R. Michael Buehrer

Harish K. Dureppagari, Chiranjib Saha, R. Michael Buehrer et al.

In this paper, we propose a sequence construction framework that extends prime-length Björck sequences, a class of Constant Amplitude Zero Autocorrelation (CAZAC) sequences, to arbitrary lengths using Goldbach's conjecture for even and odd integers. The framework is generic and applies to any CAZAC family defined for prime lengths and supports extensions to both cyclically shifted sequences and sequences with different root indices. We analytically characterize the resulting correlation behavior and show that the construction preserves orthogonality among cyclic shifts while maintaining favorable zero-lag cross-correlation across different root-index sequences. We further investigate Björck sequences as candidates for reference signals in next-generation wireless systems. Using the proposed framework, we extend Björck sequences to arbitrary lengths and evaluate their time- and frequency-offset estimation performance in terrestrial (TNs) and non-terrestrial networks (NTNs). Results show performance comparable to Zadoff--Chu (ZC) sequences in low-Doppler TN environments and improved robustness in high-Doppler NTN scenarios due to superior ambiguity-function properties. We also identify an inherent Doppler-dependent behavior that can cause sequence misidentification under large Doppler shifts. To address this, we propose two mitigation strategies: (i) leveraging coarse Doppler estimates prior to detection, and (ii) selecting appropriately spaced subsets of orthogonal sequences. Ambiguity function-based analysis demonstrates the effectiveness of these approaches in improving estimation reliability. Overall, this work enables practical arbitrary-length CAZAC sequence design and establishes Björck sequences as a strong alternative for reference signal design in high-Doppler environments.

Charles E. Thornton, R. Michael Buehrer

It has been shown (Amuru et al. 2015) that online learning algorithms can be effectively used to select optimal physical layer parameters for jamming against digital modulation schemes without a priori knowledge of the victim's transmission strategy. However, this learning problem involves solving a multi-armed bandit problem with a mixed action space that can grow very large. As a result, convergence to the optimal jamming strategy can be slow, especially when the victim and jammer's symbols are not perfectly synchronized. In this work, we remedy the sample efficiency issues by introducing a linear bandit algorithm that accounts for inherent similarities between actions. Further, we propose context features which are well-suited for the statistical features of the non-coherent jamming problem and demonstrate significantly improved convergence behavior compared to the prior art. Additionally, we show how prior knowledge about the victim's transmissions can be seamlessly integrated into the learning framework. We finally discuss limitations in the asymptotic regime.

Charles E. Thornton, William W. Howard, R. Michael Buehrer

This paper describes important considerations and challenges associated with online reinforcement-learning based waveform selection for target identification in frequency modulated continuous wave (FMCW) automotive radar systems. We present a novel learning approach based on satisficing Thompson sampling, which quickly identifies a waveform expected to yield satisfactory classification performance. We demonstrate through measurement-level simulations that effective waveform selection strategies can be quickly learned, even in cases where the radar must select from a large catalog of candidate waveforms. The radar learns to adaptively select a bandwidth for appropriate resolution and a slow-time unimodular code for interference mitigation in the scene of interest by optimizing an expected classification metric.

Harish K. Dureppagari, Harikumar Krishnamurthy, Chiranjib Saha et al.

The integration of non-terrestrial networks (NTN) into 5G new radio (NR) enables a new class of positioning capabilities based on cellular signals transmitted by Low-Earth Orbit (LEO) satellites. In this paper, we investigate joint delay-and-carrier-phase positioning for LEO-based NR-NTN systems and provide a convergence-centric comparison with Global Navigation Satellite Systems (GNSS). We show that the rapid orbital motion of LEO satellites induces strong temporal and geometric diversity across observation epochs, thereby improving the conditioning of multi-epoch carrier-phase models and enabling significantly faster integer-ambiguity convergence. To enable robust carrier-phase tracking under intermittent positioning reference signal (PRS) transmissions, we propose a dual-waveform design that combines wideband PRS for delay estimation with a continuous narrowband carrier for phase tracking. Using a realistic simulation framework incorporating LEO orbit dynamics, we demonstrate that LEO-based joint delay-and-carrier-phase positioning achieves cm-level accuracy with convergence times on the order of a few seconds, whereas GNSS remains limited to meter-level accuracy over comparable short observation windows. These results establish LEO-based cellular positioning as a strong complement and potential alternative to GNSS for high-accuracy positioning, navigation, and timing (PNT) services in future wireless networks.

