Hello again, I am still struggling with BPSK demodulation :) OK, now I am trying to implement Costas Loop for carrier synchronization, which involves Inphase and Quadrature Phase paths. Inphase is looking good, and works as expected, however, the Q component looks awkward. Take a look at these waveforms: http://www.alteraforum.com/forum/attachment.php?attachmentid=10363&stc=1 I understand that multiplying sin * cos will produce a high frequency component, which is a sin modulated by half amplitude of the data signal. BPSK(t) * sin(2*pi*f*t) = 0.5 * [DATA(t) * sin(0) + DATA(t) * sin(2*pi*f*t)] => 0.5 * DATA(t) * sin(2*pi*f*t) => LPF{0.5 * DATA(t) * sin(2*pi*f*t)} = 0 I feel that problem is in my LPF. I used the same Matched RRC filter that I used in the in-phase arm. Papers I read didn't mention that these two filters should be different, that's why I used the same filter. (I think those are unpractical DSP writers, KAZ :D ) So, should I use a separate Loop Filter for Q component? How do I determine it's parameters?

How did you design the costas loop? How do you control the loop> loop filter has to be separate filter from rrc. You will use it to control the lock of your costas loop and usually a simple IIR will do I have used rrc after costas locking section but I know some do it before but not as loop filter (there are different rx configurations and you better model it matlab before going to hardware).

I am sorry, it's my mistake... I didn't mention that after multiplication there is CIC filter... before RRC. So these are the waveforms: https://www.alteraforum.com/forum/attachment.php?attachmentid=10365 Basically, I am trying to design this loop: https://www.alteraforum.com/forum/attachment.php?attachmentid=10366 Instead of LPF, I used CIC filters, as they do filtering and decimation at the same time. Am I wrong? You are right, RRC has nothing to do with Costas Loop.

You need one filter per branch to remove the f1+f2 (sum term) leaving signal at dc (f1-f2). Any LPF will do (including rrc if you wish). The loop itself needs error detector and filter to smooth out the error. This loop filter can be an IIR with variable gain. The IIR filter represents the integral part of your loop control system. You may need further control terms such as proportional term. The filter error is then used to shift phase(or frequency) of NCO in the opposite sense. It takes sometime for the loop to lock. You observe the error and this should converge and settle with low jitter. I notice your bb_signal_I has plenty of zeros in it but not Q I wouldn't advice you to do any decimation inside loop as it could get complicated on you.

--- Quote Start --- You need one filter per branch to remove the f1+f2 (sum term) leaving signal at dc (f1-f2). Any LPF will do (including rrc if you wish). The loop itself needs error detector and filter to smooth out the error. This loop filter can be an IIR with variable gain. The IIR filter represents the integral part of your loop control system. You may need further control terms such as proportional term. The filter error is then used to shift phase(or frequency) of NCO in the opposite sense. --- Quote End --- The error detector you referred to is the mixer at the end of the loop, right? Regarding loop filter, I saw some structures that combine both integral and proportional terms, is it the same as you are suggesting? http://www.alteraforum.com/forum/attachment.php?attachmentid=10367&stc=1 --- Quote Start --- I notice your bb_signal_I has plenty of zeros in it but not Q --- Quote End --- You mean zero crossings? is this bad? --- Quote Start --- I wouldn't advice you to do any decimation inside loop as it could get complicated on you. --- Quote End --- I thought decimating is beneficial before doing any further signal processing as this relaxes the requirements. I'll use regular LPFs then. How to choose the cutoff frequency of these LPFs?

The bb_I difference from bb_Q may be due to your nco phase. For now assume it is ok and focus on cutting off the f1+f2 term in each branch. The wanted signal will move close to dc and depending on your signal bandwidth. you need to cutoff clear of your signal bandwidth but kill the f1+f2 copy. So far you have downconverted your signal to dc but now and since signal centre may shift either side of dc due to uncertainties of oscilillators bewteen Tx and Rx you need to force it to dc all the time. The error detector is just a multiplier as you have found out. apply IIR LPF (integrator) to the error as it will be very noisy. The gain of IIR need to be manually adjusted until error shows dampened oscillations heading towards zero with some jitter. For testing you will need to move your RF centre either side and see that the loop does not lose lock otherwise the radio user will have to keep adjusting the tuning knob and lose interest in music. If your loop fails to lock try adding the proportional term to the output of IIR through a scaler that can be adjusted.

