In this paper, we propose an explainable neural network for decomposing channel kernels into Eigenwaves and implement practical Multi-dimensional Eigenwave Multiplexing (MEM) over doubly selective channels. The quality of Eigenwave decomposition is evaluated using three key metrics: 1) eigenvalue, 2) orthogonality, and 3) duality. The eigenvalue determines the subchannel gains in the eigen domain, while orthogonality and duality impact the interference from other symbols and the distortion of the target symbol, respectively. We prove that maximizing the sum of eigenvalues is equivalent to minimizing the MSE loss function and demonstrate that the duality and orthogonality constraints not only minimize interference for multiplexing but also guide the convergence for NN. Furthermore, we show that these duality and orthogonality constraints are equivalent, allowing them to be combined for model simplification. To further enhance the adaptability of the proposed method, we introduce a second NN architecture that incorporates the Augmented Lagrangian Method (ALM). This approach eliminates the need for parameter tuning under different MIMO scales. We evaluate the proposed methods under two scenarios: 1) 2D doubly selective channels, and 2) 4D doubly selective MIMO channels with both perfect imperfect Channel State Information (CSI) and imperfect CSI.

Learning the principal eigenfunctions of a kernel is at the core of many machine-learning problems. Common methods usually deal with symmetric kernels based on Mercer’s Theorem. However, in the communication systems, the channel kernel is usually asymmetric due to the inconsistencies between the uplink and the downlink propagation environment. In this paper, we propose an explainable Neural Network for extracting eigenfunctions from generic multi-dimensional asymmetric channel kernels based on a recent method called High Order Generalized Mercer’s Theorem (HOGMT), by decomposing it into jointly orthogonal eigenfunctions. The proposed neural network based approach is efficient and can be easily implemented compared to the conventional SVD based solutions used for eigen decomposition. We also discuss the effect of different hyperparameters on the training time, constraint satisfaction, and overall performance. Finally, we show that multiplexing using these eigenfunctions mitigates interference across all the available Degrees of Freedom (DoF), both mathematically as well as via neural network based system-level simulations.

Eigenfunctions are widely used to characterize ker-nels in many data-driven analyses. In machine learning, eigen- function decomposition is primarily based on Mercer's theorem, which requires the kernel to be symmetric. This is difficult to satisfy in communication systems as the channel kernel is usually asymmetric due to the different downlink and uplink propagation environments. High Order Generalized Mercer's Theorem (HOGMT) provides a principled way to decompose any multi-dimensional asymmetric kernel into eigenfunctions. To manage the complexity of the eigen-decomposition, we propose an equivalent Neural Network (NN) for decomposing a gen-eral channel kernel. This is further improved by applying the Augmented Lagrangian Method (ALM) to reduce the training time and parameter tuning, which avoids additional tuning rounds when the size of the kernel or the number of eigen- components change depending on the wireless environment. We validate the adaptability of the proposed NN and its accu-racy using simulations in PyTorch. The code is available at https://github.com/ZBZou/HOGMT-ALM/tree/main.

OFDM modulation and OTFS modulation have demonstrated their efficacy in mitigating interference in the time and frequency domains, respectively, caused by path delay and Doppler shifts. However, no established modulation technique exists to address inter-Doppler interference (IDI) resulting from time-varying Doppler shifts. Additionally, both OFDM and OTFS require supplementary precoding techniques to mitigate inter-user interference (IUI) in MU-MIMO channels. To address these limitations, we present a generalized modulation method for any multidimensional channel, based on Higher Order Mercer's Theorem (HOGMT) [1], [2] which has been proposed recently to decompose multi-user non-stationary channels into independent fading subchannels (Eigenwaves). The proposed method, called multidimensional Eigenwaves Multiplexing (MEM) modulation, uses jointly orthogonal eigenwaves decomposed from the multidimensional channel as subcarriers, thereby avoiding interference from other symbols transmitted over multidimensional channels. We show that MEM modulation achieves diversity gain in eigenspace, which in turn achieves the total diversity gain across each degree of freedom(e.g., space (users/antennas), time-frequency and delay-Doppler). The accuracy and generality of MEM modulation are validated through simulation studies on three non-stationary channels.

