arXiv subjects

André Bourdoux

Publications and source records attributed to André Bourdoux.

At least 19 recordsLinked to original sources

arXiv2026

Analysis and Approximation of Spatially Wideband Array Factor of Thinned Antenna Arrays

This work investigates the spatially wideband (SWB) array factor (AF) of linear thinned antenna arrays. The SWB AF is formulated as a matched filter and expressed as a spatially variant convolution of a spatially narrowband (SNB) AF and a SWB kernel. Originally derived for uniform arrays, the SWB AF approximation is revisited and extended to thinned arrays. The approximation is shown to remain accurate across a wide range of parameters. Representing the SWB AF as a convolution offers an intuitive interpretation of how the bandwidth-aperture product modifies the SNB AF. Specifically, the SWB kernel acts as an averaging window for the SNB AF, suppressing the sidelobe levels (SL) of the SNB AF. In thinned arrays, the sidelobes away from the mainlobe can be treated as random, noise-like, making averaging and suppression particularly effective. Next, the analytical formulas for the expected SL and peak-to-sidelobe level (PSL) in SNB thinned arrays are first introduced and subsequently extended to the SWB regime. Finally, simple closed-form expressions for the expected SL and PSL levels of the uniformly thinned arrays with a uniform spectrum are provided. The expected SWB SL and PSL are formulated as functions of the bandwidth-aperture product and are shown to steadily decrease with distance from the mainlobe.

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arXiv2026

3D Radar Imaging from the UAV Nadir

Radars improve the sensing robustness of UAVs by operating under poor lighting and weather conditions and seeing through occlusions such as vegetation. However, they suffer from poor angular resolution, which can be addressed using synthetic aperture radar (SAR) algorithms. State-of-the-art UAV SAR methods operate at a depression angle and are not suitable for sensor fusion applications where the data are collected from areas directly below the UAV (i.e., the UAV nadir). In this paper, we present an interferometric SAR (InSAR) framework for reconstructing 3D images from the UAV nadir using a low-cost multi-input-multi-output (MIMO) mm-wave radar. Additionally, an effective method based on the phase gradient autofocus (PGA) is presented for compensating the phase error across the virtual receive antennas. We demonstrate the effectiveness of our 3D imaging algorithm in both simulation and experimental scenarios.

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arXiv2026

Analysis and Approximation of a Spatially Wideband Antenna Array Factor

This work investigates the spatially wideband (SWB) antenna array factor (AF) of uniform linear arrays. First, the SWB AF approximation is derived for narrowband (NB) signals and a large aperture with element spacing satisfying the Nyquist criterion. The derivation accounts for different spatial and spectral windows. Next, an approximation of the SWB AF for a wideband (WB) signal is developed under uniform spatial and spectral weighting. The analysis shows that for fully populated arrays, increasing the bandwidth effectively suppresses the AF sidelobes. Finally, a universal SWB AF approximation is introduced, which is based on recognizing the SWB AF as a spatially variant convolution. In this formulation, the SWB AF is expressed as a convolution of the spatially narrowband (SNB) AF and the SWB kernel, providing insight into how the bandwidth and the spectral weighting affect the resulting SWB AF. The proposed approximation is shown to be accurate for a wide range of bandwidths and element spacings, including sparse arrays. In particular, for sparse arrays, the bandwidth enables suppression of grating-lobe amplitudes by spreading their energy over a wider angular range. An approximation of the grating lobe envelope as a function of the bandwidth-aperture product is provided.

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arXiv2026

Aliased Time-Modulated Array OFDM Transmit System

The time-modulated array is a simple array architecture in which each antenna is connected to an RF switch that serves as a modulator. The phase shift is achieved by digitally controlling the relative delay between the periodic modulating sequences of the antennas. Two factors limit the practical use of this architecture for communication and sensing. First, the switching frequency is high, as it must be a multiple of the sampling frequency. Second, the discrete modulating sequence introduces undesired harmonic replicas of the signal, which are out-of-band interference. This paper proposes the OFDM modulation with an appropriate precoder to facilitate the aliasing of the harmonic components to simultaneously reduce sideband radiation and switching frequency. The transmit signal has a repeated block structure in the frequency domain to facilitate coherent combining of the aliased signal blocks. As a result, a factor $A$ reduction in switching frequency is achieved at the cost of a factor $A$ reduction in communication capacity. Doubling $A$ reduces sideband radiation by around 2.9 dB. The feasibility of the proposed method is experimentally validated for wideband signals. Full-wave simulations are performed to validate the beamforming performance based on the experimental results.

