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 kHz. The data file I have is highly oversampled at 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 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 Hz. The result is shown in Video 2:
The results in Video 1 show that the cycle frequency of kHz is routinely detected when the DMR signal is present. Video 2 clearly shows that the signal can exhibit many cycle frequencies smaller than 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 seconds, which corresponds to a frequency of 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 seconds with those near 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.