Dirty Paper Coding (DPC) is considered as the optimal precoding which achieves capacity for the Gaussian Multiple-Input Multiple-Output (MIMO) broadcast channel (BC). However, to find the optimal precoding order, it needs to repeat$N!$times for$N$users as there are$N!$possible precoding orders. This extremely high complexity limits its practical use in modern wireless networks. In this paper, we show the equivalence of DPC and the recently proposed Higher Order Mercer's Theorem (HOGMT) precoding [1], [2] in 2-D (spatial) case, which provides an alternate implementation for DPC. Furthermore, we show that the proposed implementation method is linear over the permutation operator when permuting over multi-user channels. Therefore, we present a low complexity algorithm that optimizes the precoding order for DPC with beamforming, eliminating repeated computation of DPC for each precoding order. Simulations show that our method can achieve the same result as conventional DPC with$\approx 20\text{dB}$lower complexity for$N=5$users.

Radio Frequency Interference (RFI) from cellular and other communication networks is commonly mitigated at the radio telescope without any active collaboration with the interfering sources. The expanding Universe and simultaneous proliferation of Earth-based and LEO communication infrastructure is causing unprecedented RFI that require collaborative strategies to maintain the scientific and societal goals of each. In this work, we develop deep learning based models that enable collaboration with minimal overhead while also providing accurate RFI characterization and simplified cancellation strategies. This multistage system design is adaptable to changing statistics of the RFI signals generated from cellular networks and allows single step RFI cancellation by signal processing chain modeling (e.g. filtering and digitization loss) at the Telescope. Through our analysis and simulation using real astronomical signals, we are able to remove RFI generated from cellular networks with comparable accuracy to the state of the art with only 25% of the communication overhead and overall reduced computation complexity from O(n3) to O(n2).

Direction of arrival (DoA) estimation has an important role in various applications and is widely used in modern communication, where signal power is higher than noise power for it to be decoded. Existing methods do not perform as accurately in low signal to noise ratio (SNR) as they do in higher SNR. However, passive sensing like radio astronomy or remote sensing operates at extremely low SNR, where the weakest radio frequency interference (RFI) from communication system impairs the scientific observations. Hence, it is essential to estimate the DoA of RFI at low SNR so that it can be removed at the telescopes or radiometers. In this paper, we propose a three stage algorithm that methodically exploits digital beamforming, creates virtual subarrays, inspects multiple options and introduces clustering to estimate the DoA in low SNRs. The proposed algorithm is simulated with sinusoidal as well as Automatic Dependent Surveillance-Broadcast (ADS-B) signals in Additive White Gaussian Noise (AWGN) and multipath fading channels. Experimental results show the proposed method outperforms well-known MUSIC (MUltiple SIgnal Classification) algorithm in low SNR.

The high mobility, density and multi-path evident in modern wireless systems makes the channel highly non-stationary. This causes temporal variation in the channel distribution that leads to the existence of time-varying joint interference across multiple degrees of freedom (DoF, e.g., users, antennas, frequency and symbols), which renders conventional precoding sub-optimal in practice. In this work, we derive a High-Order Generalization of Mercer’s Theorem (HOGMT), which decomposes the multi-user non-stationary channel into two (dual) sets of jointly orthogonal subchannels (eigenfunctions), that result in the other set when one set is transmitted through the channel. This duality and joint orthogonality of eigenfuntions ensure transmission over independently flat-fading subchannels. Consequently, transmitting these eigenfunctions with optimally derived coefficients eventually mitigates any interference across its degrees of freedoms and forms the foundation of the proposed joint spatio-temporal precoding. The transferred dual eigenfuntions and coefficients directly reconstruct the data symbols at the receiver upon demodulation, thereby significantly reducing its computational burden, by alleviating the need for any complementary post-coding. Additionally, the eigenfunctions decomposed from the time-frequency delay-Doppler channel kernel are paramount to extracting the second-order channel statistics, and therefore completely characterize the underlying channel. We evaluate this using a realistic non-stationary channel framework built in Matlab and show that our precoding achieves${\geqslant }4$orders of reduction in BER at SNR${\geqslant }15$dB in OFDM systems for higher-order modulations and less complexity compared to the state-of-the-art precoding.

