MATLAB Simulation

MATLAB is commonly used to design filters and determine frequency responses of systems, but it is also very useful as a simulation tool.

Use the following MATLAB code skeleton to simulate the QPSK transmitter from Digital Transmitter: Introduction to Quadrature Phase-Shift Keying and fill in the incomplete portions. Note that the code is not complete and will not execute properly as written. How does the spectrum of the transmitted signal change with T symb T symb ? How do you interpret the figure created by plot(rI,rQ)?

	
	1  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	2  % MATLAB Code Skeleton for QPSK Digital Transmitter 
	3
	4  % Generate random bits
	5  bits_per_symbol=2;
	6  num_symbols=128;
	7  numbits=bits_per_symbol*num_symbols;
	8  bits=rand(1,numbits)>0.5;
	9  
	10  Tsymb = 16;                  % symbol length
	11  omega = pi/2;                % carrier frequency
	12
	13  %%%%%%%%%%%%%%%%%%%%%%%%
	14  % Transmitter section
	15                             % initialize transmit sequence
	16  t = zeros(1,num_symbols*Tsymb);
	17  i = 1;                       % initialize bit index
	18  n = 1;                       % initialize time index
	19  
	20  while (n <= num_symbols*Tsymb)
	21   if ( bits(i:i+1) == [ 0 0])
	22       Igain = 1/sqrt(2);
	23       Qgain = 1/sqrt(2);
	24   % ------>Insert code here<-------
	25
	26   end;
	27   i = i+2;                    % next 2 bits
	28
	29   % Generate symbol to be transmitted
	30   t(n:n+Tsymb-1) =    %------>Insert code here<-------
	31                  
	32   n = n+Tsymb;                % next symbol
	33  end;
	34
	35  % Show the transmitted signal and its spectrum
	36  % ------>Insert code here<-------
	37
	38  % Show the transmitted signal constellation 
	39  rI = t.*cos(omega*[1:num_symbols*Tsymb]);
	40  rQ = t.*sin(omega*[1:num_symbols*Tsymb]);
	41
	42  % Filter out the double-frequency term
	43  low_pass=fir1(512,0.5);
	44  rI=conv(rI,low_pass);
	45  rQ=conv(rQ,low_pass);
	46  figure;
	47  plot(rI,rQ);