why do I always receive the error: Unrecognized function or variable 'Pt'.

function [Cout,iter_time] = PGM_opt(Pt,Hdir,H1,H2,maxIter,Qinit,myomegaunitball,c)

[Dyuman Joshi]

Please show your full code, how you call the function and the full error.

[LoCi]

% Function that implements the PGM iterative optimization

function [Cout,iter_time] = PGM_opt(Pt,Hdir,H1,H2,maxIter,Qinit,myomegaunitball,c)

% Load the initial covariance matrix and RIS phase shifts  
myomegaunitcirc = myomegaunitball.';
Q = Qinit; 

% Line-search parameters 
delta = 1e-5;       
rho = 0.5;

iIter = 0;         
stepsize = 10000;   % Inital step size 


Cout = [RIScap(Hdir,H2,H1,myomegaunitcirc,Q)]; % Initial achievable rate 
Cprev = Cout;

iter_time = 0;
tic
while iIter<maxIter
    iIter = iIter+1;
    q_Q = gracov(Hdir,H2,H1,myomegaunitcirc,Q);     % gradient w.r.t. Q
    g_RIS = gradRIS(Hdir,H2,H1,myomegaunitcirc,Q);  % gradient w.r.t. RIS
    
    for iLineSearch = 0:30
        
        % Updated covariance (Q) matrix, line 3 of Algorithm 1 
        Qnew = Q + stepsize*q_Q;
        Qnew = cov_mat_proj_modified(Qnew,Pt*c^2);
        
        % Updated RIS phase shifts, line 4 of Algorithm 1
        yunitcirc = myomegaunitcirc + stepsize*g_RIS;
        myomegaunitcircnext = projectontounitcircle(yunitcirc)/c;
        
        % New achievable rate 
        Cnew = RIScap(Hdir,H2,H1,myomegaunitcircnext,Qnew);
        
        % Line-search procedure
        if (((Cnew-Cprev) >= delta*(norm(Qnew-Q)^2+ ...
                norm(myomegaunitcircnext-myomegaunitcirc)^2)) ...
                || (stepsize<1e-4) )
            % If the step size satisfies (35c) OR it is too small:    
            % Obtained Q matrix and RIS phase shifts
            myomegaunitcirc = myomegaunitcircnext;
            Q = Qnew;
            Cprev = Cnew;
            break
        else 
            % Reduce the step size 
            stepsize=stepsize*rho;
        end
    end
    % New achievable rate
    Cout = [Cout Cnew];
    % Exection time of an iteration
    iter_time = [iter_time toc];
end
end

% Calculation of gradient w.r.t. Q
function y = gracov(Hdir,H2,H1,myomega,Q)
Z = Hdir+H2*diag(myomega)*H1;
Nr = size(H2,1);
y = Z'*inv(eye(Nr)+Z*Q*Z')*Z;
end

% Calculation of gradient w.r.t. RIS
function y = gradRIS(Hdir,H2,H1,myomega,Q)
Z = Hdir+H2*diag(myomega)*H1;
Nr = size(H2,1);
y = diag(H2'*inv(eye(Nr)+Z*Q*Z')*Z*Q*H1');
end

% Achievable rate calculation
function y = RIScap(Hdir,H2,H1,myomega,Q)
Z = Hdir+H2*diag(myomega)*H1;
Nr = size(H2,1);
y = real(log(det(eye(Nr)+Z*Q*Z')))/log(2);
end

% RIS projection
function y = projectontounitcircle(x)
y = x./abs(x);
end

% Covarinace matrix projection
function Qnew = cov_mat_proj_modified(Qold,Pt)
[U,D] = eig(Qold);
Dnew = water_fill(Pt,real(diag(D))).';
Qnew = U*diag(Dnew)*U';
end 

% Water-filling algorithm
function vect_out = water_fill(Pt,vect_in)
vect_in = vect_in.';
[sort_val,sort_idx] = sort(vect_in,'descend');
for n = length(vect_in):-1:1
    water_level = (sum(sort_val(1:n))-Pt)/n;
    di = sort_val(1:n)-water_level;
    if di(:)>=0
        break
    end   
end
vect_out = zeros(1,length(vect_in));
vect_out(sort_idx(1:n)) = di;
end 

[Dyuman Joshi]

You still haven't attached how you call the function and what the full error is.