Recently, there has been great interest in facilitating coexistence of active and passive users of the electromagnetic (EM) spectrum, with the primary objective of higher spectral utilization. The major challenge for passive users, such as Radio Astronomy Services (RAS), is the need for extremely quiet skies to make astronomical observations with maximum sensitivity of the radio telescope. This is increasingly difficult to guarantee because of densification of allocated spectrum, exponential growth of ubiquitous wireless communication and out-of-band astronomical observations required to observe fast radio bursts. This requires either bidirectional collaboration between active and passive users or innovative signal processing at the telescope site to cancel any incident Radio Frequency Interference (RFI). In this work, we show the feasibility of such a paradigm, where RFI from airborne sources, e.g., aircraft, LEO satellites, etc., is cancelled at the receiver of a Radio Telescope, by shaping the EM wavefront by an array of Reconfigurable Intelligent Surfaces (RIS). In contrast to conventional beam-nulling applications for RIS, this method requires precise calculation of the phase and the amplitude of the reflected signal by the RIS in order to guarantee complete cancellation of the incident RFI. We simulate this approach in a practical setting to study its error performance and boundary conditions of the system parameters, that will lead to a demonstrable prototype in near future. Our results indicate that an RIS array with 364 elements can fully cancel RFI for ADS-B systems at an elevation of$60^{\circ}$and an altitude of 10000 m.

Modern wireless channels are increasingly dense and mobile making the channel highly non-stationary. The time-varying distribution and the existence of joint interference across multiple degrees of freedom (e.g., users, antennas, frequency and symbols) in such channels render conventional precoding sub-optimal in practice, and have led to historically poor characterization of their statistics. The core of our work is the derivation of a high-order generalization of Mercer’s Theorem to decompose the non-stationary channel into constituent fading sub-channels (2-D eigenfunctions) that are jointly orthogonal across its degrees of freedom. Consequently, transmitting these eigenfunctions with optimally derived coefficients eventually mitigates any interference across these dimensions and forms the foundation of the proposed joint spatio-temporal precoding. The precoded symbols directly reconstruct the data symbols at the receiver upon demodulation, thereby significantly reducing its computational burden, by alleviating the need for any complementary decoding. These eigenfunctions are paramount to extracting the second-order channel statistics, and therefore completely characterize the underlying channel. Theory and simulations show that such precoding leads to >104× BER improvement (at 20dB) over existing methods for non-stationary channels.

We introduceRFEye, a generalized technique to locate signals independent of the waveform, using a single Unmanned Aerial Vehicle (UAV) equipped with only one omnidirectional antenna. This is achieved by acquiring signals from uncoordinated positions within a sphere of 1-meter radius at two nearby locations and formulating an asynchronous, distributed receiver beamforming at the UAV to compute the Direction of Arrival (DoA) from the unknown transmitter. The proposed method includes four steps: 1) Blind detection and extraction of unique signature in the signal to be localized, 2) Asynchronous signal acquisition and conditioning, 3) DoA calculation by creating a virtual distributed antenna array at UAV and 4) Obtaining position fix of emitter using DoA from two locations. These steps are analyzed for various sources of error, computational complexity and compared with widely used signal subspace-based DoA estimation algorithms.RFEyeis implemented using an Intel-Aero UAV, equipped with a USRP B205 software-defined radio to acquire signals from a ground emitter. Practical outdoor experiments show thatRFEyeachieves a median accuracy of 1.03m in 2D and 2.5m in 3D for Wi-Fi, and 1.15m in 2D and 2.7m in 3D for LoRa (Long Range) waveforms, and is robust to external factors like wind and UAV position errors.

Neural Network (NN) based receivers have seen limited adoption in practical systems due to a lack of explainability and performance guarantees, despite their efficacy as a data-driven tool for physical layer signal processing. In order to bridge this gap in explainability, we present an equivalent NN-based receiver that performs the same optimizations used by classical receivers for symbol detection. Achieving equivalence is crucial to explaining how a NN-based receiver classifies symbols in high-dimensional channels and determining its structure that is robust to the underlying channel with minimum training. We realize this by deriving the risk function that guarantees equivalence, which also provides a measure of the disparity between NN-based and classical receivers. Consequently, this information allows us to derive mathematically tight data-dependent bounds on the bit error rate of NN-based receivers, and empirically determine its structure that achieves minimum error rate. Extensive simulation results show the efficacy of the derived bounds and structure of NN-based receivers for single and multi-antenna systems over a variety of channels.

Modern wireless systems are increasingly dense and dynamic that makes the channel highly non-stationary, rendering conventional receivers sub-optimal in practice. Predicting the channel characteristics for non-stationary channels has the distinct advantage of pre-conditioning the waveform at the transmitter to match the expected fading profile. The difficulty lies in extracting an accurate model for the channel, especially if the underlying variables are uncorrelated, unobserved and immeasurable. Our work implements this prescience by assimilating the Channel State Information (CSI), obtained as feedback from the receiver, over time and space to adjust the modulation vectors such that the channel impairments are significantly diminished at the receiver, improving the Bit Error Rate (BER). We design a channel recommender, in which an adaptive smoother is used to filter the noise in CSI, while a tensor factorization & completion approach is used to track the ephemeral changes in non-stationary channel statistics by observing the changes in certain measurable parameters. V2X communication is used as an example of non-stationary channels to shows the efficacy of this approach. Overall, the system is shown to operate with a prediction accuracy of 10-3MSE even in dense scattering environments over space and time, improving the BER at the receiver by 90% for higher-order modulations.

