filter outputs
53   if (dsource(i)==0),
54     r=-3*d+gngauss(sgma);          % if the source output is "00"
55   elseif (dsource(i)==1),
56     r=-d+gngauss(sgma);            % if the source output is "01"
57   elseif (dsource(i)==2)  
58     r=d+gngauss(sgma);             % if the source output is "10"
59   else
60     r=3*d+gngauss(sgma);           % if the source output is "11"
61   end;
62   % Detector follows.
63   if (r<-2*d),
64     decis=0;                     % Decision is "00."
65   elseif (r<0),
66     decis=1;                     % Decision is "01."
67   elseif (r<2*d),
68     decis=2;                     % Decision is "10."
69   else
70     decis=3;                     % Decision is "11."
71   end;
72   if (decis~=dsource(i)),           % If it is an error, increase the error counter.
73     numoferr=numoferr+1;
74   end;
75 end;
76 p=numoferr/N;                       % probability of error estimate


Simulation Result

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis