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  • 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

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  • 原文地址:https://www.cnblogs.com/zzyzz/p/13635899.html
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