Charles E. Thornton, R. Michael Buehrer, Anthony F. Martone

A key component of cognitive radar is the ability to generalize, or achieve consistent performance across a range of sensing environments, since aspects of the physical scene may vary over time. This presents a challenge for learning-based waveform selection approaches, since transmission policies which are effective in one scene may be highly suboptimal in another. We address this problem by strategically biasing a learning algorithm by exploiting high-level structure across tracking instances, referred to as meta-learning. In this work, we develop an online meta-learning approach for waveform-agile tracking. This approach uses information gained from previous target tracks to speed up and enhance learning in new tracking instances. This results in sample-efficient learning across a class of finite state target channels by exploiting inherent similarity across tracking scenes, attributed to common physical elements such as target type or clutter statistics. We formulate the online waveform selection problem within the framework of Bayesian learning, and provide prior-dependent performance bounds for the meta-learning problem using Probability Approximately Correct (PAC)-Bayes theory. We present a computationally feasible meta-posterior sampling algorithm and study the performance in a simulation study consisting of diverse scenes. Finally, we examine the potential performance benefits and practical challenges associated with online meta-learning for waveform-agile tracking.

Charles E. Thornton, R. Michael Buehrer

When should an online reinforcement learning-based frequency agile cognitive radar be expected to outperform a rule-based adaptive waveform selection strategy? We seek insight regarding this question by examining a dynamic spectrum access scenario, in which the radar wishes to transmit in the widest unoccupied bandwidth during each pulse repetition interval. Online learning is compared to a fixed rule-based sense-and-avoid strategy. We show that given a simple Markov channel model, the problem can be examined analytically for simple cases via stochastic dominance. Additionally, we show that for more realistic channel assumptions, learning-based approaches demonstrate greater ability to generalize. However, for short time-horizon problems that are well-specified, we find that machine learning approaches may perform poorly due to the inherent limitation of convergence time. We draw conclusions as to when learning-based approaches are expected to be beneficial and provide guidelines for future study.

Haozhou Hu, Harpreet S. Dhillon, R. Michael Buehrer

Many modern wireless devices with accurate positioning needs also have access to vision sensors, such as a camera, radar, and Light Detection and Ranging (LiDAR). In scenarios where wireless-based positioning is either inaccurate or unavailable, using information from vision sensors becomes highly desirable for determining the precise location of the wireless device. Specifically, vision data can be used to estimate distances between the target (where the sensors are mounted) and nearby landmarks. However, a significant challenge in positioning using these measurements is the inability to uniquely identify which specific landmark is visible in the data. For instance, when the target is located close to a lamppost, it becomes challenging to precisely identify the specific lamppost (among several in the region) that is near the target. This work proposes a new framework for target localization using range measurements to multiple proximate landmarks. The geometric constraints introduced by these measurements are utilized to narrow down candidate landmark combinations corresponding to the range measurements and, consequently, the target's location on a map. By modeling landmarks as a marked Poisson point process (PPP), we show that three noise-free range measurements are sufficient to uniquely determine the correct combination of landmarks in a two-dimensional plane. For noisy measurements, we provide a mathematical characterization of the probability of correctly identifying the observed landmark combination based on a novel joint distribution of key random variables. Our results demonstrate that the landmark combination can be identified using ranges, even when individual landmarks are visually indistinguishable.

Charles E. Thornton, R. Michael Buehrer, Harpreet S. Dhillon et al.

Online selection of optimal waveforms for target tracking with active sensors has long been a problem of interest. Many conventional solutions utilize an estimation-theoretic interpretation, in which a waveform-specific Cramér-Rao lower bound on measurement error is used to select the optimal waveform for each tracking step. However, this approach is only valid in the high SNR regime, and requires a rather restrictive set of assumptions regarding the target motion and measurement models. Further, due to computational concerns, many traditional approaches are limited to near-term, or myopic, optimization, even though radar scenes exhibit strong temporal correlation. More recently, reinforcement learning has been proposed for waveform selection, in which the problem is framed as a Markov decision process (MDP), allowing for long-term planning. However, a major limitation of reinforcement learning is that the memory length of the underlying Markov process is often unknown for realistic target and channel dynamics, and a more general framework is desirable. This work develops a universal sequential waveform selection scheme which asymptotically achieves Bellman optimality in any radar scene which can be modeled as a $U^{\text{th}}$ order Markov process for a finite, but unknown, integer $U$. Our approach is based on well-established tools from the field of universal source coding, where a stationary source is parsed into variable length phrases in order to build a context-tree, which is used as a probabalistic model for the scene's behavior. We show that an algorithm based on a multi-alphabet version of the Context-Tree Weighting (CTW) method can be used to optimally solve a broad class of waveform-agile tracking problems while making minimal assumptions about the environment's behavior.

Jianyuan Yu, Pu, Wang et al.

Complementary to the fine-grained channel state information (CSI) from the physical layer and coarse-grained received signal strength indicator (RSSI) measurements, the mid-grained spatial beam attributes (e.g., beam SNR) that are available at millimeter-wave (mmWave) bands during the mandatory beam training phase can be repurposed for Wi-Fi sensing applications. In this paper, we propose a multi-band Wi-Fi fusion method for Wi-Fi sensing that hierarchically fuses the features from both the fine-grained CSI at sub-6 GHz and the mid-grained beam SNR at 60 GHz in a granularity matching framework. The granularity matching is realized by pairing two feature maps from the CSI and beam SNR at different granularity levels and linearly combining all paired feature maps into a fused feature map with learnable weights. To further address the issue of limited labeled training data, we propose an autoencoder-based multi-band Wi-Fi fusion network that can be pre-trained in an unsupervised fashion. Once the autoencoder-based fusion network is pre-trained, we detach the decoders and append multi-task sensing heads to the fused feature map by fine-tuning the fusion block and re-training the multi-task heads from the scratch. The multi-band Wi-Fi fusion framework is thoroughly validated by in-house experimental Wi-Fi sensing datasets spanning three tasks: 1) pose recognition; 2) occupancy sensing; and 3) indoor localization. Comparison to four baseline methods (i.e., CSI-only, beam SNR-only, input fusion, and feature fusion) demonstrates the granularity matching improves the multi-task sensing performance. Quantitative performance is evaluated as a function of the number of labeled training data, latent space dimension, and fine-tuning learning rates.

C. Tanner Fredieu, Anthony Martone, R. Michael Buehrer

In this paper, we examine the use of a deep multi-layer perceptron architecture to classify received signals as one of seven common waveforms, single carrier (SC), single-carrier frequency division multiple access (SC-FDMA), orthogonal frequency division multiplexing (OFDM), linear frequency modulation (LFM), amplitude modulation (AM), frequency modulation (FM), and phase-coded pulse modulation used in communication and radar networks. Synchronization of the signals is not needed as we assume there is an unknown and uncompensated time and frequency offset. The classifier is open-set meaning it assumes unknown waveforms may appear. Isolation forest (IF) models acting as binary classifiers are used for each known signal class to perform detection of possible unknown signals. This is accomplished using the 32-length feature vector from a dense layer as input to the IF models. The classifier and IF models work together to monitor the spectrum and identify waveforms along with detecting unknown waveforms. Results showed the classifier had 100% classification rate above 0 dB with an accuracy of 83.2% and 94.7% at -10 dB and -5 dB, respectively, with signal impairments present. Results for the IF models showed an overall accuracy of 98% when detecting known and unknown signals with signal impairments present. IF models were able to reject all unknown signals while signals similar to known signals were able to pass through 2% of the time due to the contamination rate used during training. Overall, the entire system can classify correctly in an open-set mode with 98% accuracy at SNR greater than 0 dB.

C. Tanner Fredieu, Justin Bui, Anthony Martone et al.

In this paper, we examine the use of a deep multi-layer perceptron model architecture to classify received signal samples as coming from one of four common waveforms, Single Carrier (SC), Single-Carrier Frequency Division Multiple Access (SC-FDMA), Orthogonal Frequency Division Multiplexing (OFDM), and Linear Frequency Modulation (LFM), used in communication and radar networks. Synchronization of the signals is not needed as we assume there is an unknown and uncompensated time and frequency offset. An autoencoder with a deep CNN architecture is also examined to create a new fifth classification category of an unknown waveform type. This is accomplished by calculating a minimum and maximum threshold values from the root mean square error (RMSE) of the radar and communication waveforms. The classifier and autoencoder work together to monitor a spectrum area to identify the common waveforms inside the area of operation along with detecting unknown waveforms. Results from testing showed the classifier had 100\% classification rate above 0 dB with accuracy of 83.2\% and 94.7\% at -10 dB and -5 dB, respectively, with signal impairments present. Results for the anomaly detector showed 85.3\% accuracy at 0 dB with 100\% at SNR greater than 0 dB with signal impairments present when using a high-value Fast Fourier Transform (FFT) size. Accurate detection rates decline as additional noise is introduced to the signals, with 78.1\% at -5 dB and 56.5\% at -10 dB. However, these low rates seen can be potentially mitigated by using even higher FFT sizes also shown in our results.

Charles E. Thornton, R. Michael Buehrer, Anthony F. Martone

In tracking radar, the sensing environment often varies significantly over a track duration due to the target's trajectory and dynamic interference. Adapting the radar's waveform using partial information about the state of the scene has been shown to provide performance benefits in many practical scenarios. Moreover, radar measurements generally exhibit strong temporal correlation, allowing memory-based learning algorithms to effectively learn waveform selection strategies. This work examines a radar system which builds a compressed model of the radar-environment interface in the form of a context-tree. The radar uses this context tree-based model to select waveforms in a signal-dependent target channel, which may respond adversarially to the radar's strategy. This approach is guaranteed to asymptotically converge to the average-cost optimal policy for any stationary target channel that can be represented as a Markov process of order U < $\infty$, where the constant U is unknown to the radar. The proposed approach is tested in a simulation study, and is shown to provide tracking performance improvements over two state-of-the-art waveform selection schemes.

Charles E. Thornton, R. Michael Buehrer, Anthony F. Martone

A sequential decision process in which an adaptive radar system repeatedly interacts with a finite-state target channel is studied. The radar is capable of passively sensing the spectrum at regular intervals, which provides side information for the waveform selection process. The radar transmitter uses the sequence of spectrum observations as well as feedback from a collocated receiver to select waveforms which accurately estimate target parameters. It is shown that the waveform selection problem can be effectively addressed using a linear contextual bandit formulation in a manner that is both computationally feasible and sample efficient. Stochastic and adversarial linear contextual bandit models are introduced, allowing the radar to achieve effective performance in broad classes of physical environments. Simulations in a radar-communication coexistence scenario, as well as in an adversarial radar-jammer scenario, demonstrate that the proposed formulation provides a substantial improvement in target detection performance when Thompson Sampling and EXP3 algorithms are used to drive the waveform selection process. Further, it is shown that the harmful impacts of pulse-agile behavior on coherently processed radar data can be mitigated by adopting a time-varying constraint on the radar's waveform catalog.

Charles E. Thornton, R. Michael Buehrer, Anthony F. Martone

This paper describes a sequential, or online, learning scheme for adaptive radar transmissions that facilitate spectrum sharing with a non-cooperative cellular network. First, the interference channel between the radar and a spatially distant cellular network is modeled. Then, a linear Contextual Bandit (CB) learning framework is applied to drive the radar's behavior. The fundamental trade-off between exploration and exploitation is balanced by a proposed Thompson Sampling (TS) algorithm, a pseudo-Bayesian approach which selects waveform parameters based on the posterior probability that a specific waveform is optimal, given discounted channel information as context. It is shown that the contextual TS approach converges more rapidly to behavior that minimizes mutual interference and maximizes spectrum utilization than comparable contextual bandit algorithms. Additionally, we show that the TS learning scheme results in a favorable SINR distribution compared to other online learning algorithms. Finally, the proposed TS algorithm is compared to a deep reinforcement learning model. We show that the TS algorithm maintains competitive performance with a more complex Deep Q-Network (DQN).

Charles E. Thornton, Mark A. Kozy, R. Michael Buehrer et al.

In this paper, dynamic non-cooperative coexistence between a cognitive pulsed radar and a nearby communications system is addressed by applying nonlinear value function approximation via deep reinforcement learning (Deep RL) to develop a policy for optimal radar performance. The radar learns to vary the bandwidth and center frequency of its linear frequency modulated (LFM) waveforms to mitigate mutual interference with other systems and improve target detection performance while also maintaining sufficient utilization of the available frequency bands required for a fine range resolution. We demonstrate that our approach, based on the Deep Q-Learning (DQL) algorithm, enhances important radar metrics, including SINR and bandwidth utilization, more effectively than policy iteration or sense-and-avoid (SAA) approaches in a variety of realistic coexistence environments. We also extend the DQL-based approach to incorporate Double Q-learning and a recurrent neural network to form a Double Deep Recurrent Q-Network (DDRQN). We demonstrate the DDRQN results in favorable performance and stability compared to DQL and policy iteration. Finally, we demonstrate the practicality of our proposed approach through a discussion of experiments performed on a software defined radar (SDRadar) prototype system. Our experimental results indicate that the proposed Deep RL approach significantly improves radar detection performance in congested spectral environments when compared to policy iteration and SAA.

Jianyuan Yu, William W. Howard, Daniel Tait et al.

A vector sensor, a type of sensor array with six collocated antennas to measure all electromagnetic field components of incident waves, has been shown to be advantageous in estimating the angle of arrival and polarization of the incident sources. While angle estimation with machine learning for linear arrays has been well studied, there has not been a similar solution for the vector sensor. In this paper, we propose neural networks to determine the number of the sources and estimate the angle of arrival of each source, based on the covariance matrix extracted from received data. Also, we provide a solution for matching output angles to corresponding sources and examine the error distributions with this method. The results show that neural networks can achieve reasonably accurate estimation with up to 5 sources, especially if the field-of-view is limited.

Jianyuan Yu, R. Michael Buehrer

Modern techniques in the Internet of Things or autonomous driving require more accuracy positioning ever. Classic location techniques mainly adapt to outdoor scenarios, while they do not meet the requirement of indoor cases with multiple paths. Meanwhile as a feature robust to noise and time variations, Channel State Information (CSI) has shown its advantages over Received Signal Strength Indicator (RSSI) at more accurate positioning. To this end, this paper proposes the neural network method to estimate the centimeter-level indoor positioning with real CSI data collected from linear antennas. It utilizes an amplitude of channel response or a correlation matrix as the input, which can highly reduce the data size and suppress the noise. Also, it makes use of the consistency in the user motion trajectory via Recurrent Neural Network (RNN) and signal-noise ratio (SNR) information, which can further improve the estimation accuracy, especially in small datasize learning. These contributions all benefit the efficiency of the neural network, based on the results with other classic supervised learning methods.

Jianyuan Yu, Mohammad Alhassoun, R. Michael Buehrer

The recent success in implementing supervised learning to classify modulation types suggests that other problems akin to modulation classification would eventually benefit from that implementation. One of these problems is classifying the interference type added to a signal-of-interest, also known as interference classification. In this paper, we propose an interference classification method using a deep neural network. We generate five distinct types of interfering signals then use both the power-spectral density (PSD) and the cyclic spectrum of the received signal as input features to the network. The computer experiments reveal that using the received signal PSD outperforms using its cyclic spectrum in terms of accuracy. In addition, the same experiments show that the feed-forward networks yield better accuracy than classic methods. The proposed classifier aids the subsequent stage in the receiver chain with choosing the appropriate mitigation algorithm and also can coexist with modulation-classification methods to further improve the classifier accuracy.

Charles E. Thornton, R. Michael Buehrer, Anthony F. Martone et al.

