Matlab Code:

clc;
clear all;
close all;
N = 10^6;                % number of bits or symbols
rand(100);              % initializing the rand() function
randn(200);            % initializing the randn() function
% Transmitter—————————————————————————————————-
x = rand(1,N)>0.5; % generating 0,1 with equal probability
s = (2*x)-1;              % BPSK modulation 0 -> -1; 1 -> 1
n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % white gaussian noise, 0dB variance
Eb_N0_dB = [-3:10]; % multiple Eb/N0 values
for v = 1:length(Eb_N0_dB)
y = s + 10^(-Eb_N0_dB(v)/20)*n; % additive white gaussian noise
% receiver – hard decision decoding———————————————————————
ipHat = real(y)>0;
% counting the errors——————————————————————————————-
nErr(v) = size(find([x- ipHat]),2);
end
simBer = nErr/N; % simulated ber
theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber
% plot——————————————————————————————————————–
close all;
figure
semilogy(Eb_N0_dB,theoryBer,’b.-‘);
hold on
semilogy(Eb_N0_dB,simBer,’mx-‘);
axis([-3 10 10^-5 0.5]);
grid on;
legend(‘theory’, ‘simulation’);
xlabel(‘Eb/No, dB’);
ylabel(‘Bit Error Rate’);
title(‘Bit error probability curve for BPSK modulation’);

Result: