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.

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.

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

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.

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.

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.