In this work, we first describe a framework for the application of Reinforcement Learning (RL) control to a radar system that operates in a congested spectral setting. We then compare the utility of several RL algorithms through a discussion of experiments performed on Commercial off-the-shelf (COTS) hardware. Each RL technique is evaluated in terms of convergence, radar detection performance achieved in a congested spectral environment, and the ability to share 100MHz spectrum with an uncooperative communications system. We examine policy iteration, which solves an environment posed as a Markov Decision Process (MDP) by directly solving for a stochastic mapping between environmental states and radar waveforms, as well as Deep RL techniques, which utilize a form of Q-Learning to approximate a parameterized function that is used by the radar to select optimal actions. We show that RL techniques are beneficial over a Sense-and-Avoid (SAA) scheme and discuss the conditions under which each approach is most effective.

Bryse Flowers, R. Michael Buehrer, William C. Headley

Recent advancements in radio frequency machine learning (RFML) have demonstrated the use of raw in-phase and quadrature (IQ) samples for multiple spectrum sensing tasks. Yet, deep learning techniques have been shown, in other applications, to be vulnerable to adversarial machine learning (ML) techniques, which seek to craft small perturbations that are added to the input to cause a misclassification. The current work differentiates the threats that adversarial ML poses to RFML systems based on where the attack is executed from: direct access to classifier input, synchronously transmitted over the air (OTA), or asynchronously transmitted from a separate device. Additionally, the current work develops a methodology for evaluating adversarial success in the context of wireless communications, where the primary metric of interest is bit error rate and not human perception, as is the case in image recognition. The methodology is demonstrated using the well known Fast Gradient Sign Method to evaluate the vulnerabilities of raw IQ based Automatic Modulation Classification and concludes RFML is vulnerable to adversarial examples, even in OTA attacks. However, RFML domain specific receiver effects, which would be encountered in an OTA attack, can present significant impairments to adversarial evasion.

Daniel J. Jakubisin, R. Michael Buehrer, Claudio R. C. M. da Silva

Receiver algorithms which combine belief propagation (BP) with the mean field (MF) approximation are well-suited for inference of both continuous and discrete random variables. In wireless scenarios involving detection of multiple signals, the standard construction of the combined BP-MF framework includes the equalization or multi-user detection functions within the MF subgraph. In this paper, we show that the MF approximation is not particularly effective for multi-signal detection. We develop a new factor graph construction for application of the BP-MF framework to problems involving the detection of multiple signals. We then develop a low-complexity variant to the proposed construction in which Gaussian BP is applied to the equalization factors. In this case, the factor graph of the joint probability distribution is divided into three subgraphs: (i) a MF subgraph comprised of the observation factors and channel estimation, (ii) a Gaussian BP subgraph which is applied to multi-signal detection, and (iii) a discrete BP subgraph which is applied to demodulation and decoding. Expectation propagation is used to approximate discrete distributions with a Gaussian distribution and links the discrete BP and Gaussian BP subgraphs. The result is a probabilistic receiver architecture with strong theoretical justification which can be applied to multi-signal detection.

SaiDhiraj Amuru, Cem Tekin, Mihaela van der Schaar et al.

Can an intelligent jammer learn and adapt to unknown environments in an electronic warfare-type scenario? In this paper, we answer this question in the positive, by developing a cognitive jammer that adaptively and optimally disrupts the communication between a victim transmitter-receiver pair. We formalize the problem using a novel multi-armed bandit framework where the jammer can choose various physical layer parameters such as the signaling scheme, power level and the on-off/pulsing duration in an attempt to obtain power efficient jamming strategies. We first present novel online learning algorithms to maximize the jamming efficacy against static transmitter-receiver pairs and prove that our learning algorithm converges to the optimal (in terms of the error rate inflicted at the victim and the energy used) jamming strategy. Even more importantly, we prove that the rate of convergence to the optimal jamming strategy is sub-linear, i.e. the learning is fast in comparison to existing reinforcement learning algorithms, which is particularly important in dynamically changing wireless environments. Also, we characterize the performance of the proposed bandit-based learning algorithm against multiple static and adaptive transmitter-receiver pairs.