problem in the my matlab code at demodulation with counting error (xor) bits are not equal / balance it showing in command prompt

clc;
clear;
close all;

N=1e5; %Number of data bits to send over the channel

EbN0dB=0:1:20;

N=N+rem((3-rem(N,3)),3); %add additional bits to the data to make the length multiple of 3
% one 8-PSK symbol contains 3 binary bits
x=rand(1,N)>=0.5;%Generate random 1's and 0's as data;
figure(1);
grid on;
stem( x(1:30),'filled')
%Club 3 bits together and gray code it individually
inputSymBin=reshape(x,3,N/3)';
g=bin2gray(inputSymBin);
%Convert each Gray coded symbols to decimal value this is to ease the process
%of mapping based on array index
b=bin2dec(num2str(g,'%-1d'))';
%8-PSK Constellation Mapper
%8-PSK mapping Table
map=[1.414 0.707;0.707 1.414;-0.707 1.414;-1.414 0.707;-1.414 -0.707;-0.707 -1.414;0.707 -1.414;1.414 -0.707];
s=map(b(:)+1,1)+1i*map(b(:)+1,2);
figure;
plot(real(s),imag(s),'ko','MarkerFaceColor','g','MarkerSize',7);
grid;
%plot(s);
% Filter Definition
%square root raised cosine filter at tansmitter for avoid the inter symbol
%interference (ISI).
% Define filter-related parameters. 
filtorder = 16; % Filter order
nsamp=4;
delay = filtorder/(nsamp*2); % Group delay (# of input samples)
rolloff = 0.35; % Rolloff factor of filter
%Create a square root raised cosine filter.
rrcfilter = rcosine(1,nsamp,'fir/sqrt',rolloff,delay);

% Plot impulse response.
figure; impz(rrcfilter,1);
% Transmitted Signal
% Upsample and apply square root raised cosine filter.
ys = rcosflt(s,1,nsamp,'filter',rrcfilter);
%figure;
%impz(ys,1);
% Create Rayleigh fading channel object.
tau12 = [0 1e-6];
pdb12 = [0 3];
%h12 = rayleighchan(Ts,fd,tau12,pdb12);
%h12.PathGains
chan = rayleighchan(1/10000,100,tau12,pdb12);
ys1 = filter(chan,ys);    % Apply the channel effects
%Simulation for each Eb/N0 value
M=8; %Number of Constellation points M=2^k for 8-PSK k=3
Rm=log2(M);   %Rm=log2(M) for 8-PSK M=8
Rc=1;   %Rc = code rate for a coded system. Since no coding is used Rc=1

simulatedBER = zeros(1,length(EbN0dB));
theoreticalBER = zeros(1,length(EbN0dB));
count=1;
figure; 
for i=EbN0dB
    %-------------------------------------------
    %Channel Noise for various Eb/N0
    %-------------------------------------------
    %Adding noise with variance according to the required Eb/N0
    EbN0 = 10.^(i/10); %Converting Eb/N0 dB value to linear scale
    noiseSigma = sqrt(2)*sqrt(1./(2*Rm*Rc*EbN0)); %Standard deviation for AWGN Noise
    %Creating a complex noise for adding with 8-PSK s signal
    %Noise is complex since 8-PSK is in complex representation
    n = noiseSigma*(randn(1,length(ys1))+1i*randn(1,length(ys1)))';
    y = ys1 + n;

      plot(real(y),imag(y),'r*');hold on;
      plot(real(s),imag(s),'ko','MarkerFaceColor','g','MarkerSize',7);hold off;
      title(['Constellation plots - ideal 8-PSK (green) Vs Noisy y signal for EbN0dB =',num2str(i),' dB']);
      grid;
      %pause;
      y=2;
      %Demodulation
      %Find the signal points from MAP table using minimum Euclidean distance
      demodSymbols = zeros(1,length(y));
      for j=1:length(y)
          [minVal,minindex]=min(sqrt((real(y(j))-map(:,1)).^2+(imag(y(j))-map(:,2)).^2));
          demodSymbols(j)=minindex-1
      end
      demodBits=dec2bin(demodSymbols)-'0'; %Dec to binary vector    

      xBar=gray2bin(demodBits)'; %gray to binary
      xBar=xBar(:)'
      bitErrors=sum(sum(xor(x,xBar))); 
      simulatedBER(count) = log10(bitErrors/N);    
      theoreticalBER(count) = log10(1/3*erfc(sqrt(EbN0*3)*sin(pi/8)));
      count=count+1;       
  end
  figure; 
  grid;
  plot(EbN0dB,theoreticalBER,'r-*');hold on;
  plot(EbN0dB,simulatedBER,'k-o');

title('BER Vs Eb/N0 (dB) for 8-PSK');legend('Theoretical','Simulated');grid on;
xlabel('Eb/N0 dB');
ylabel('BER - Bit Error Rate'); 
grid on;

Answer 1

[Sean de Wolski]

So what is the problem?

Type:

dbstop if error

and then run it, the program will stop when an error occurs and you can inspect it to see what's going on.