There is a growing interest towards enabling practical, dynamic and agile wireless applications by systems of independent or cooperative mobile agents such as Unmanned Aerial Vehicles (UAVs). Such mobile UAVs are often constrained on resources like storage, power and radio capabilities and require accurate position information to facilitate many of these wireless applications. In this paper, we introduce HiPER-V, which is a generalized UAV prototype platform to enable a broad range of applications in wireless communications using a single UAV or can be extended to a swarm of UAVs. We implement HiPER-V by using an UAV, equipped with resource constrained radio devices, and high precision position information available via RTK-GPS modules, achieving a median position accuracy of 3.8 cm. The details of implementation of HiPER-V and its applicability to a wide variety of applications in wireless communications are presented in this paper. With minimal payload and simple software modification, our solution can be ported to any UAV platform and extended to multiple UAV testbeds that enable an array of research in wireless applications using UAVs.

Recommending channel characteristics for V2X communication has the distinct advantage of pre-conditioning the waveform at the transmitter to match the expected fading profile. The difficulty lies in extracting an accurate model for the channel, especially if the underlying variables are uncorrelated, unobserved and immeasurable. Our work implements this prescience by assimilating the Channel State Information (CSI), obtained as a feedback from vehicles, over time and space to adjust the modulation vectors such that the channel impairments are significantly diminished at the receiver, improving the Bit Error Rate (BER) by 96% for higher order modulations. To account for the multivariate, non-stationary V2X channel, a tensor decomposition and completion approach is used to mitigate the effects of sparsity and noise in the CSI measurements. Overall, the system is shown to operate with a prediction accuracy of 10-3MSE even in dense scattering environments over space and time.

We model and analyze a User-Equipment (UE) based wireless network selection method where individuals act on their stochastic knowledge of the expected behavior off their available networks. In particular, we focus on networks with millimeter-wave (mmWave) radio. Modeling mmWave radio access technologies (RATs) as a stochastic 3-state process based on their physical layer characteristics in Line-of-Sight (LOS), Non-Line-of-Sight (NLOS), and Outage states, we make the realistic assumption that users have no knowledge of the statistics of the RATs and must learn these while maximizing the throughput obtained. We develop an online learning-based approach to access network selection: a user-centric Multi-Armed Bandit Problem that incorporates the cost of switching access networks. We develop an online learning policy that groups network access to minimize costs for RAT selection, analyze the regret (loss due to uncertainty) of our algorithm. We also show that our algorithm obtains optimal regret and in numerical examples achieves 24% increase in total throughput compared to existing techniques for high throughput mmWave RATs that vary over a fast timescale.

As sharing agreements are being ratified by the Federal Communications Commission (FCC) for various spectrum bands for commercial broadband use, it also opens up an equally challenging problem of enforcing these policies. The efficacy of an enforcement system greatly depends on the accuracy of evidential information and the speed of adjudication. The inherent unguided and unbounded nature of radio wave propagation allows spectrum infractions to cause widespread damage and makes it hard to locate at the same time. On the other hand, it also lends itself to distributed methods for efficient enforcement of spectrum etiquette. We leverage a crowd of mobile users to implement a paradigm of “eye-witness” for detecting violations of spectrum policies. We design and analyze the crowdsourced enforcement architecture and show three main results: 1) it detects an infraction with a consistent high degree of accuracy (> 90%); 2) it is able to accurately locate the source of infraction and 3) it lowers the frequency of policy infractions over time.

The recently proposed 3-Tier access model for Whitespace by the Federal Communications Commission (FCC) mandates certain classes of devices to share frequency bands in space and time. These devices are envisioned to be a heterogeneous mixture of licensed (Tier-1 and Tier-2) and unlicensed, opportunistic devices (Tier-3). The hierarchy in accessing the channel calls for superior adaptation of Tier-3 devices with varying spectral opportunity. While policies are being ratified for efficient sharing, it also calls for redesigning many common applications to adapt to this novel paradigm. In this paper, we focus on the ever-increasing demand for video streaming and present a methodology suitable for Tier-3 devices in the shared access model. Our analysis begins with a stress test of commonly adopted video streaming methods under the new sharing model. This is followed by the design of a robust MDP-based solution that proactively adapts to fast-varying channel conditions, providing better user quality of experience when compared to existing solutions, such as MPEG-DASH. We evaluate our solution on an experimental testbed and find that our MDP-based algorithm outperforms DASH, and partial information of Tier-2 dynamics improves video quality.

