QPSK BER with Rayleigh fading simulation question on equalization

[KaluzaKlein]

How do I perform equalization before QPSK demodulation with a Rayleigh fading channel of more than one paths in simulink? (using the complex paths output of the Rayleigh block)

 

[KaluzaKlein]

I decided to multiply all the complex paths together and then divide the signal (with AWGN added to it) by them. I'm not sure it works though because I get high error rates (0.5).

 

[KaluzaKlein]

It seems that if you cheat a bit more you can get some results: I used the complex phase difference and complex phase shift blocks to inverse the phase rotation introduced by the rayleigh channel. Got results very close to theoretical.

 

[elecstudward]

It seems that if you cheat a bit more you can get some results: I used the complex phase difference and complex phase shift blocks to inverse the phase rotation introduced by the rayleigh channel. Got results very close to theoretical.

Hi KaluzaKlein,
I need to simulate BER of QAM for RAyleigh Channel model, and i've search for examples in simulink. One of them also suggests removal of phase rotation, like you said...

I am not familiar with this term 'phase rotation', does anyone care to give me clue?
Thank you

 

[RBB]

Frequency offsets between the transmitter & receiver, will cause the phase of the constellations to rotate.

 

[KaluzaKlein]

You can visualize it by thinking about your receiver.
You probably already know that a wave has amplitude and phase components. You should also know that the multipath components of a fading channel are just waves that arrive at the receiver at different instants of time. This time shift is what we call phase shift.
Now, think about your constellation diagram (the unit circle). A wave is represented in this circle by a vector whose magnitude is the amplitude of the wave, and the angle with the x axis is the phase. Whenever there is a phase shift, this angle changes, causing the vector to rotate. This is phase rotation.
Now, back to the receiver. This is where all the multipath components add together. Since every one of them has its own amplitude and phase, when added to the original signal, it will cause amplitude distortion and phase shift (phase rotation).

 

[elecstudward]

Whenever there is a phase shift, this angle changes, causing the vector to rotate. This is phase rotation.
Now, back to the receiver. This is where all the multipath components add together. Since every one of them has its own amplitude and phase, when added to the original signal, it will cause amplitude distortion and phase shift (phase rotation).

Thank you for explaining it to me. I get the individual phase rotation but not the summed up received 'amplitude distortion' and 'phase rotation'. So, you were saying that you could inverse the phase rotation to get some result, but leave the amplitude distortion as the effect of fading?? Does it mean that the phase distortion is independent to the amplitude distortion and hence can be separated?

Thank you, and regards

 

[KaluzaKlein]

Does it mean that the phase distortion is independent to the amplitude distortion and hence can be separated?

Yes. Each symbol is a complex number which represents the waveform of your signal for that symbol. The real part is the amplitude and the imaginary part is the frequency (or phase).

In theory, we can describe the effects of the fading channel by first realizing that the latter is a time-variant system. This means that as your signal passes through this system the effects on it will be different for different timing instants. Now, the result of the signal "coming out" of the fading channel is:
r(t) = s(t)*h(t)
r(t) is the received signal, s(t) is the transmitted signal and h(t) the impulse response of your system which in this case is the fading channel. I believe this is a convolution, but in many books it looks like multiplication, I'm still confused about that too.
Time variance is the result of Doppler spread. If there is no motion, the response of the system will be the same every time so if we feed our system with a known signal and observe the output we can deduce some useful conclusions about the multipath components. With some more dsp-magic we can also detect them in a time-varying system (this is what equalizers do), but I really don't know that much yet.

Now, getting back to what I feel more comfortable with, in a simulation we have everything we need to reverse the effects of fading. If you are using simulink you can find the exact equations that they use to scramble your signal with multipath fading. If you understand those you can derive a more elaborate way of doing the reversing. But an even easier shortcut to that is to measure the phase before fading and using that to put it back where it was after the fading.

So, you were saying that you could inverse the phase rotation to get some result, but leave the amplitude distortion as the effect of fading??

Ok, now watch this: Because you are using QAM which is an amplitude and phase modulation scheme, amplitude distortion will also affect your BER. I'm not sure how this is combated in a real world scenario and how exactly equalizers work. You might want to look at what techniques are used in reality and then take the same measures concerning amplitude distortion and whether you should do something about it or not. If this is what you meant by the first question of whether they can be separated or not I hope this gives you an answer to that too.

 

[elecstudward]

Thanks Kaluzakein,

I see what you have done now, but the idea of signal representation: 'real part for amplitude and imaginary part for phase' is new to me. Do you have any reference i might find to read about it? What i knew was that in exponential representation of complex number r*exp(j*theta). r is the amplitude and theta is the phase..

thanks,

 

[KaluzaKlein]

You're totally right about r and theta. I'm talking nonsense about that part. I don't know how I got this idea about real and complex part! They're sin/cosine representations, and I think they are behind the whole quadratute idea and how we can send two carriers simultaneously. I'm so new at this, I shouldn't be talking!

 

[elecstudward]

ok yeah i agree, it's something to do with I and Q part, don't worry, i think i get how confusing it can be,
cheers =)