BPSK Demodulation | Altera Community

66 Replies

Altera_Forum
Honored Contributor
11 years ago
Amazing! Thanks for presaging me!
You are right about scaling... signal is in the range 0~400 which can't control the NCO which is in the range +/- 0.5
But I didn't get this: "set addition of error to zero to kill the loop effect", what do you mean?
And are you referring to the control signal by "final error"?
Altera_Forum
Honored Contributor
11 years ago
That was for initial testing of error sense. Once done close the feedback loop. final error is tha t value you add or subtract to nco word

Altera_Forum

Honored Contributor

11 years ago

Hello Mr Kazem, here is my latest attempt:


clear
clc
load RRC.mat
rf_signal = cos(2*pi*(1:5000)*0.1);
fc = 0.1;
N = length(rf_signal);
phi_inc = zeros(1, N);
bb = zeros(1, N);
bb_f = zeros(1, N);
I_f = zeros(1, N);
Q_f = zeros(1, N);
I_r = zeros(1, N);
Q_r = zeros(1, N);
error = zeros(1, N);
error_f = zeros(1, N);
%loop filter coefficients
alpha = 0.1;
b = alpha;
a = ;
for i = 1:N
    % Downconverting to Baseband
    bb(i) = rf_signal(i).*exp(j*2*pi*fc*i);
    % Filtering
    bb_f = filter(RRC, bb(1:i));
    I_f(i) = real(bb_f(i));
    Q_f(i) = imag(bb_f(i));
    
    % Slicing
    if I_f(i) > 0
        I_r(i) = 1;
    else
        I_r(i) = -1;
    end
    
    if Q_f(i) > 0
        Q_r(i) = 1;
    else
        Q_r(i) = -1;
    end
    
    % Error
    error(i) = I_f(i) .* Q_r(i) - Q_f(i) .* I_r(i);
    
    % Loop Filter
    error_f = filter(b, a, error(1:i));
    phi_inc(i+1) = phi_inc(i) - error_f(i)/2^10;
end
figure
subplot 221
plot(real(bb))
title('I Channel')
subplot 222
plot(imag(bb))
title('Q Channel')
subplot 223
plot(I_f)
title('I Channel Filter')
subplot 224
plot(Q_f)
title('Q Channel Filter')
figure; plot(error); title('Error');
figure; plot(error_f); title('Filtered Error');
figure; plot(phi_inc); title('Final Error');

I just scaled down the filtered error by 2^10. I think it is gentle as you mentioned and scaling bring it to range +/- 0.5.

Error:

https://www.alteraforum.com/forum/attachment.php?attachmentid=10413

Filtered Error:

https://www.alteraforum.com/forum/attachment.php?attachmentid=10414

Final Error:

https://www.alteraforum.com/forum/attachment.php?attachmentid=10415

Of course loop is open as you can see from code. So, what do you think?

multiple-attachments.zip24 KB

Altera_Forum
Honored Contributor
11 years ago
Hi Siraj,

Diagrams of Costas loops are different and reflects different rx structures. For demo purposes use the easiest one.
work on control loops is no small job though you can readily see a diagram and follow it but you will need weeks of work to get the loop tuned.

The second step is to use actual qpsk signal from your tx and pass through your rx until you get the constellations.

To keep your test structure simple I suggest you:
1)generate random qpsk
2) pass through rrc upsampling by 2 or higher
3) mix with a frquency
4) keep it complex to rx (so you don't require lpf if you wish)
5) downconvert inside the costas loop using your basic slicer
6) after the loop(outside it) apply rrc again decimating by 2.
plot(I,Q,'.')

