Charles E. Thornton

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.

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.

Charles E. Thornton, Jamie Sloop, Samuel Brown et al.

We investigate the end-to-end altitude estimation performance of a convolutional autoencoder-based interference mitigation approach for frequency-modulated continuous-wave (FMCW) radar altimeters. Specifically, we show that a Temporal Convolutional Network (TCN) autoencoder effectively exploits temporal correlations in the received signal, providing superior interference suppression compared to a Least Mean Squares (LMS) adaptive filter. Unlike existing approaches, the present method operates directly on the received FMCW signal. Additionally, we identify key challenges in applying deep learning to wideband FMCW interference mitigation and outline directions for future research to enhance real-time feasibility and generalization to arbitrary interference conditions.

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.

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.

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.