100-MHz Amplitude Modulation? Comments on “Sub-Nyquist Cyclostationary Detection for Cognitive Radio” by Cohen and Eldar

I came across a paper by Cohen and Eldar, researchers at the Technion in Israel. You can get the paper on the Arxiv site here. The title is “Sub-Nyquist Cyclostationary Detection for Cognitive Radio,” and the setting is spectrum sensing for cognitive radio. I have a question about the paper that I’ll ask below.

In the standard cognitive radio problem, it is desired to set up a radio network that communicates over RF bands that are licensed to other RF operators. The users that want to access the RF bands do so on a non-interference basis relative to the radios of licensed users. The former set of users are referred to as secondary and the latter as primary.

So the secondary users want to operate on the RF bandwidth that is more-or-less the property of the primary users. The hope is that the secondary radios have such good spectrum sensing that they can reliably tell when the RF bands are going unused by the primaries. The secondaries set up shop and start transmitting and receiving RF signals in the primary users bands, and when a primary user shows up, the secondaries quickly evacuate the bands. The primary users receivers ideally suffer no interference, and the secondary users are able to communicate over their preferred RF bands, at least some of the time. Everybody wins!

But the hard part is the “reliably” in “reliably tell.” So a lot of effort has been expended worldwide to create, develop, and evaluate high-performance (highly sensitive) signal detectors for the cognitive-radio problem.

In some versions of the problem, much is known about the signals used by the primary users. In such cases, perhaps the signals contain periodically repeated bursts that are known from published standards, and so matched filtering could be profitably applied. In other versions, the signal types might be known, but no known-signal components are available, so matched-filtering is out, and energy detection or feature detection (for example, using the spectral correlation function) could be applied.

For cognitive radios that can tune their transmitters and receivers over a wide frequency band, it is of interest to perform rapid, reliable spectrum sensing over wide–possibly very very wide–RF bands. How can we do this with our admittedly computationally burdensome CSP algorithms? Enter compressive sensing and the paper that is the topic of this post.

The authors want to use CSP to detect signals that may be present in a large RF bandwidth, and know that if they tried to directly sample the desired band they’d have trouble with the ADC and of course lots of computational trouble even if they could get the high-rate samples. So they try to undersample the desired band, in the compressive-sensing sense, and use those relatively low-rate samples to reconstruct the spectral correlation function for the full wideband RF scene. Presumably, signal detection can take place based on the reconstructed spectral correlation.

That is all good! I want to do that too. But I have doubts that this can work in a realistic setting. And I see in the paper the use of highly unrealistic RF scenes. This goes even beyond what I call the problem of pervasive textbook signals. I note that the authors set out their signal model in their first equations ((1) and (2)), which correspond to textbook digital QAM/PSK signals.

In Section V, simulations are presented to illustrate and confirm the compressive sensing approach to estimating the spectral correlation function. The first set of results is intended to show how the method reconstructs the PSD and the SCF. The authors consider an RF band having width of 3.2 GHz (the band is actually [0, 3.2] GHz). They populate this band with

… N_sig = 3 AM transmissions.


Each transmission has bandwidth B = 80 MHz“.

A few paragraphs later, they want to consider SCF-based signal detection for

… AM modulated signals …“,

and switch to

… a blind scenario where the carrier frequencies of the signals occupying the wideband channel are unknown and we have N_sig = 3 potentially active transmissions, with single-sided bandwidth B = 100 MHz.

A little while later, they consider BPSK signals with

… bandwidth B = 18 MHz …“.

I note that the reconstructed power spectrum and spectral correlation functions are incorrect (Figures 5 and 8). The SCF plot contains more than the three expected peaks at the doubled-carrier cycle frequencies for the three AM signals, and the PSD contains all kinds of false energy lumps (which the authors admit to). So if this compressive-sensing method doesn’t work even in this high-SNR (Figure 5, upper plot) highly simplified RF scene, can it work with realistic signals that possess, say, tens-to-hundreds of cycle frequencies? Or RF scenes that contain hundreds of signals?

So I have two questions:

  1. Why focus on AM signals in a cognitive-radio spectrum-sensing problem?
  2. Has anybody ever heard of AM with bandwidth of 80 or 100 MHz? What would the message source be?

Leave your answers, questions, or corrections to my post in the comments.

Author: Chad Spooner

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.

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