Recent work has examined techniques to estimate the “best” modulation rate for data networks such as 802.11a/g. While accurate rate estimation yields better rate-selection decisions and increased throughput, those methods must still choose between a handful of modulation rates. Each modulation rate is effective in a range of actual signal-to-noise ratios (SNRs) but the limited number of practical rates means that transmitters are often forced to “step down” to a lower data rate despite having a higher SNR than the minimum required for that lower rate. In this paper we describe, evaluate and implement a practical multiuser communication scheme that exploits these discrete “steps” in modulation rates to transmit two packets in the time normally needed to transmit a single packet, increasing aggregate throughput precisely when it is most needed—when the network is busy and suffers from rate unfairness. Because the method transmits a group of packets simultaneously, we call this scheme Group Rate Transmission with Intertwined Symbols, or GRaTIS. In addition to up to 120% improvement in network throughput achieved by GRaTIS, the technique is backward compatible with 802.11 and doesn’t require complex DSP algorithms as required by competing methods.

As we move forward towards the next generation of wireless protocols, the push for a better radio physical layer is ever increasing. Conventional radio architectures are limited to narrow operating regions and fails to adapt with changing technology. This is further strengthened with the advent of cognitive radio, which needs a more versatile and flexible framework that is programmable within the timing constraints of a protocol. In this paper we present an architecture for Software Defined Cognitive Radio that caters to the specific baseband processing requirements in a changing environment. We aim to provide more flexibility by de-constructing the radio pipeline into a framework of user controlled kernels that can be reconfigured at run-time. This architecture provides the bare-bones of a OFDM based radio physical layer that can adapt to perform a varied number of tasks in different radio networks. We also present a novel message based real-time reconfiguration method to transmit and receive a wide range of waveforms used in concurrent wireless protocols.

Vehicular safety systems for collisions or sensing rapid changes in traffic typically use two methods to communicate and disseminate traffic hazards. Many current systems use RADAR systems that transmit a radio wave and sense the reflective waves for angle-of-arrival or time-of-arrival information. Several proposed systems use vehicular networks to disseminate information about braking, emergencies or road conditions; when coupled with accelerometer or GPS information, these radio systems may also offer information on speed, traffic density or distance. In-vehicle RADAR systems are relatively expensive; vehicular radio based systems are less expensive. In this paper, we present a cooperative technology that combines these two techniques, seeking to adopt characteristics of both systems by employing a software defined radio for “cooperative RADAR” and vehicular networking. Our method uses multicarrier wireless communication to detect and disseminate. Using precise timing and synchronization, we can detect the distance of each of the vehicles, their current velocity and current acceleration or deceleration conditions. Using simultaneous, multi-party acknowledgments, we can rapidly disseminate or determine information about a number of vehicles in an efficient manner.

Network protocols have traditionally been designed using a layered method in part because it is easier to implement some portions of network protocols in software and other portions must be implemented in hardware for performance reasons. These different implementation techniques enforce layer boundaries. In this paper, we show that with the advent of software defined radios, it becomes possible to blur those layer boundaries and produce higher performance network protocols as a result. In this paper we exploit a programmable physical layer and simultaneous transmission to have clients signal whether they have packets to send. By detecting the high energy at the simultaneous transmission, the AP gets the following information: a) which stations have packets to send and b) whether the traffic load is high, medium or low. Again, using the programmable physical layer, the AP schedules clients efficiently while wasting little of the spectrum on signaling overhead. The proposed protocol is a) fast, since no packet transmission is required for polling responses and all clients respond concurrently; b) reliable, as the poll response is contention free and c) scalable. We demonstrate the feasibility of implementing such a system using a FPGA based prototype software defined radio platform. We then show how the MAC protocol can scale using the QualNet network simulator and compare the performance to a contention based protocol.

Network protocol designers, both at the physical and network level, have long considered interference and simultaneous transmission in wireless protocols as a problem to be avoided. This, coupled with a tendency to emulate wired network protocols in the wireless domain, has led to artificial limitations in wireless networks.