Anthony F. Martone

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.

Samuel Haug, Austin Egbert, Robert J. Marks et al.

Radar must adapt to changing environments, and we propose changepoint detection as a method to do so. In the world of increasingly congested radio frequencies, radars must adapt to avoid interference. Many radar systems employ the prediction action cycle to proactively determine transmission mode while spectrum sharing. This method constructs and implements a model of the environment to predict unused frequencies, and then transmits in this predicted availability. For these selection strategies, performance is directly reliant on the quality of the underlying environmental models. In order to keep up with a changing environment, these models can employ changepoint detection. Changepoint detection is the identification of sudden changes, or changepoints, in the distribution from which data is drawn. This information allows the models to discard "garbage" data from a previous distribution, which has no relation to the current state of the environment. In this work, bayesian online changepoint detection (BOCD) is applied to the sense and predict algorithm to increase the accuracy of its models and improve its performance. In the context of spectrum sharing, these changepoints represent interferers leaving and entering the spectral environment. The addition of changepoint detection allows for dynamic and robust spectrum sharing even as interference patterns change dramatically. BOCD is especially advantageous because it enables online changepoint detection, allowing models to be updated continuously as data are collected. This strategy can also be applied to many other predictive algorithms that create models in a changing environment.

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.

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).