arXiv subjects

Adam Wunderlich

Publications and source records attributed to Adam Wunderlich.

4 recordsLinked to original sources

arXiv2025

The Expected Peak-to-Average Power Ratio of White Gaussian Noise in Sampled I/Q Data

One of the fundamental endeavors in radio frequency (RF) metrology is to measure the power of signals, where a common aim is to estimate the peak-to-average power ratio (PAPR), which quantifies the ratio of the maximum (peak) to the mean value. For a finite number of discrete-time samples of baseband in-phase and quadrature (I/Q) white Gaussian noise (WGN) that are independent and identically distributed with zero mean, we derive a closed-form, exact formula for mean PAPR that is well-approximated by the natural logarithm of the number of samples plus Euler's constant. Additionally, we give related theoretical results for the mean crest factor (CF). After comparing our main result to previously published approximate formulas, we examine how violations of the WGN assumptions in sampled I/Q data result in deviations from the expected value of PAPR. Finally, utilizing a measured RF I/Q acquisition, we illustrate how our formula for mean PAPR can be applied to spectral analysis with spectrograms to verify when measured RF emissions are WGN in a given frequency band.

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arXiv2022

Data-Driven Modeling of Noise Time Series with Convolutional Generative Adversarial Networks

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing and data analysis tasks. Given the recent interest in generative adversarial networks (GANs) for data-driven modeling, it is important to determine to what extent GANs can faithfully reproduce noise in target data sets. In this paper, we present an empirical investigation that aims to shed light on this issue for time series. Namely, we assess two general-purpose GANs for time series that are based on the popular deep convolutional GAN (DCGAN) architecture, a direct time-series model and an image-based model that uses a short-time Fourier transform (STFT) data representation. The GAN models are trained and quantitatively evaluated using distributions of simulated noise time series with known ground-truth parameters. Target time series distributions include a broad range of noise types commonly encountered in physical measurements, electronics, and communication systems: band-limited thermal noise, power law noise, shot noise, and impulsive noise. We find that GANs are capable of learning many noise types, although they predictably struggle when the GAN architecture is not well suited to some aspects of the noise, e.g., impulsive time-series with extreme outliers. Our findings provide insights into the capabilities and potential limitations of current approaches to time-series GANs and highlight areas for further research. In addition, our battery of tests provides a useful benchmark to aid the development of deep generative models for time series.

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arXiv2021

Feasibility of Modeling Orthogonal Frequency-Division Multiplexing Communication Signals with Unsupervised Generative Adversarial Networks

High-quality recordings of radio frequency (RF) emissions from commercial communication hardware in realistic environments are often needed to develop and assess spectrum-sharing technologies and practices, e.g., for training and testing spectrum sensing algorithms and for interference testing. Unfortunately, the time-consuming, expensive nature of such data collections together with data-sharing restrictions pose significant challenges that limit data set availability. Furthermore, developing accurate models of real-world RF emissions from first principles is often very difficult because system parameters and implementation details are at best only partially known, and complex system dynamics are difficult to characterize. Hence, there is a need for flexible, data-driven methods that can leverage existing data sets to synthesize additional similar waveforms. One promising machine-learning approach is unsupervised deep generative modeling with generative adversarial networks (GANs). To date, GANs for RF communication signals have not been studied thoroughly. In this paper, we present the first in-depth investigation of generated signal fidelity for GANs trained with baseband orthogonal frequency-division multiplexing (OFDM) signals, where each subcarrier is digitally modulated with quadrature amplitude modulation (QAM). Building on prior GAN methods, we developed two novel GAN models and evaluated their performance using simulated data sets with known ground truth. Specifically, we investigated model performance with respect to increasing data set complexity over a range of OFDM parameters and conditions, including fading channels. The findings presented here inform the feasibility of use cases and provide a foundation for further investigations into deep generative models for RF communication signals.

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arXiv2018

Deep Learning Classification of 3.5 GHz Band Spectrograms with Applications to Spectrum Sensing

In the United States, the Federal Communications Commission has adopted rules permitting commercial wireless networks to share spectrum with federal incumbents in the 3.5~GHz Citizens Broadband Radio Service band. These rules require commercial systems to vacate the band when sensors detect radars operated by the U.S. military; a key example being the SPN-43 air traffic control radar. Such sensors require highly-accurate detection algorithms to meet their operating requirements. In this paper, using a library of over 14,000 3.5~GHz band spectrograms collected by a recent measurement campaign, we investigate the performance of thirteen methods for SPN-43 radar detection. Namely, we compare classical methods from signal detection theory and machine learning to several deep learning architectures. We demonstrate that machine learning algorithms appreciably outperform classical signal detection methods. Specifically, we find that a three-layer convolutional neural network offers a superior tradeoff between accuracy and computational complexity. Last, we apply this three-layer network to generate descriptive statistics for the full 3.5~GHz spectrogram library. Our findings highlight potential weaknesses of classical methods and strengths of modern machine learning algorithms for radar detection in the 3.5~GHz band.

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