Re: Demodulating QPSK



John E. Hadstate wrote:


After extensive tests, I've hit upon one robust, sure-fire system for demodulating long-duration QPSK. (This system is not especially useful for signals that occur in short bursts.)

Why reinventing a wheel?

Demodulation of the long duration QPSK without noise, fading and frequency wander is a piece of cake task, and there is 10000 solutions for that.

As always with this type of system, you will probably need to re-map your recovered dibits based on some knowledge of the signal's contents and internal structure.

In my implementation, all filters were two-pole IIR filters. The low-pass filters were designed by applying the BLT to Butterworth pole placements from the analog domain.

Minor technical detail. Why does it matter?


The band-pass filters were designed with complex-conjugate poles just inside the unit circle and on the radial lines corresponding to the desired center frequency. All of the critical frequencies were either a multiple or a fraction of the baud rate of the dibits.

Too many of the clever scientific words. Understood nothing.


Here's the block diagram in text form:

1. What is new about it?

2. Why this is better then a classic approach?

1. Re-tune t QPSK signal so that its frequency is an integral multiple of the baud rate.

Having all frequencies coupled is inflexible and inconvenient.

To do this, you need to have some estimate of frequency of the incoming signal. You don't necessarily know the exact frequency of the original signal, but you must estimate "close enough". Initialize a frequency accumulator to the re-tuned frequency.

2. Square the signal from (1). Bandpass filter around 2x the nominal (re-tuned) frequency.

3. Square the signal from (2). Bandpass filter around 4x the nominal (re-tuned) frequency.

4-th order loop classics.

4. Multiply the signal from (3) by a sin and cos from a quadrature Numerically Controlled Oscillator (NCO) running at 4x the frequency indicated by the frequency accumulator.

5. Low-pass filter the I and Q arms to remove the 8x component.

Trivial implementation of a bandpass in complex domain.

Note: At this point you are dealing with frequencies of at least 8x the re-tuned signal (which might be higher than the frequency of your original signal). Make sure your sample rate is adequate to handle these frequencies.

Another stupid limitation.

6. Use the first difference of atan2(Q,I) to estimate the rate-of-change of phase angle between I and Q. Unwrap this result so it stays between -Pi and +Pi. Using this technique makes your PLL's loop gain less vulnerable to changes in signal level.

And less noise resistant, too.

7. Filter the phase rate-of-change, multiply by a gain constant and subtract it from the frequency accumulator. (This is the same frequency accumulator that is multiplied by 4 and used as the control frequency of the NCO in step (4).

This could be done much simpler.

At this point, if you've got all the filters right and the gain right, you will have constructed a PLL that will lock-up fairly quickly at a frequency of 4x the re-tuned frequency and it will follow changes in the carrier frequency of the re-tuned signal.

Not any different from the 4-th order Costas Loop.

The double squaring will have wiped out most of the effect of modulation on the frequency estimation.

Classics. So what is new?

8. Apply the frequency from the frequency accumulator in (7) directly to another quadrature NCO. It is this NCO that produces the reconstructed carrier.

So?

9. Multiply the re-tuned signal from (1) by the sin and cos from the NCO in (8).

So?

10. Low-pass filter the I and Q arms from (9) to eliminate the 2x frequency.

So?

11. Look at the signs of the signal on the I and Q arms in (10) to decide which quadrant the signal is in. You have to invent the necessary logic to synchronize, decimate, and recover the demodulated dibits. Hint: it helps if you sampled the incoming signal at a rate that was an integral multiple of the baud rate (in addition to being at least 16x the re-tuned frequency).

What is the point of this very trivial exersize?


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
.

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