QPSK modulation with constant envelope.

[GeoM]

Hello to all RF people out there.

My knowledge of RF is somewhat flawed so, here's a theoretical question for you:

My understanding is that QPSK modulation will produce a constant envelope output waveform if the symbols are shaped as square pulses. As soon as you apply a different pulse shape (e.g. by filtering symbols with a Root-Raised Cosine filter) the output waveform will no longer be constant envelope.

However, what would happen if prior to applying the Root-Raised Cosine filter you converted I and Q form Cartesian to Polar form? This way, you can have Amplitude and Phase in place of I and Q, then apply the Root-Raised Cosine to the Phase information, convert back to Cartesian and mix I and Q with the carrier as usual.

Would that work? And why go through all this trouble you may ask? Here's the second part of my question: My understanding is that applying the Root Raised Cosine filter to the Phase data will reduce the transmitted bandwidth just like the in traditional IQ modulation. Is this assumption correct?

Thank you all in advance,
Geo

 

[biff44]

qpsk is NOT constant envelope! Who told u that. U would need infinite bandwidth to have a constant envelope qpsk...which I am sure u do not have.

 

[GeoM]

So are you saying that the envelope variations between square-pulsed QPSK and Root Raised Cosine-pulsed QPSK will be the same?

 

[biff44]

of course not

 

[GeoM]

I see. How about my original question? Can you convert I and Q from Cartesian to Polar, RRC filter, convert back to I and Q and then modulate? Would that produce a constant envelope output?

 

[biff44]

No, and here is how to imagine it. Think of the carrier in the time domain. Lets say that you are going from 00 to 10. So the carrier starts off with constant peak to peak voltage at zero degrees phase.

At some time, you change phase to 180 degrees, and in the steady state you end up with the same peak to peak voltage.

But typically a system needs some sort of filtering element. It is needed to remove local oscillator signals, restrict bandwidth to comply with FCC masks, reduce mixer spurious signals. So lets say there is a bandpass filter somewhere in the system.

When you apply a 0 degree signal to your bandpass filter, and then suddenly change the input to be 180 degrees, the output of your bandpass filter does NOT change instantly. Depending on your filter bandwidth, there is a group delay component. So U start at 0 degrees, then the trajectory sends the carrier vector towards the 180 degree point. The quickest way is straight thru the origin. So the signal amplitude at 0 degrees gets smaller, smaller, and finally hits zero. Then it continues thru and becomes 180 degrees, and gets bigger, and bigger, and finally in steady state ends up at the original peak to peak voltage.

So, by changing phase, your envelope was NOT constant.

In real life, the trajectory may not go right thru the origin due to the modulation method and non-linearities, but the amplitudes is definitely NOT constant during the transition.

 

[GeoM]

Thank you biff44.