The CSP Blog recently received a comment from a signal processor that needed a small amount of debugging help with their python spectral correlation estimator code.
The code uses a form of the time-smoothing method and aims to compute and plot the spectral correlation estimate as well as the corresponding coherence estimate. What is cool about this code is that it is clear, well-organized, on github, and is written using Jupyter Notebook. Moreover, there is a Google Colab function so that anyone can run the code from a chrome browser and see the results, even a python newbie like me. Tres moderne.
It’s too close to home, and it’s too near the bone …
Park the car at the side of the road You should know Time’s tide will smother you… And I will too
“That Joke Isn’t Funny Anymore” by The Smiths
I applaud the intent behind the paper in this post’s title, which is The Literature [R183], apparently accepted in 2022 for publication in IEEE Access, a peer-reviewed journal. That intent is to list all the found ways in which researchers preprocess radio-frequency data (complex sampled data) prior to applying some sort of modulation classification (recognition) algorithm or system.
The problem is that this attempt at gathering up all of the ‘representations’ gets a lot of the math wrong, and so has a high potential to confuse rather than illuminate.
Neural networks with CSP-feature inputs DO generalize in the modulation-recognition problem setting.
In some recently published papers (My Papers [50,51]), my ODU colleagues and I showed that convolutional neural networks and capsule networks do not generalize well when their inputs are complex-valued data samples, commonly referred to as simply IQ samples, or as raw IQ samples by machine learners.(Unclear why the adjective ‘raw’ is often used as it adds nothing to the meaning. If I just say Hey, pass me those IQ samples, would ya?, do you think maybe he means the processed ones? How about raw-I-mean–seriously-man–I-did-not-touch-those-numbers-OK? IQ samples? All-natural vegan unprocessed no-GMO organic IQ samples?Uncooked IQ samples?) Moreover, the capsule networks typically outperform the convolutional networks.
In a new paper (MILCOM 2022: My Papers ; arxiv.org version), my colleagues and I continue this line of research by including cyclic cumulants as the inputs to convolutional and capsule networks. We find that capsule networks outperform convolutional networks and that convolutional networks trained on cyclic cumulants outperform convolutional networks trained on IQ samples. We also find that both convolutional and capsule networks trained on cyclic cumulants generalize perfectly well between datasets that have different (disjoint) probability density functions governing their carrier frequency offset parameters.
That is, convolutional networks do better recognition with cyclic cumulants and generalize very well with cyclic cumulants.
So why don’t neural networks ever ‘learn’ cyclic cumulants with IQ data at the input?
The majority of the software and analysis work is performed by the first author, John Snoap, with an assist on capsule networks by James Latshaw. I created the datasets we used (available here on the CSP Blog [see below]) and helped with the blind parameter estimation. Professor Popescu guided us all and contributed substantially to the writing.
Another brick in the wall, another drop in the bucket, another windmill on the horizon …
Let’s talk more about The Cult. No, I don’t mean She Sells Sanctuary, for which I do have considerable nostalgic fondness. I mean the Cult(ure) of Machine Learning in RF communications and signal processing. Or perhaps it is more of an epistemic bubble where there are The Things That Must Be Said and The Unmentionables in every paper and a style of research that is strictly adhered to but that, sadly, produces mostly error and promotes mostly hype. So we have shibboleths, taboos, and norms to deal with inside the bubble.
Time to get on my high horse. She’s a good horse named Ravager and she needs some exercise. So I’m going to strap on my claymore, mount Ravager, and go for a ride. Or am I merely tilting at windmills?
Let’s take a close look at another paper on machine learning for modulation recognition. It uses, uncritically, the DeepSig RML 2016 datasets. And the world and the world, the world drags me down…
Introducing swag for the best CSP-Blog commenters.
The comments that CSP Blog readers have made over the past six years are arguably the most helpful part of the Blog for do-it-yourself CSP practitioners. In those comments, my many errors have been revealed, which then has permitted me to attempt post corrections. Many unclear aspects of a post have been clarified after pondering a reader’s comment. At least one comment has been elevated to a post of its own.
The readership of the CSP Blog has been steadily growing since its inception in 2015, but the ratio of page views to comments remains huge–the vast majority of readers do not comment. This is understandable and perfectly acceptable. I rarely comment on any of the science and engineering blogs that I frequent. Nevertheless, I would like to encourage more commenting and also reward it.
Back in 2018 I posted a dataset consisting of 112,000 I/Q data files, 32,768 samples in length each, as a part of a challenge to machine learners who had been making strong claims of superiority over signal processing in the area of automatic modulation recognition. One part of the challenge was modulation recognition involving eight digital modulation types, and the other was estimating the carrier frequency offset. That dataset is described here, and I’d like to refer to it as CSPB.ML.2018.
Then in 2022 I posted a companion dataset to CSPB.ML.2018 called CSPB.ML.2022. This new dataset uses the same eight modulation types, similar ranges of SNR, pulse type, and symbol rate, but the random variable that governs the carrier frequency offset is different with respect to the random variable in CSPB.ML.2018. The purpose of the CSPB.ML.2022 dataset is to facilitate studies of the dataset-shift, or generalization, problem in machine learning.
Throughout the past couple of years I’ve been working with some graduate students and a professor at Old Dominion University on merging machine learning and signal processing for problems involving RF signal analysis, such as modulation recognition. We are starting to publish a sequence of papers that describe our efforts. I briefly describe the results of one such paper, My Papers , in this post.
Can we fix peer review in engineering by some form of payment to reviewers?
Let’s talk about another paper about cyclostationarity and correntropy. I’ve critically reviewed two previously, which you can find here and here. When you look at the correntropy as applied to a cyclostationary signal, you get something called cyclic correntropy, which is not particularly useful except if you don’t understand regular cyclostationarity and some aspects of garden-variety signal processing. Then it looks great.
But this isn’t a post that primarily takes the authors of a paper to task, although it does do that. I want to tell the tale to get us thinking about what ‘peer’ could mean, these days, in ‘peer-reviewed paper.’ How do we get the best peers to review our papers?
In this Signal Processing ToolKit post we take a close look at the basic sampling theorem used daily by signal-processing engineers. Application of the sampling theorem is a way to choose a sampling rate for converting an analog continuous-time signal to a digital discrete-time signal. The former is ubiquitous in the physical world–for example all the radio-frequency signals whizzing around in the air and through your body right now. The latter is ubiquitous in the computing-device world–for example all those digital-audio files on your DiscmanItunesIpodDVDSmartphoneCloudNeuralink Singularity.
So how are those physical real-world analog signals converted to convenient lists of finite-precision numbers that we can apply arithmetic to? For that’s all [digital or cyclostationary] signal processing is at bottom: arithmetic. You might know the basic rule-of-thumb for choosing a sampling rate: Make sure it is at least twice as big as the largest frequency component in the analog signal undergoing the sampling. But why, exactly, and what does ‘largest frequency component’ mean?
Let’s take a look at an even faster spectral correlation function estimator. How useful is it for CSP applications in communications?
Reader Gideon pointed out that Antoni had published a paper a year after the paper that I considered in my first Antoni post. This newer paper, The Literature [R172], promises a faster fast spectral correlation estimator, and it delivers on that according to the analysis in the paper. However, I think the faster fast spectral correlation estimator is just as limited as the slower fast spectral correlation estimator when considered in the context of communication-signal processing.
And, to be fair, Antoni doesn’t often consider the context of communication-signal processing. His favored application is fault detection in mechanical systems with rotating parts. But I still don’t think the way he compares his fast and faster estimators to conventional estimators is fair. The reason is that his estimators are both severely limited in the maximum cycle frequency that can be processed, relative to the maximum cycle frequency that is possible.
Another RF-signal dataset to help push along our R&D on modulation recognition.
In this post I provide a second dataset for the Machine-Learning Challenge I issued in 2018 (CSPB.ML.2018). This dataset is similar to the original dataset, but possesses a key difference in that the probability distribution of the carrier-frequency offset parameter, viewed as a random variable, is not the same, but is still realistic.
Blog Note: By WordPress’ count, this is the 100th post on the CSP Blog. Together with a handful of pages (like My Papers and The Literature), these hundred posts have resulted in about 250,000 page views. That’s an average of 2,500 page views per post. However, the variance of the per-post pageviews is quite large. The most popular is The Spectral Correlation Function (> 16,000) while the post More on Pure and Impure Sinewaves, from the same era, has only 316 views. A big Thanks to all my readers!!
What are the ranges of spectral frequency and cycle frequency that we need to consider in a discrete-time/discrete-frequency setting for CSP?
Let’s talk about that diamond-shaped region in the plane we so often see associated with CSP. I’m talking about the principal domain for the discrete-time/discrete-frequency spectral correlation function. Where does it come from? Why do we care? When does it come up?
The Fast Spectral Correlation estimator is a quick way to find small cycle frequencies. However, its restrictions render it inferior to estimators like the SSCA and FAM.
In this post we take a look at an alternative CSP estimator created by J. Antoni et al (The Literature [R152]). The paper describing the estimator can be found here, and you can get some corresponding MATLAB code, posted by the authors, here if you have a Mathworks account.
The merging of conventional probability theory with signal theory leads to random processes, also known as stochastic processes. The ideas involved with random processes are central to cyclostationary signal processing.
In this Signal Processing ToolKit post, I provide an introduction to the concept and use of random processes (also called stochastic processes). This is my perspective on random processes, so although I’ll introduce and use the conventional concepts of stationarity and ergodicity, I’ll end up focusing on the differences between stationary and cyclostationary random processes. The goal is to illustrate those differences with informative graphics and videos; to build intuition in the reader about how the cyclostationarity property comes about, and about how the property relates to the more abstract mathematical object of a random process on one hand and to the concrete data-centric signal on the other.
So … this is the first SPTK post that is also a CSP post.
Why does zero-padding help in various estimators of the spectral correlation and spectral coherence functions?
Update to the exchange: May 7, 2021.May 14, 2021.
Reader Clint posed a great question about zero-padding in the frequency-smoothing method (FSM) of spectral correlation function estimation. The question prompted some pondering on my part, and I went ahead and did some experiments with the FSM to illustrate my response to Clint. The exchange with Clint (ongoing!) was deep and detailed enough that I thought it deserved to be seen by other CSP-Blog readers. One of the problems with developing material, or refining explanations, in the Comments sections of the CSP Blog is that these sections are not nearly as visible in the navigation tools featured on the Blog as are the Posts and Pages.
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.
Another post-publication review of a paper that is weak on the ‘RF’ in RF machine learning.
Let’s take a look at a recently published paper (The Literature [R148]) on machine-learning-based modulation-recognition to get a data point on how some electrical engineers–these are more on the side of computer science I believe–use mathematics when they turn to radio-frequency problems. You can guess it isn’t pretty, and that I’m not here to exalt their acumen.
Spectral correlation surfaces for real-valued and complex-valued versions of the same signal look quite different.
In the real world, the electromagnetic field is a multi-dimensional time-varying real-valued function (volts/meter or newtons/coulomb). But in mathematical physics and signal processing, we often use complex-valued representations of the field, or of quantities derived from it, to facilitate our mathematics or make the signal processing more compact and efficient.
So throughout the CSP Blog I’ve focused almost exclusively on complex-valued signals and data. However, there is a considerable older literature that uses real-valued signals, such as The Literature [R1, R151]. You can use either real-valued or complex-valued signal representations and data, as you prefer, but there are advantages and disadvantages to each choice. Moreover, an author might not be perfectly clear about which one is used, especially when presenting a spectral correlation surface (as opposed to a sequence of equations, where things are often more clear).
Last evening the CSP Blog crossed the 50,000 page-view threshold for 2020, a yearly total that has not been achieved previously!
I want to thank each reader, each commenter, and each person that’s clicked the Donate button. You’ve made the CSP Blog the success it is, and I am so grateful for the time you spend here.
On these occasions I put some of the more interesting CSP-Blog statistics below the fold. If you have been wanting to see a post on a particular CSP or Signal Processing ToolKit topic, and it just hasn’t appeared, feel free to leave me a note in the Comments section.