Random Research Ramblings Roundup


LSM 101


The images on this page were captured using Ettus USRP1. All software used including GNU Radio is free software.

We focus here on a single Frame Sync (FS) sequence as seen on a local P25 Phase I simulcast (LSM/CQPSK) system. This is convenient because the FS is or should be very familiar to all P25 researchers and because it contains in a nutshell all that we need for this analysis. This particular FS was chosen completely at random and was not hand-picked for use on this page.



Fig. 1. P25 Frame Sync Sequence (LSM; all 24 symbols)


In Fig. 1 we have one complete Frame Sync sequence (24 symbols). The signal has been translated to zero IF, or very close to it, and low-pass channel filtering is applied to eliminate any other signals present in the spectrum. Finally, there is some AGC to bring the signal magnitude into the normalized range between zero and one.

Note that in contrast to a constant-magnitude FM signal (in which all of the energy would be confined to the unit circle), we see that the signal passes close to the (0,0) origin while in transit between constellation points. In the complex representation shown here we can clearly see the amplitude variations; when the signal is near the (0,0) origin there is much less transmitted power than when the signal is near the circumference of the circle.


Fig. 2. P25 Frame Sync Sequence (LSM; showing first six symbol transitions)


Same as Fig. 1, except we show only the first six symbols (111113). The beginning of the sequence is in the lower left-hand quadrant. The first five of the six symbols each comprise a 135° transition, and the last one also transits through 135° except in the opposite direction. Again we clearly see the signal energy is greatly reduced as it passes near the origin. The proper sampling points for the signal are at the constellation points located on the circumference (not at the center of each arc where it passes near the origin).


Fig. 3. P25 Frame Sync Sequence (same as Fig.1 after FM demodulation)


The complex constellation of Fig. 1 is quadrature (FM) demodulated and the resulting real-valued baseband signal is shown in Fig. 3. This corresponds to the signal as it would be seen at the output of a hardware FM discriminator.


Fig. 4. P25 Frame Sync Sequence - first six symbols only


In Fig. 4 we once again confine our view to the first six symbols (111113) in the FS sequence. The upper (green) plot is the same as in Fig. 3, although truncated; and we also include (in red) a plot of the signal magnitude-squared. In simple essence the green line is the output of the FM discriminator, and the red one is a plot of the signal's amplitude (AM).

It's important to note that the "FM" and "AM" waveforms are synchronized in time; that is, the red plot demonstrates that the received signal strength varies at the symbol rate (4800 cycles) and the signal strength is at its lowest value (approaching zero strength) at time T=10 (and at time 30, 50, 70, ...).

[Note that samples-per-symbol is set to twenty throughout this page].

Looking back at Fig. 2 from which this plot was derived, we see the beginning of the FS starting at the lower left-hand quadrant, which is at time T=0. From there the arc flows near the center of the circle (T=10) and ends 135° later at the right-hand side, approx. halfway between the top and bottom of the circle, at time T=20.


Conclusions

See Fig. 4. When using the FM demodulation method, the symbol timing recovery loop must use the transition peaks (at time T=10,30,50,...) in order to form decisions about what symbol was transmitted. However these points correspond to the minimum-energy portion of the waveform.

In contrast, when CQPSK is properly demodulated the symbol timing recovery is done at times T=0,20,40,60,... (when the signal magnitude is at its peak).

This is the essence of the problem. The symbol timing (clock) recovery must be done at the point in the cycle where the transmitter power is maximum for proper demodulation. Ironically however, when the FM demodulation method is used the receiver's clock recovery logic must make its decisions based on the samples which appear at the points in time when transmitter power is at minimum. Thus we see that when we attempt to demodulate CQPSK as if it were C4FM our clock recovery loop is making decisions at the exact opposite of the correct times.

As a side note, we see by inspection of the "AM" demodulated waveform (Fig. 4, red plot) the reason why there's such a loud audible 4.8 K.C. tone in the signal, which can be clearly heard when listening to the signal in the AM mode.


In case you want to reproduce these results, here is the raw data (see Fig. 1). All other graphs on this page are derived from this initial data.
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© Copyright 2014 Max H. Parke KA1RBI. All Rights Reserved