How to create random users in a defined area of a circle

Hello,

I am trying to create three random users, each in any of the drawn circles, with a base station at the center (0+0i). Attached is the code and the output.

I will be glad if someone can help me out.

clc;
close all;
clear all

xu = 0; yu = 0;
BS_loc = xu+1i*yu; %BaseStation location

R1 = 15; %diameter of cells
R2 = 10;
R3 = 5;

vectX1=[]; vectX2=[]; vectX3=[];
vectY1=[]; vectY2=[]; vectY3=[];

 for theta = -pi:0.01:pi
     
     x1=R1*cos(theta);
     y1=R1*sin(theta);
     x2=R2*cos(theta);
     y2=R2*sin(theta);
     x3=R3*cos(theta);
     y3=R3*sin(theta);
         
     vectX1=[vectX1 x1]; vectX2=[vectX2 x2]; vectX3=[vectX3 x3]; 
     vectY1=[vectY1 y1]; vectY2=[vectY2 y2]; vectY3=[vectY3 y3];
               
 end

 plot(vectX1,vectY1,'r'); 
 hold on
 plot(vectX2,vectY2,'g'); 
 hold on
 plot(vectX3,vectY3,'b'); 
 hold on
 plot(xu,yu,'kx','MarkerSize',6, 'LineWidth',2); 
 grid on

Answer 1

[BhaTTa]

Hey @Eugene Fab, Here's how you can modify your code to place three random users within a specified circle (let's say R1 for now, then you can adapt it for different circles or zones). I have provided an updated script below:

clc;
close all;
clear all;

xu = 0; yu = 0;
BS_loc = xu + 1i * yu; % Base Station location

R1 = 15; % Radius of outermost cell
R2 = 10; % Radius of middle cell
R3 = 5;  % Radius of innermost cell

% --- Plotting the circles (your existing code, slightly cleaner) ---
figure; % Create a new figure
hold on; % Keep plots on the same axes

theta_plot = linspace(0, 2*pi, 100); % Use linspace for smoother circles

plot(R1 * cos(theta_plot), R1 * sin(theta_plot), 'r', 'LineWidth', 1.5);
plot(R2 * cos(theta_plot), R2 * sin(theta_plot), 'g', 'LineWidth', 1.5);
plot(R3 * cos(theta_plot), R3 * sin(theta_plot), 'b', 'LineWidth', 1.5);

plot(xu, yu, 'kx', 'MarkerSize', 8, 'LineWidth', 2); % Base Station

grid on;
axis equal; % Ensure circles look circular
xlabel('X-coordinate');
ylabel('Y-coordinate');
title('Base Station and Random Users in Circular Cells');

% --- Generating Random Users ---

num_users = 3; % Number of users to generate

% Method 1: Randomly place users within the *entire* R1 circle
% Each user has an equal chance of being anywhere in R1
disp('Generating users in the outermost (R1) circle:');

Generating users in the outermost (R1) circle:

for i = 1:num_users
    % Generate a random angle between 0 and 2*pi
    random_theta = 2 * pi * rand;

    % Generate a random radius between 0 and R1, but NOT linearly
    % For uniform distribution in a circle, radius squared should be uniform
    random_r = R1 * sqrt(rand);

    % Convert polar to Cartesian coordinates
    user_x = random_r * cos(random_theta);
    user_y = random_r * sin(random_theta);

    plot(user_x, user_y, 'mo', 'MarkerSize', 6, 'MarkerFaceColor', 'm'); % Plot user
    text(user_x + 0.5, user_y + 0.5, ['User ' num2str(i)]); % Label user
    fprintf('User %d: (%.2f, %.2f)\n', i, user_x, user_y);
end

User 1: (1.93, 11.23)
User 2: (7.44, -3.01)
User 3: (4.19, -3.12)

% You mentioned "each in any of the drawn circles". Let's show how to place
% them specifically within the *annulus* between R2 and R1.

% Method 2: Randomly place users in the annulus (R2 to R1)
fprintf('\nGenerating users in the annulus between R2 (green) and R1 (red):\n');

Generating users in the annulus between R2 (green) and R1 (red):

num_users_annulus = 2; % Example: 2 users in the annulus
for i = 1:num_users_annulus
    % Generate a random angle between 0 and 2*pi
    random_theta_annulus = 2 * pi * rand;

    % Generate a random radius for the annulus: R_inner^2 + (R_outer^2 - R_inner^2) * rand
    random_r_annulus = sqrt(R2^2 + (R1^2 - R2^2) * rand);

    user_x_annulus = random_r_annulus * cos(random_theta_annulus);
    user_y_annulus = random_r_annulus * sin(random_theta_annulus);

    plot(user_x_annulus, user_y_annulus, 'cs', 'MarkerSize', 7, 'MarkerFaceColor', 'c'); % Plot user as square
    text(user_x_annulus + 0.5, user_y_annulus + 0.5, ['Annulus User ' num2str(i)]); % Label user
    fprintf('Annulus User %d: (%.2f, %.2f)\n', i, user_x_annulus, user_y_annulus);
end

Annulus User 1: (10.05, -5.13)
Annulus User 2: (3.39, 14.01)

hold off;