function BER = ComputeBER_Numerically_4(SNR_dB, alpha, Rs_symbol, clock_offset)

%Numerically.

Eb = 1;

a = 1;

Es = a^2 * Eb;

Ts_symbol = 1 / Rs_symbol;

signal_length = 4000;

%Sampling parameters

Fs = 20e6;

Ts = 1 / Fs;

%According to Relative Frequency Theorem, Many trials are required in order to converge to the real probabilty of error.

num_iterations = 50;

BER = zeros(size(SNR_dB));

SNR_dim = 10.^(SNR_dB/10);

%SRRC Pulse with its matched pulse gives RRC

p = rcosdesign(alpha, 100, Fs / Rs_symbol, 'sqrt');

p_matched = rcosdesign(alpha, 100, Fs / Rs_symbol, 'sqrt');

%LPF

channel_f = 1e6;

t=-0.000025:1/Fs:0.000025;

LPF = 2 * channel_f * sinc (2 * channel_f * t); %Limited channel frequency response to 1MHZ, this is in time domain.

for i = 1 : length(SNR_dB)

accumulated_BER = 0; %Required for averaging.

No = Es / SNR_dim(i); %WTF

for j = 1 : num_iterations

num_bit_errors = 0;

%Delta Stream

t = 0 : Ts : Ts_symbol * (signal_length - 1);

deltas = zeros(size(t));

deltas(1 : Fs * Ts_symbol : end) = randi([1 2], 1, signal_length);

deltas(deltas == 2) = -1;

%PROCESS OF TRANSIMITION AND RECEPTION

%Pulse Convolution

s = conv(deltas, p, 'same');

%LPF Convolution

s_LPF = conv(s, LPF, 'same') / Fs;

%Noise Addition

N = sqrt(No/2) * randn(1,length(s_LPF)); %Generate AWGN

r = s_LPF + N; %Received Signal

%Matched Pulse Convolution

X = conv(r, p_matched, 'same');

%Decision Making

for k=1:length(t)

if k + int32(Fs * Ts_symbol * clock_offset) <= length(t) %For avoiding comparison, when index is out of range.

%Clock offset is implemented, such that the index to

%be compared with the deltas index is shifted to give

%the same effect.

if ((X(k + int32(Fs * Ts_symbol * clock_offset)) > 0 && deltas(k) < 0)||(X(k + int32(Fs * Ts_symbol * clock_offset)) < 0 && deltas(k) > 0))

num_bit_errors=num_bit_errors+1;

end

end

end

avg_bit_error = num_bit_errors / signal_length;

accumulated_BER = accumulated_BER + avg_bit_error;

end

BER(i) = accumulated_BER / num_iterations;

end

end