you should get clean constellations if your loop gets fc it to dc
else it will be circle.
When you decimate, you will have two output phases to choose. watch both
you will spend a lot of time to tune the loop controlling it through various loop filters and error sense and scaling.
Altera_Forum
Honored Contributor
11 years ago
I see... but that's all for MATLAB, and I'm afraid I won't have time to deploy it to FPGA! Since I am aware of additional work in hardware domain!
I am reading an article from Matlab help about CORDIC-Based QPSK Carrier Synchronization. Do you recommend following it?
Altera_Forum
Honored Contributor
11 years ago
--- Quote Start ---
I see... but that's all for MATLAB, and I'm afraid I won't have time to deploy it to FPGA! Since I am aware of additional work in hardware domain!
I am reading an article from Matlab help about CORDIC-Based QPSK Carrier Synchronization. Do you recommend following it?
--- Quote End ---

what is the cordic computing? is'it a feedback loop based as well?

you may also try your first loop design and use proper qpsk system(as suggested above) instead of single tone and see if it behaves. directly observing constellations.
Altera_Forum
Honored Contributor
11 years ago
Can you give a rule of thumb for controlling the NCO? Do I control phase of frequency? As they give different behaviors.
Altera_Forum
Honored Contributor
11 years ago
--- Quote Start ---
Can you give a rule of thumb for controlling the NCO? Do I control phase of frequency? As they give different behaviors.
--- Quote End ---

you change nco frequency by changing the increment value which points to phase. The actual sine values of 1 cycle (or half or quarter) are stored in lut.

for negative frequency you can still add the negative increment (well subtract) so pointer goes backwards, or use positive increment but swap sin/cos or invert one of them

Altera_Forum

Honored Contributor

11 years ago

Hello Kazem :)

I think I did it this time. Please take your time and test it at your leisure before judging :D


clear
clc
load RRC.mat
fc = 0.1 % 0.11  %0.09
rf_signal = cos(2*pi*(1:5000)*0.1);
N = length(rf_signal);
bb = zeros(1, N);
bb_f = zeros(1, N);
I_f = zeros(1, N);
Q_f = zeros(1, N);
I_r = zeros(1, N);
Q_r = zeros(1, N);
error = zeros(1, N);
PhErr = zeros(1, N);
error_integral = zeros(1, N);
Theta = zeros(1, N);
% Loop Filter Coefficients
BW = 200;  % Hz
loop_theta = 2*pi*BW;
C1 = 4*(loop_theta)^2/(1+sqrt(2)*loop_theta+loop_theta^2);
C2 = 2*sqrt(2)*loop_theta/(1+sqrt(2)*loop_theta+loop_theta^2);
for i = 2:N
    % Downconverting to Baseband
    bb(i) = rf_signal(i).*exp(j*2*pi*fc*i).*exp(j*Theta(i-1));
    % Filtering
    bb_f = filter(RRC, bb(1:i));
    I_f(i) = real(bb_f(i));
    Q_f(i) = imag(bb_f(i));
    
    % Slicing
    if I_f(i) > 0
        I_r(i) = 1;
    else
        I_r(i) = -1;
    end
    
    if Q_f(i) > 0
        Q_r(i) = 1;
    else
        Q_r(i) = -1;
    end
    
    % Error
    error(i) = I_f(i) .* Q_r(i) - Q_f(i) .* I_r(i);
    
    % Loop Filter
    error_integral(i) = error(i).*C1 + error_integral(i-1);
    PhErr(i) = error(i).*C2 + error_integral(i);
    
    % Phase Accumulator
    Theta(i) = Theta(i-1) + PhErr(i);
    
end
figure
subplot 221
plot(real(bb))
title('I Channel')
subplot 222
plot(imag(bb))
title('Q Channel')
subplot 223
plot(I_f)
title('I Channel Filter')
subplot 224
plot(Q_f)
title('Q Channel Filter')
figure; subplot 311; plot(error); title('Phase Error');
subplot 312; plot(PhErr); title('Loop Filter');
subplot 313; plot(Theta); title('Control Signal \theta');

Just to motivate you, look at these signals:

https://www.alteraforum.com/forum/attachment.php?attachmentid=10422

https://www.alteraforum.com/forum/attachment.php?attachmentid=10423

multiple-attachments.zip28 KB

Altera_Forum
Honored Contributor
11 years ago
A true Rx down converter has several front end functions such as clock recovery and carrier tracking.

carrier tracking has two components (frequency and phase). the nominal tx freq is used at rx to downconvert to dc and the the phase must also be locked at localrx nco.

If you are not concerned about frequency but only phase (e.g. for demo) then your very first design of cos*sin should do.

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