So why do I obsess over cyclostationary signals and cyclostationary signal processing? What’s the big deal, in the end? In this post I discuss my view of the ultimate use of cyclostationary signal processing (CSP): Radio-Frequency Scene Analysis (RFSA). Eventually, I hope to create a kind of Star Trek Tricorder for RFSA.
The idea of RFSA is to use signal processing techniques to fully understand a particular radio-frequency (RF) scene. But what does “understand a scene” actually mean? I take it to mean the ability to answer all important questions about the scene, such as the number of signals that are present, their parameters, their relationships to each other (if any), the systems (standards) to which the signals may belong, and even things like the location of their transmitters and the propagation-channel effects experienced between the transmitter and the RFSA receiver(s).
The “scene analysis” in RFSA is similar to other kinds of scene analysis. For example, consider crime-scene analysis. The analyst must perform whatever tasks are needed to discover all facts that are relevant to reconstructing the crime; the whole picture must be examined and brought into focus. Crime-scene analysis isn’t just one concept or procedure, such as dusting for fingerprints or identification using DNA. It comprises many tasks that develop multiple lines of evidence, and also the integration of that evidence into a coherent story of what happened and why.
Another kind of scene analysis is a little closer to home: auditory scene analysis. In this kind of analysis, the scene is an acoustic scene. Perhaps the scene contains multiple human speakers, ambient noise, machine noise, animal sounds, reflections, etc., and the auditory scene analyst uses one or more microphones and computing machines to automatically determine answers to important questions about the acoustic scene: How many speakers, their genders, the languages being spoken, the positions of the speakers in the room, etc. This kind of scene analysis is sometimes referred to as the cocktail-party problem or the cocktail-party effect. You enter a room filled with partying people, engaged in multiple conversations spread throughout the room, and there could be music and other non-speech sounds as well. Can you focus on a single conversation in spite of all the cochannel interference? Can you then switch your focus to another conversation? Can you just listen to the music? Many people can do this, but it is a big challenge to automate the process with machines.
A third kind of scene analysis is dramatic scene analysis (or, perhaps, script analysis). Here a scene from a movie or play is fully studied with the goal of holistic understanding of the scene: what are all the parts and how do they all relate and work together to achieve the writer’s goals?
RFSA: The Cocktail-Party Problem for Radios
The cocktail-party problem for radios involves RF signals instead of sound waves, and instead of human interlocutors, we’ve got multiple radio transmitters and receivers (or transceivers) operating in either the same frequency band or a set of closely spaced bands. We enter the region blindly, armed with one or more RF receivers and a whole lot of signal-processing tools. We collect data and attempt to answer the RF-versions of the original cocktail-party problem:
What are the modulation types of each transmitter?
What are the modulation parameters for each signal?
What are the directions of arrival for all signals?
What are the system types, if any, for each signal?
What are the SINRs for each signal?
What are the temporal parameters (hold times, interarrival times) for each signal?
In some versions of the problem, the information contained in the RF transmissions is also of interest, and so the individual signals must be isolated and demodulated. However, that is not part of the RFSA problem that I am attempting to solve with CSP.
Why it is a Difficult Problem
It is difficult when the scene is complicated. By analogy to the cocktail-party problem for humans, when the party is a good one, there will be many spectrally and temporally overlapping signals. A bad party, on the other hand, might consist of just a few signals, perhaps easily separable in either time or frequency. So the RF scene can be arbitrarily complicated, and that is what makes the problem so hard.
Most of the work on RF signal detection that you can find in the literature (a small subset is in The Literature) focuses on simple RF scenes, such as those containing a single textbook signal in white Gaussian noise. Don’t get me wrong–those are indeed important scenes for building intuition and for attempting the construction of optimal signal-processing algorithms. And maybe there are real-world situations for which they apply quite well.
However, when you want to do RFSA over large bandwidths, or for multiple bands scattered throughout the spectrum, you may encounter more difficult scenes, and you may find your textbook-signal-based toolbox becomes inadequate to the task. For example, consider the scene below, which is admittedly a synthetic scene, but one that does contain only captured signals:
The traditional view of this RF scene is summarized by the power spectral density (PSD), which as we know is the non-conjugate spectral correlation function (SCF) evaluated at a cycle frequency of zero. This is shown here as the rear-most slice of the upper SCF plot. I’ve also indicated, using hand-drawn dotted lines, the approximate PSDs for the individual signals. If you had only the PSD estimate, could you determine the number of signals that are present? Estimate their parameters? Probably not.
The remainder of the non-conjugate and the entire conjugate SCF contain the SCFs for the various signals, which are largely separable because each signal possesses at least a few unique cycle frequencies. Unique in the context of this particular RF scene, that is.
So RFSA has a chance if one can analyze the RF data using CSP tools, which allow detection, sorting, and parameter estimation in the cycle-frequency domain. The difficulty is building an automated analyzer for SCF surfaces such as those above. That’s very hard, but I have hope that it can be done.