Plotting AWGN in baseband binary transmission

How do I plot this?

S0(t)= sqrt(2*E/T) sin(pi*t/T) 
S1(t)= sqrt(2*E/T) sin(2*pi*t/T)

where T is the period and E is normalized.

Can someone teach me how to plot this because I dont know how to plot E and T.

Answer 1

[UJJWAL]

Hi Phoon,

Your question is not clear. In the equation you have mentioned there is no mention of AWGN. It is not clear what you want to plot. The expression you have mentioned , it seems that it is of a signal of Symbol period 'T' for binary trnasmission. Multiplication by Sqrt[2*E/T) is done so as to ensure that the energy of the signal is 1. This is also a kind of normalization. For transmitting 1 and 0 usually the amplitudes are inverted. So Amplitude will be like Sqrt[2*E/T) for 1 and negetive of that for 0. So I dont know what you want to plot. I am below mentioning a plot for the BPSK transmission of a sequence of bits

x = [0,1,0,0,0,1,1,1]; % Bits to be transmitted
T= 1 ; % Symbol Period
len = length(0:0.001:1);
p=1;
for i = 1:length(x)
    s(1,p:p+len-1) = (-1)^(1+x(i)) * sqrt(2*0.1/1) * sin(2*pi*(0:0.001:1)/T);
    p=p+len;
end
t= 0:0.001:0.001*(p-2);
plot(t,s);
xlabel('Time\rightarrow','fontsize',18);
ylabel('s(t)\rightarrow','fontsize',18);
title('Baseband Signal','fontsize',20);
grid on;

For details clarify your question and reply back. Hope this helps

HAPPY TO HELP

UJJWAL

Answer 2

[Phoon]

Hi, this is my code.

I am supposed to make the lines into a sine wave, can you help me?

function MatFil1(name)
    if(nargin==0)
        name='PHOON JIAN';                     % Generate name 'PHOON JIAN' AWGN bit sequence
    end

      name(name==' ')=[];                         % Delete white space in the name string
      name=upper(name);
      nameAWGN=ones(1,length(name));
      nameAWGN(name<='M')=0;                      

      b0 = 3*ones(1,100) ;                        % Waveform for bit 0
      b1 = 3*[ones(1, 50) -ones(1,50)] ;          % Waveform for bit 1

      input=[];                                   % Generate signal input for name 'PHOON JIAN'
      for i=1:length(nameAWGN)
         if nameAWGN(i)==0
             input=[input b0];
         else
             input=[input b1];
         end
      end

      h0 = 3*ones(1,100) ;                        % impulse response for match filter 0
      h1 = 3*[-ones(1, 50) ones(1,50)] ;          % impulse response for match filter 1

      r0=conv(input,h0);                          % matched output for match filter 0
      r1=conv(input,h1);                          % matched output for match filter 1
      d=r1-r0;                                    % detector output

      figure;
      maxnum=max([r0,r1]);    minnum=min([r0,r1]);

      subplot(3,1,1); plot(1:length(r0),r0); 
      xlabel('Time (Tb=100)'); title(['r0 output for ' name]);
      hold on;                                    % plot matched output r0
      for i=100:100:length(r0)            
         if r0(i)==maxnum 
             plot([i,i],[minnum,maxnum],'r--');   % plot r0 markers
         end
      end

      subplot(3,1,2); plot(1:length(r1),r1); 
      xlabel('Time (Tb=100)'); title(['r1 output for ' name]);
      hold on;                                    % plot matched output r1
      for i=100:100:length(r1)            
         if r1(i)==maxnum 
             plot([i,i],[minnum,maxnum],'r--');   % plot r1 markers
         end
      end

      subplot(3,1,3); plot(1:length(d),d); xlabel('Time (Tb=100)'); title(['detector output for ' name]);
      hold on;                                    % plot detector output 
      for i=100:100:length(d) 
         if d(i)==maxnum || d(i)==minnum
             plot(i,d(i),'r*');                   % plot detector marker
         end
      end
  end

[Walter Roberson]

You don't even have a pi in the above code, let alone a sin() or sqrt(), and you do not have any comments such as "I want to do S0 here!" such that we could get an idea of how you want S0 and S1 to relate to the rest of your program.

At present it does not appear that this program has anything to do with the question you asked ?