The problem is given as follows

Since the problem is convex with respect to power \ro_i and p_i .

I solve the problem for n = 1.

I use the cvx toolbox for solving it.

The code is given as follows:

clc

clear all

close all

xs = 0; ys = 50;

xe = 100; ye = -50;

x_source = 0; y_source = 0;

xy(1,1) = 2;

xy(2,1) = 48;

x_destination = 100; y_destination = 0;

H = 20;

V = 4;

a = 3;

B = 0;

delta = 2e-13;

gama = 10^(10/10);

gama0 = 10^(80/10);

N = 50;

Ps = 10;

step_beta = .001;

n_x = 1;

d_sr(n_x) = sqrt((xy(1,n_x)-x_source)^2 + (xy(2,n_x)-y_source)^2 + H^2);

d_rd(n_x) = sqrt((x_destination - xy(1,n_x))^2 + (y_destination - xy(1,n_x))^2 + H^2);

d_sd(n_x) = sqrt((x_destination - x_source)^2 + (y_destination - y_source)^2 );

cvx_begin

% cvx_solver sedumi

variables x y

% minimize ( -.5* log10(1 + Ps*gama +â€¦
% (Ps * gama0.^2 * y * x /((x+a)*(d_sr(n_x) * d_sr(n_x)).^2))â€¦

% /(1+Ps * gama0 * x /((x+a)

*d_sr(n_x).^2) + y * gama0 /d_rd(n_x).^2) ) )*

% subject to

% y <= B+(1+Psgama0/d_sr(n_x).^2)

% subject to

% y <= B+(1+Ps

*delta*(1-x);

% 0<= x <=1;

% y>=0;

minimize ( -.5* (-rel_entr(1,(1 + Ps*gama +â€¦
(Ps * gama0.^2 * y * x /((x+a)*(d_sr(n_x) * d_sr(n_x)).^2))â€¦

/(1+Ps * gama0 * x /((x+a)

*d_sr(n_x).^2) + y * gama0 /d_rd(n_x).^2) ) )))*

subject to

y <= B+(1+Psgama0/d_sr(n_x).^2)

subject to

y <= B+(1+Ps

*delta*(1-x);

0<= x <=1;

y>=0;

cvx_end

this Error is apear:

Error using .* (line 262)

Disciplined convex programming

error:

Invalid quadratic form(s): not a

square.

Error in * (line 36)

z = feval( oper, x, y );

Error in Untitled (line 36)

(Ps * gama0.^2 * y * x

/((x+a)*(d_sr(n_x) *

d_sr(n_x)).^2))â€¦