Skip to content

Instantly share code, notes, and snippets.

Last active October 27, 2022 13:43
Show Gist options
  • Save sp5wwp/fc24815ae8812016e209f233c495130a to your computer and use it in GitHub Desktop.
Save sp5wwp/fc24815ae8812016e209f233c495130a to your computer and use it in GitHub Desktop.
% root-Nyquist (M) filter design %
% Source: %
% %
% Edited by Wojciech SP5WWP to work with rcosdesign() %
% %
% parameters: %
% N: filter order (filter length = N+1) %
% M: number of samples per symbol period %
% alpha: rolloff factor (range 0 to 1) %
% gmaZ: Weight factor for middle tap and zero crossings %
% gmaT: Weight factor for the tails of g=h*h (used for %
% designs with robust behavor against timing jitter) %
% eta: Weight factor for tails of h (used for designs %
% with reduced PAR) %
% itns: Number of iterations for the least-squares %
% optimization %
function h=rNyquistM(N,M,alpha,gmaZ,gmaT,eta,itns)
%%% Set up the weight matrix Gamma %%%
Gamma=zeros(1,1+N); Gamma(M+2:end)=gmaT;
Gamma(1:M:end)=gmaZ; Gamma=[Gamma ones(1,1+N/2)];
Gamma2=Gamma.^2; Gamma2=diag(Gamma2);
%%% Initial filter %%%
if rem(N+1,2)==0 h1=h(1:(N+1)/2);else h1=h(1:N/2+1); end
%%% Set up constraint matrices, Sn %%%
S=zeros(N+1,N+1,N+1); temp=ones(N+1,1);
for n=1:N+1
%%% Set up the matrix Phi %%%
Phi=zeros(N+1,N+1); fo=(1/2/M)*(1+alpha);
Phi=[1-2*fo -2*fo*sinc(2*fo*[1:N])]; Phi=toeplitz(Phi);
Phi=Phi+1e-10*eye(size(Phi)); %to stabilize Chol fac.
%%% Form the matrices S′ and Phi′ %%%
I=eye(Lh1); J=hankel([zeros(Lh1-1,1); 1]);
if rem(N+1,2)==1 J=J(2:end,:); end
E=[I; J]; Phi1=E'*Phi*E; S1=[];
for n=1:N+1 S1=[S1; E'*S(:,:,n)*E]; end
%%% Add tail constraint to reduce PAR %%%
X=zeros(Lh1,1); X(1:end-M)=eta; Phi1=Phi1+diag(X);
%%% Iterative least-squares optimization %%%
C=chol(Phi1); % Cholesky factorization
for kk=1:itns
B=kron(eye(N+1),h1')*S1; D=[B; C]; u=[1;zeros(N+Lh1,1)];
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment