“The place where I come from is a small town
They think so small, they use small words
But not me, I’m smarter than that
I worked it out
I’ve been stretching my mouth
To let those big words come right out”
‘Big Time’ by Peter Gabriel
The CSP Blog is now linked-to at the top of cyclostationarity.com, Professor Gardner’s online repository of all things cyclostationary! (See also The Literature [R1].)
Continue reading “The Big Time”“Five different voices behind him bellowed, “REDUCTO!” Five curses flew in five different directions and the shelves opposite them exploded as they hit; the towering structure swayed as a hundred glass spheres burst apart, pearly-white figures unfurled into the air and floated there, their voices echoing from who knew what long-dead past amid the torrent of crashing glass and splintered wood now raining down upon the floor…”
J. K. Rowling, Harry Potter and the Order of the Phoenix
We know that if we subject a cyclostationary signal to a squaring or delay-and-multiply operation we will obtain finite-strength additive sine-wave components at the output of the operation, where at least one of the sine waves has a non-zero frequency.
But I want to make a conjecture: All of CSP can be reduced to interpretations involving sine-wave generation by nonlinear operations. Let’s see if we can show this conjecture is true. After I make my attempt, I’ll also show what ChatGPT comes up with. Any guesses about how well it does?
Continue reading “CSP Reduction to Sine-Wave Generation”Update December 2024: The likely date for this course at GTRI is February 4-5, 2025.
Update September 2024: This course is postponed until Spring 2025. I’ll post further updates here as they become available.
I’ll be part of a team of researchers and practicing engineers, led by the estimable Dr. Ryan Westafer, that will be teaching a class on radio-frequency interference mitigation in September. The class is hosted by the Georgia Tech Research Institute (GTRI) and will be held on the Georgia Tech campus on September 10-11, 2024.
Continue reading “Interference Mitigation Course at GTRI”Oldies but goodies.
It took some years, for sure, but my two most-viewed posts have gathered over 20,000 views each:
Continue reading “Two CSP-Blog Posts Turn 20,000”“Alive in the Superunknown
First it steals your Mind, and then it steals your … Soul”
–Soundgarden
An advantage of using and understanding the statistics of communication signals ™, the basics of signal processing, and the rich details of cyclostationary signal processing is that a practitioner can deal with, to some useful degree, unknown unknowns. The unknown unknowns I’m talking about here on the CSP Blog are, of course, signals. We know about the by-now-familiar known-type detection, multi-class modulation-recognition, and RF scene-analysis problems, in which it is often assumed that we know the signals we are looking for, but we don’t know their times of arrival, some of their parameters, or how they might overlap in time, frequency, and space. Then there are the less-familiar problems involving unknown unknowns.
Sometimes we just don’t know the signals we are looking for. We still want to do as good a job on RF scene analysis as we can, but there might be signals in the scene that do not conform to the body of knowledge we have, to date, of manmade RF signals. Or, in modern parlance, we didn’t even know we left such signals out of our neural-network training dataset; we’re a couple steps back from even worrying about generalization, because we don’t even know we can’t generalize since we are ignorant about what to generalize to.
In this post I look at the broadcast TV band, seen in downtown Monterey, California, sometime in the recent past. I expect to see ATSC DTV signals (of the older 8VSB/16VSB or the newer OFDM types), and I do. But what else is there? Spoiler: Unknown unknowns.
Let’s take a look.
Continue reading “Desultory CSP: What’s That Under the TV?”Another dataset aimed at the continuing problem of generalization in machine-learning-based modulation recognition. This one is a companion to CSPB.ML.2023, which features cochannel situations.
Quality datasets containing digital signals with varied parameters and lengths sufficient to permit many kinds of validation checks by signal-processing experts remain in short supply. In this post, we continue our efforts to provide such datasets by offering a companion unlabeled dataset to CSPB.ML.2023.
Continue reading “CSPB.ML.2023G1”For completeness, I also correct the CSPB.ML.2022 dataset, which is aimed at facilitating neural-network generalization studies.
The same random-number-generator (RNG) error that plagued CSPB.ML.2018 corrupts CSPB.ML.2022, so that some of the files in the dataset correspond to identical signal parameters. This makes the CSPB.ML.2018 dataset potentially problematic for training a neural network using supervised learning.
In a recent post, I remedied the error and provided an updated CSPB.ML.2018 dataset and called it CSPB.ML.2018R2. Both are still available on the CSP Blog.
In this post, I provide an update to CSPB.ML.2022, called CSPB.ML.2022R2.
Continue reading “CSPB.ML.2022R2: Correcting an RNG Flaw in CSPB.ML.2022”KIRK: Everything that is in error must be sterilised.
NOMAD: There are no exceptions.
KIRK: Nomad, I made an error in creating you.
NOMAD: The creation of perfection is no error.
KIRK: I did not create perfection. I created error.
I’ve had to update the original Challenge for the Machine Learners post, and the associated dataset post, a couple times due to flaws in my metadata (truth) files. Those were fairly minor, so I just updated the original posts.
But a new flaw in CSPB.ML.2018 and CSPB.ML.2022 has come to light due to the work of the estimable research engineers at Expedition Technology. The problem is not with labeling or the fundamental correctness of the modulation types, pulse functions, etc., but with the way a random-number generator was applied in my multi-threaded dataset-generation technique.
I’ll explain after the fold, and this post will provide links to an updated version of the dataset, CSPB.ML.2018R2. I’ll keep the original up for continuity and also place a link to this post there. Moreover, the descriptions of the truth files over at CSPB.ML.2018 are still valid–the truth file posted here has the same format as the truth files available on the CSPB.ML.2018 and CSPB.ML.2022 posts.
We are attempting to force a neural network to learn the features that we have already shown deliver simultaneous good performance and good generalization.
ODU doctoral student John Snoap and I have a new paper on the convergence of cyclostationary signal processing, machine learning using trained neural networks, and RF modulation classification: My Papers [55] (arxiv.org link here).
Previously in My Papers [50-52, 54] we have shown that the (multitudinous!) neural networks in the literature that use I/Q data as input and perform modulation recognition (output a modulation-class label) are highly brittle. That is, they minimize the classification error, they converge, but they don’t generalize. A trained neural network generalizes well if it can maintain high classification performance even if some of the probability density functions for the data’s random variables differ from the training inputs (in the lab) relative to the application inputs (in the field). The problem is also called the dataset-shift problem or the domain-adaptation problem. Generalization is my preferred term because it is simpler and has a strong connection to the human equivalent: we can quite easily generalize our observations and conclusions from one dataset to another without massive retraining of our neural noggins. We can find the cat in the image even if it is upside-down and colored like a giraffe.
Continue reading “The Next Logical Step in CSP+ML for Modulation Recognition: Snoap’s MILCOM ’23 Paper [Preview]”The third in a series of posts on visualizing the multidimensional functions characterizing the fundamental statistics of communication signals.
Let’s continue our progression of galleries showing plots of the statistics of communication signals. So far we have provided a gallery of spectral correlation surfaces and a gallery of cyclic autocorrelation surfaces. Here we introduce a gallery of cyclic-cumulant matrices.
When we look at the spectral correlation or cyclic autocorrelation surfaces for a variety of communication signal types, we learn that the cycle-frequency patterns exhibited by modulated signals are many and varied, and we get a feeling for how those variations look (see also the Desultory CSP posts). Nevertheless, there are large equivalence classes in terms of spectral correlation. That simply means that a large number of distinct modulation types map to the exact same second-order statistics, and therefore to the exact same spectral correlation and cyclic autocorrelation surfaces. The gallery of cyclic cumulants will reveal, in an easy-to-view way, that many of these equivalence classes are removed once we consider, jointly, both second- and higher-order statistics.
Continue reading “A Gallery of Cyclic Cumulants”Everything is just fine.
The IEEE sent me their annual report for 2022. I was wondering how they were responding to the poor quality of many of their published papers, including faked papers and various paper retractions. Let’s take a quick look.
Another step forward in the merging of CSP and ML for modulation recognition, and another step away from the misstep of always relying on convolutional neural networks from image processing for RF-domain problem-solving.
My Old Dominion colleagues and I have published an extended version of the 2022 MILCOM paper My Papers [52] in the journal MDPI Sensors. The first author is John Snoap, who is one of those rare people that is an expert in signal processing and in machine learning. Bright future there! Dimitrie Popescu, James Latshaw, and I provided analysis, programming, writing, and research-direction support.
Continue reading “Latest Paper on CSP and Deep-Learning for Modulation Recognition: An Extended Version of My Papers [52]”The cyclostationarity of frequency-shift-keyed signals depends strongly on the way the carrier phase evolves over time. Many distinct cycle-frequency patterns and spectral correlation shapes are possible.
Let’s get back to basics by looking at a large class of signals known as frequency-shift-keyed (FSK) signals. We will leave to the side, for the most part, the very large class of signals that goes by the name of continuous-phase modulation (CPM), which includes continuous-phase FSK (CPFSK), MSK, GMSK, and many more (The Literature [R188]-[R190]). Those are treated in My Papers [8], and in a future CSP Blog post.
Here we want to look at more conventional forms of FSK. These signal types don’t necessarily have a continuous phase function. They are generally easier to demodulate and are more robust to noise and interference than the more complicated CPM signal types, but generally have much lower spectral efficiency. They are like the rectangular-pulse PSK of the FSK/CPM world. But they are still used.
Continue reading “Cyclostationarity of Frequency-Shift-Keyed Signals”Final Update on “Future Posts” Poll:
So among the CSP Blog readers that voted, I think the consensus is to produce more “on brand” posts on CSP and the Signal-Processing ToolKit. Also, there is significant interest in doing CSP with GNU Radio, which I have considerable experience with, and so I’ll likely be posting some flowgraph ideas and results at some point in 2023.
Thanks everybody! (But I’ll still rant and rave from time to time; sorry!)
Update June 25, 2023: When I said you can vote multiple times, I didn’t mean to ‘spam’ the poll (as my kids would say). Someone just voted for one of the responses ten times in a row (same IP address ten votes within one minute). I meant you can vote for several different items in the poll! So I did remove some of those identical votes. I’ll close the poll at the end of the day June 30.
Update May 11, 2023: Please vote in the Reader Poll below (multiple times if you’d like) soon! As of today, CSP Applications and Signal Processing ToolKit are in the lead, with Rants and Datasets at the bottom.
The CSP Blog is rolling along here in 2023!
March 2023 broke a record for pageviews in a calendar month with over 7,000 as of this writing early in the day on March 31.
Let’s note some other milestones and introduce a poll.
What a month! We’re at about 7,145 views right now, and the previous monthly record is 6,482.
2023 was the year that a CSP Blog post crossed the 20,000-view milestone: The Spectral Correlation Function. The Cyclic Autocorrelation Function is not far behind.
About 84,000 visitors have been counted over the years since the CSP Blog launched in 2015, with 5,500 this year already. I believe this is just a count of the unique IP addresses that have accessed a page. But the number of subscribers is only 198! You can subscribe (“Follow”) to the CSP Blog by entering an email address in the “Follow Blog via Email” box on the right edge of any viewed page, near the top of the page. You’ll get notified through that email address whenever there is a new post. CSP Blog readers cannot see that email address, just as they cannot see the email address associated with any comment, unless there is an associated gravatar.
I’m planning to have more time available to devote to improving and extending the CSP Blog over the next few months. If you want to have input into that process, consider voting in the poll below.
Thanks so much to all my readers!
CSP can be used to separate cochannel contemporaneous signals. The involved signal-processing structure is linear but periodically time-varying.
In most of the posts on the CSP Blog we’ve applied the theory and tools of CSP to parameter estimation of one sort or another: cycle-frequency estimation, time-delay estimation, synchronization-parameter estimation, and of course estimation of the spectral correlation, spectral coherence, cyclic cumulant, and cyclic polyspectral functions.
In this post, we’ll switch gears a bit and look at the problem of waveform estimation. This comes up in two situations for me: single-sensor processing and array (multi-sensor) processing. At some point, I’ll write a post on array processing for waveform estimation (using, say, the SCORE algorithm The Literature [R102]), but here we restrict our attention to the case of waveform estimation using only a single sensor (a single antenna connected to a single receiver). We just have one observed sampled waveform to work with. There are also waveform estimation methods that are multi-sensor but not typically referred to as array processing, such as the blind source separation problem in acoustic scene analysis, which is often solved by principal component analysis (PCA), independent component analysis (ICA), and their variants.
The signal model consists of the noisy sum of two or more modulated waveforms that overlap in both time and frequency. If the signals do not overlap in time, then we can separate them by time gating, and if they do not overlap in frequency, we can separate them using linear time-invariant systems (filters).
Relevant FRESH filtering publications include My Papers [45, 46] and The Literature [R6].
Continue reading “Frequency Shift (FRESH) Filtering for Single-Sensor Cochannel Signal Separation”The next step in dataset complexity at the CSP Blog: cochannel signals.
I’ve developed another dataset for use in assessing modulation-recognition algorithms (machine-learning-based or otherwise) that is more complex than the original sets I posted for the ML Challenge (CSPB.ML.2018 and CSPB.ML.2022). Half of the new dataset consists of one signal in noise and the other half consists of two signals in noise. In most cases the two signals overlap spectrally, which is a signal condition called cochannel interference.
We’ll call it CSPB.ML.2023.
Continue reading “PSK/QAM Cochannel Dataset for Modulation Recognition Researchers [CSPB.ML.2023]”Am I out of a job?
Update January 31, 2023: I’ve added numbers in square brackets next to the worst of the wrong things. I’ll document the errors at the bottom of the post.
Of course I have to see what ChatGPT has to say about CSP. Including definitions, which I don’t expect it to get too wrong, and code for estimators, which I expect it to get very wrong.
Let’s take a look.
Continue reading “ChatGPT and CSP”How can we train a neural network to make use of both IQ data samples and CSP features in the context of weak-signal detection?
I’ve been working with some colleagues at Northeastern University (NEU) in Boston, MA, on ways to combine CSP with machine learning. The work I’m doing with Old Dominion University is focused on basic modulation recognition using neural networks and, in particular, the generalization (dataset-shift) problem that is pervasive in deep learning with convolution neural networks. In contrast, the NEU work is focused on specific signal detection and classification problems and looks at how to use multiple disparate data types as inputs to neural-networks; inputs such as complex-valued samples (IQ data) as well as carefully selected components of spectral correlation and spectral coherence surfaces.
My NEU colleagues and I will be publishing a rather lengthy conference paper on a new multi-input-data neural-network approach called ICARUS at InfoCom 2023 this May (My Papers [53]). You can get a copy of the pre-publication version here or on arxiv.org.
Continue reading “ICARUS: More on Attempts to Merge IQ Data with Extracted-Feature Data in Machine Learning”The CSP Blog took a big step forward in 2022, with 66,700 67,965 page views and counting, which is 10,000 12,000 more than last year’s (record) number of about 56,000. Thanks to all my readers!
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.
Continue reading “CSP Community Spotlight: A Publicly Available python-Based SCF Estimator”