MATLAB Code for Sampling Frequency Offset Impairment

This section of MATLAB source code covers Sampling Frequency offset impairment and Sampling Frequency offset effect on the constellation diagram using MATLAB code. Part A and PART C of the MATLAB code are the same as mentioned on the AWGN page.

Source Code

Part B

SCO = 50e-6; % value of SCO
out = RX_SCO(out,SCO);
figure;
plot(real(out),imag(out),'b+');
title('constellation with Sampling Frequency Offset impairment');


### RX_SCO.m

```matlab
function out = RX_SCO(in,SCO);
[M N] = size(in);
if(SCO ~= 0)
    indx = (1:M)*(1+SCO);
    if SCO > 0
        in = [in; zeros(fix(indx(end))-M,N)]; % zero-padding: extra samples are needed
        for kk=1:N
            in2(:,kk) = lrange_interp(in(:,kk),indx,'cubic');
        end
    else
        in = [zeros(1,N); in];
        indx = indx+1;
        for kk=1:N
            in2(:,kk) = lrange_interp(in(:,kk),indx,'cubic');
        end
    end
    out = in2;
else
    out = in;
end

lrange_interp.m

function yi = lrange_interp(y,xi,interptype)
% Check arguments
if(nargin ~= 3)
    error('fast_interp expects 3 arguments');
end
if( (xi > length(y)) | (xi < 1) )
    error('xi must be between 1 and the length of y');
end
if(~ischar(interptype))
    error('Interpolation type must be a string');
end

% For linear interpolation, just use matlab's linear
% interpolation function
if(strcmp(interptype,'linear') == 1)
    yi = interp1(1:length(y),y,xi,'*linear');

% For cubic interpolation, calculate piecewise lagrange
% polynomial at specified points
elseif(strcmp(interptype,'cubic') == 1)
    yi = cubic_lrange(y,xi);

% Otherwise print an error to the screen
else
    error('interptype must be either linear or cubic');
end

lrange_coeff.m

function [coeffs] = lrange_coeff(order,mu)
% Calculates the coefficients of an interpolator filter with
% a given interpolation order and a time shift 'mu'.
% mu is centered around a symmetrical interval [-1,1]

mu = (mu-0.5)*2/order;
% coefficients are calculated following Lagrange interpolation
if (order == 1) % linear
    coeffs = [0.5+0.5.*mu 0.5-0.5.*mu];
elseif (order == 2) % quadratic
    coeffs = [ 0.5.*mu + 0.5.*mu.^2 ...
               1 - mu.^2 ...
               -0.5.*mu + 0.5.*mu.^2 ];
elseif (order == 3) % cubic
    mu2 = mu.*mu; % mu squared
    mu3 = mu2.*mu;% mu cubed
    coeffs = [ -0.0625 - 0.0625.*mu + 0.5625.*mu2 + 0.5625.*mu3 ...
               0.5625 + 1.6875.*mu - 0.5625.*mu2 - 1.6875.*mu3 ...
               0.5625 - 1.6875.*mu - 0.5625.*mu2 + 1.6875.*mu3 ...
               -0.0625 + 0.0625.*mu + 0.5625.*mu2 - 0.5625.*mu3 ];
end

cubic_lrange.m

function yi = cubic_lrange(y,xi);

y = reshape(y,length(y),1); % make sure y is a column vector
y(end+1:end+2) = 0;
y = [0;y];

xi = xi + 1;
% Get fractional part of indices
mu = xi - floor(xi);

% Get integer part of indices
xi = floor(xi);

% Get values from y used for cubic interpolation
xi = reshape([y(xi+2) y(xi+1) y(xi) y(xi-1)],length(mu),4);

% Perform interpolation using piecewise Lagrange polynomials
yi = sum((xi.*lrange_coeff(3,mu.')).');