# understanding the result of the simulation of In-phase and quadrature part BPSK signal

I am a student and working on a hardware implementation of a transceiver and going to check an algorithm of time recovery that includes symbol synchronization and sampling clock synchronization. The proposed algorithm has a problem in realisation in hardware and I was thinking to check the algorithm and whole simulation in Matlab and probably I could to fix and improve it.

In Matlab, I would like firstly generate a test signal which will be received. Before I asked here about the time recovery algorithms and it was explained to me excellent. Thank you, guys!

My simulation in Matlab:

• 100 symbols with 4 samples
• random noise
• raised cosine filter

Code:

% create a random sequence of 1 or -1
N = 100;
bit_stream = rand(1,N)>0.5;
BPSK_symbols = 2*(bit_stream)-1;

% Filter coefficients
h=firrcos(150,.5,.2,4);

for i = 1:length(BPSK_symbols )
BPSK_symbols_zzeros(1) = BPSK_symbols (1);
BPSK_symbols_zzeros(4*i)=BPSK_symbols (i);
end

% apply filter
tx_signal = conv(filter_coeff,BPSK_symbols_zzeros);
% generate noise
noise = rand;
norm=std(tx_signal)*noise;
for j = 1:length(tx_signal)
phi = 0.89 % pi/4
tx_signal_w_phi(j) = tx_signal(j)*exp(sqrt(-1)*(phi_1))+0.7*norm*(randn+sqrt(-1)*randn);
end



My result : red - inphase , green -quadrature

I think the result is wrong. If the phase offset is pi/4, I have to get I-Signal the same as Q-Signal, isn't it?

As you see, the max amplitude (peaks) are different.

Could someone help me to fix this implementation, because I can't understand where I have mistaken...