# Cyclostationarity of DMR Signals

Let’s take a brief look at the cyclostationarity of a captured DMR signal. It’s more complicated than one might think.

In this post I look at the cyclostationarity of a digital mobile radio (DMR) signal empirically. That is, I have a captured DMR signal from sigidwiki.com, and I apply blind CSP to it to determine its cycle frequencies and spectral correlation function. The signal is arranged in frames or slots, with gaps between successive slots, so there is the chance that we’ll see cyclostationarity due to the on-burst (or on-frame) signaling and cyclostationarity due to the framing itself.

The DMR signal on an active slot is said to be a 4FSK signal with symbol rate $4.8$ kHz. The data file I have is highly oversampled at $48$ kHz, so when I process it I decimate it first to bring the signal’s occupied bandwidth closer to the sampling rate.

I slide a data-block window along the signal’s complex-valued samples. For each visited data block, I use the SSCA to blindly determine the non-conjugate cycle frequencies. I then estimate the spectral correlation function for each detected cycle frequency using the time-smoothing method and a relatively short TSM FFT block length to achieve coarse frequency resolution and reasonably high resolution product. I then plot all the blindly obtained spectral correlation slices as a surface above the $(f, \alpha)$ plane together with a plot of the corresponding inphase (real) and quadrature (imaginary) components of the signal in the data-block window. Finally, I arrange this sequence of plots in a movie for your viewing pleasure. Here it is:

The spectral correlation surfaces in Video 1 are rich with features when the DMR signal is present, but they are so closely spaced in cycle frequency that they are hard to see. I made a second video where I simply limited the range of the cycle-frequency parameter to a maximum of $400$ Hz. The result is shown in Video 2:

The results in Video 1 show that the cycle frequency of $4.8$ kHz is routinely detected when the DMR signal is present. Video 2 clearly shows that the signal can exhibit many cycle frequencies smaller than $500$ Hz. What are these cycle frequencies? Let’s take a look at a cyclic-domain profile plot for one of the blocks and try to relate the numerical values of the cycle frequencies we see there to obvious numerical parameters of the time-domain signal or underlying modulation. The cyclic-domain profile is shown in Figure 1.

If we also look carefully at the time-domain data, we can see that successive DMR bursts are separated by exactly $0.06$ seconds, which corresponds to a frequency of $1/0.06 = 16.66$ Hz. This is verified in Figure 2.

So that’s it for this brief post. The lesson is that we can almost never focus on parameters of the modulation on a slot or burst or frame to fully understand the statistical nature of a communication signal. Building a detector in advance of data analysis by focusing on ‘4FSK’ or ‘4.8 kHz’ will miss a lot of the exploitable structure. Also notice that the shapes of the DMR spectral correlation function slices change over time even for this short captured segment (compare the movie frames for times in $[5-10]$ seconds with those near $30$ seconds). What further distinguishing between different variants of DMR or its different modes might we do if we had voluminous data?

h/t Michel P.

I'm a signal processing researcher specializing in cyclostationary signal processing (CSP) for communication signals. I hope to use this blog to help others with their cyclo-projects and to learn more about how CSP is being used and extended worldwide.

## 7 thoughts on “Cyclostationarity of DMR Signals”

1. Michel P. says:

Thank you for that beautiful videos!
DMR are TDMA showing those harmonics in this one slot sample.
What do you expect with a FDMA protocol as dPMR for example, it could show interesting behaviour along the frequency axis of SCA?

1. You’re quite welcome Michel–thanks for the tip on the DMR data.

What do you expect with a FDMA protocol as dPMR for example, it could show interesting behaviour along the frequency axis of SCA?

Yes, I would predict that the variation of the features with frequency $f$ would increase, and also, depending on the details of how the FDMA signals are constructed, conjugate cyclic features, if any, would interfere with each other in interesting ways. Do you have any dPMR data? ðŸ™‚

2. One way to explain the many non-conjugate cycle frequencies with values $k 16.66$ Hz is by modeling the DMR signal as a continuous 4FSK signal with symbol rate $4.8$ kHz multiplied by a periodic rectangular pulse train with $50$% duty cycle and period $0.06$ seconds. Then one can use the results in the Signal Processing and CSP post to find all the cycle frequencies of the product, which are mixtures of the Fourier-series frequencies of the periodic pulse train and the cycle frequencies of the continuous DMR signal. But I’m not sure that model holds–the timing of the symbols within the slots might be reset or random or something else…

3. Joe Wilson says:

Awesome post. Something of note, it appears that you are looking at a mobile station transmission since only one of the timeslots is active. The base station (repeater) transmission will transmit on both timeslots.

Do you think this would effect your findings?

1. Welcome Joe, and thanks for the comment.

Yes, I do believe having both slots active will affect the SCF and cycle frequencies. The cyclostationarity of TDMA or TDMA-like signals depends heavily on the involved clock phases: symbol clock and carrier phase. Also on whether a slot contains an integer number of symbols or not. So the ultimate answer is difficult to predict without a detailed accurate mathematical model or some reliable, long-duration, high-SNR data captures. Do you know of any?

4. Anonymous Coward says:

Really appreciate this blog and love this post. Any chance you published the code that aided in this blog anywhere?