[LoCi]

clear; close all; clc;

Nt = 8;                 % Number of TX antennas
Nr = 4;                 % Number of RX antennas
Nris = 15^2;            % Number of RIS elements

K = 1;                  % Rician factor    
D = 500;                % TX-RX distance
dist_ris = 40;          % RIS distance from TX
f = 2e9;                % Frequency

lt = 20;                % TX position 
lr = 100;               % RX position 
Pt = 1;                 % Transmit power in Watts
N0 = -120;              % Noise power in dB
SNR = db2pow(-N0);      % SNR            
no_mat = 10;            % Number of channel realizations 

no_iter = 500;          % Number of iterations 
alpha_dir = 3;          % FSPL exponent of the direct link

% Generate channel matrices (WORNING: It is only works for Nris that is a square number)
[Hdirt,H1t,H2t] = chan_mat_RIS_surf_univ_new(Nt,Nr,Nris,lt,lr,D,no_mat,K,f,dist_ris,alpha_dir);

Cpgm = zeros(1,no_iter+1);

for i = 1:no_mat 
    Hdir = Hdirt{i}; H1 = H1t{i}; H2 = H2t{i};                  
    
    % Scaling factor
    c = sqrt(norm(Hdir)/norm(H2*H1))*max(sqrt(Pt),1)/sqrt(Pt)*10;     
    
    % Initial Q matrix and RIS phase shifts    
    Qinit = eye(Nt)*(Pt/Nt);
    omega_init = ones(1,Nris);
    
    % PGM iterative optimization 
    [dCpgm,~] = PGM_opt(Pt,Hdir*sqrt(SNR)/c,H1*sqrt(SNR),H2,no_iter,Qinit*c^2,omega_init/c,c);
    Cpgm = Cpgm+dCpgm;
    
end

semilogx(1:length(Cpgm),Cpgm/no_mat,'r','DisplayName','PGM');
xlabel('Iteration number'); ylabel('Achievable rate [bit/s/Hz]');
xlim([0 no_iter]); 
legend('show','Location','SouthEast');
print('../results/Achievable_Rate', '-dpdf')

[LoCi]

function [Hdir,H1,H2] = chan_mat_RIS_surf_univ_new(Nt,Nr,Nris,lt,lr,D,no_mat,K,f,dist_ris,varargin)

lambda = 3e8/f;     % Wavelength
dt = lambda/2;      % TX antenna space
dr = lambda/2;      % RX antenna space
dris = lambda/2;    % RIS element space
k = 2*pi/lambda;    % Wavenumber

% Geometrical placement
% x, y and z axis 
% TX antenna array
tx_arr(1,:) = zeros(1,Nt); 
tx_arr(2,:) = (sort(0:Nt-1,'descend')-(Nt-1)/2)*dt+lt; 
tx_arr(3,:) = zeros(1,Nt); 
% RX antenna array
rx_arr(1,:) = D*ones(1,Nr);
rx_arr(2,:) = (sort(0:Nr-1,'descend')-(Nr-1)/2)*dr+lr; 
rx_arr(3,:) = zeros(1,Nr);
% RIS 
center = [dist_ris 0]; % RIS center position 
N1 = sqrt(Nris);
N2 = N1;                                    % Number of RIS elements in two dimensions N1 and N2
ris_pos = RISPosition(N1,N2,dris,center);   % RIS elements' coordinates 
a = repmat(ris_pos{1},N1,1);                % Placing RIS elements in proper coordinates
ris_arr(1,:) = a(:)';        
ris_arr(2,:) = zeros(1,Nris);
ris_arr(3,:) = repmat(ris_pos{2},1,N2); 

if isempty(varargin)                        % Load the FSPL of the direct link
    alpha = 2;
else
    alpha = varargin{1};
end

% direct TX-RX paths/channel matrix
for i1 = 1:Nr                                        % Distance between the TX and RX antennas                                           
    for j1 = 1:Nt
        d(i1,j1) = norm(rx_arr(:,i1)-tx_arr(:,j1));
    end 
end
Hdir_los = exp(-1i*k*d);                             % Direct link, LOS matrix exponents 
tx_rx_dist = sqrt(D^2+(lt-lr)^2);                    % TX-RX distance   
FSPL_dir = (lambda/(4*pi))^2/tx_rx_dist^alpha(1);    % Inversion of the FSPL of the direct link 
Hdir = Rician(Hdir_los,sqrt(FSPL_dir),no_mat,K);     % Direct link channel matrix           


% indirect paths (TX-RIS-RX)
for l1 = 1:Nris                                      % Distance between the RIS elements and the RX antennas                                                            
    for r1 = 1:Nr  
        d2(r1,l1) = norm(rx_arr(:,r1)-ris_arr(:,l1)); 
    end
    for t1 = 1:Nt                                    % Distance between the RIS elements and the TX antennas                  
        d1(l1,t1) = norm(tx_arr(:,t1)-ris_arr(:,l1));   
    end
end

tx_ris_dist = sqrt(dist_ris^2+lt^2);                 % TX-RIS distance
ris_rx_dist = sqrt((D-dist_ris)^2+lr^2);             % RIS-RX distance   

FSPLindir = lambda^4/(256*pi^2)*...                  % Inversion of the FSPL of the indirect link 
    ((lt/tx_ris_dist+lr/ris_rx_dist)^2)*...
    1/(tx_ris_dist*ris_rx_dist)^2;

% TX-RIS channel matrix
H1_los = exp(-1i*k*d1);                             % TX-RIS link, LOS matrix exponents  
FSPL_1 = sqrt(FSPLindir);                           % FSPL of the indirect link is embedded in the TX-RIS channel matrix 
H1 = Rician(H1_los,FSPL_1,no_mat,K);

% RIS-RX channel matrix
H2_los = exp(-1i*k*d2);                             % RIS-RX link, LOS matrix exponents 
FSPL_2 = 1;
H2 = Rician(H2_los,FSPL_2,no_mat,K);
end

function pos = RISPosition(N1,N2,dist,center)                 % Determine positions of RIS elements
d1 = (0:N1-1)-(N1-1)/2;
d2 = (0:N2-1)-(N2-1)/2;
pos{1} = center(1)+d1*dist;
pos{2} = center(2)+d2*dist;
end 

function Hout = Rician(Hlos,FSPL,no_mat,K)                     % Create the Rician channel matices
Hlos = repmat(Hlos,no_mat,1);
Hnlos = sqrt(1/2)*(randn(size(Hlos))+1i*randn(size(Hlos)));
Htot = FSPL/sqrt(K+1)*(Hlos*sqrt(K)+Hnlos);
dim = size(Hlos,1)/no_mat;
for ind = 1:no_mat
    Hout{ind} = Htot((ind-1)*dim+1:ind*dim,:); 
end
end

[LoCi]

I've got this error message

Execution of script varargin as a function is not supported:

C:\Program Files\MATLAB\R2022a\toolbox\matlab\lang\varargin.m

[Voss]

@SAFA AWAD: I copied and pasted your code into an .m file (attached), and it runs without error (until the last line "print('../results/Achievable_Rate', '-dpdf')", which generates an error because I don't have a "../results/" folder).

No error about Unrecognized Pt or execution of varargin is observed.

Here it is running now:

test_script

Error using matlab.graphics.internal.name
Unable to create output file '../results/Achievable_Rate.pdf', No such file or directory.

Error in print (line 71)
pj = matlab.graphics.internal.name( pj );

Error in test_script (line 40)
print('../results/Achievable_Rate', '-dpdf')

[LoCi]

OK, what the above errors, how to SOLVE them?

[Voss]

As I said, the only error I ran into was due to not having a "../results" directory, so the SOLUTION would be, either:

• Create a directory called "results" under the directory one level up from where you are running the code, so that "..\results" exists, or
• Modify the line "print('../results/Achievable_Rate', '-dpdf')" to print to a directory that exists.

[LoCi]

I did that, but am getting the same error

[Walter Roberson]

There would have been more to the error message, showing which lines the problem was occurring in. The posted code does not use varargin so the problem must be with something that is being called, but we need the complete error message to figure out what.

[LoCi]

This is exactly the complete error:

Error using matlab.graphics.internal.name

Unable to create output file '../results/Achievable_Rate.pdf', No such file or directory.

Error in print (line 71)

pj = matlab.graphics.internal.name( pj );

Error in test_script (line 40)

print('../results/Achievable_Rate', '-dpdf')

[Voss]

Is there a directory called "results" under the directory one level up from where you are running the code, so that "../results" exists?

Example: if code is running in "/home/projects", print would try to create "/home/results/Achievable_Rate.pdf", so the directory "/home/results" needs to exist beforehand.

[LoCi]

How to create a directory one level up from where am running the code ?

[Jan]

@SAFA AWAD: It depends on what "from where I am running the code" means. If this is the current folder:

folder = cd;

If you mean the folder of the M-file:

folder = fileparts(mfilename('fullpath'));

The rest is equal in both cases:

mkdir(fullfile(folder, '..', 'results'))

[Voss]

@SAFA AWAD: Jan is correct; that's how you can do it in MATLAB.

An alternative would be to go into your operating system's File Explorer and create the folder, e.g., on Windows right-click and select 'New Folder' and rename it 'results'.

The point is that the folder has to exist before you try to write a pdf file in it.

Or you can change where the pdf file should go, e.g., to put in the working directory:

print('Achievable_Rate','-dpdf')

[LoCi]

It works now, Thank You ALL for your help