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arXiv2026

A Low-Complexity PFA-Based Autofocus Algorithm for Automotive SAR

Radars provide robust perception of vehicle surroundings by effectively functioning in poor light and adverse weather conditions. Synthetic aperture radar (SAR) algorithms are employed to address the limited angular resolution of radars by enlarging antenna aperture size synthetically as the radar moves. An autofocus algorithm is essential to improve the SAR image quality by compensating for errors mainly caused by inaccurate radar localization. Existing autofocus algorithms are mostly tailored for the frequency domain SAR techniques which are prevalent in aviation and spaceborne applications thanks to their lower complexity in large data processing. However, in the automotive context, the backprojection algorithm (BPA) is often preferred since it provides less distorted images at the cost of more complexity. Addressing the gap in efficient autofocus solutions for time-domain algorithms, this paper introduces a dual-layered autofocus strategy that integrates the Polar Format Algorithm (PFA) with BPA. The first layer employs a novel Localization Error Compensation Autofocus (LECA) processing pipeline to estimate and correct the localization errors within the PFA domain, leveraging its computational efficiency. The second layer seamlessly transfers these corrections to BPA, enabling high-quality SAR imaging while maintaining low complexity. Additionally, the strategy extends Phase Gradient Autofocus (PGA) techniques to enhance the efficiency of localization error compensation for BPA. Validated through real-world automotive experiments, the proposed pipeline delivers state-of-the-art image focus and resolution, setting a new benchmark for computationally efficient SAR imaging.

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arXiv2026

Analysis of the Range Ambiguity Function of Narrowband Near-field MIMO Sensing

This paper compares the sensing performance of a narrowband near-field system across several practical antenna array geometries and SIMO/MISO and MIMO configurations. For identical transmit and receive apertures, MIMO processing is equivalent to squaring the near-field array factor, resulting in improved beamdepth and sidelobe level. Analytical derivations, supported by simulations, show that the MIMO processing improves the maximum near-field sensing range and resolution by approximately a factor of 1.4 compared to a single-aperture system. Using a quadratic approximation of the mainlobe of the array factor, an analytical improvement factor of $\sqrt{2}$ is derived, validating the numerical results. Finally, MIMO is shown to improve the poor sidelobe performance observed in the near-field by a factor of two, due to squaring of the array factor.

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arXiv2026

Approximation of the Range Ambiguity Function in Near-field Sensing Systems

This paper investigates the range ambiguity function of near-field systems where bandwidth and near-field beamfocusing jointly determine the resolution. First, the general matched filter ambiguity function is derived and the near-field array factors of different antenna array geometries are introduced. Next, the near-field ambiguity function is approximated as a product of the range-dependent near-field array factor and the ambiguity function due to the utilized waveform and bandwidth. An approximation criterion based on the aperture-bandwidth product is formulated, and its accuracy is examined. Finally, the improvements to the ambiguity function offered by the near-field beamfocusing, as compared to the far-field case, are presented. The performance gains are evaluated in terms of resolution improvement offered by beamfocusing, peak-to-sidelobe and integrated-sidelobe level improvement for a few popular array geometries. The gains offered by the near-field regime are shown to be range-dependent and substantial only in close proximity to the array.

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arXiv2026

Sizing Antenna Arrays for Near-field Communication and Sensing

This paper presents key performance metrics for near-field communication and sensing systems and their scaling behavior as a function of the antenna array aperture. Analytical expressions are derived for several standard array geometries to ease the design of the large antenna arrays under given system requirements. First, the near-field beam focusing is analyzed and the minimum beamdepth is observed to rapidly saturate to a low asymptotic limit as the array aperture increases. In contrast, the near-field region span is shown to scale quadratically with the array aperture. Based on these two metrics, the maximum number of resolvable beamspots at 3 dB separation is derived analytically, exhibiting a linear dependence on the array aperture. Moreover, when considering a region where the beamfocusing resolution does not exceed a specified threshold, the extent of the region is also shown to scale linearly with the array size. Finally, the number of significant singular values of a channel observed at the array's broadside is estimated, showing a power-law dependence on the aperture. The resulting expressions provide practical design guidelines for evaluating aperture requirements in near-field communication and sensing applications.

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arXiv2025

Frequency Diverse Array OFDM Transmit System with Partial Overlap in Frequency

A frequency-diverse array (FDA) is an alternative array architecture in which each antenna is preceded by a mixer instead of a phase shifter. The mixers introduce a frequency offset between signals transmitted by each antenna, resulting in a time-varying beam pattern. However, time-dependent beamforming is not desirable for communication or sensing. In this paper, the FDA is combined with orthogonal frequency-division multiplexing (OFDM) modulation. The proposed beamforming method partitions the OFDM symbol transmitted by all antennas into subcarrier blocks, which carry the same data but are precoded differently. The frequency offset between the antennas is equal to the subcarrier block width. Consequently, each antenna transmits a differently precoded subcarrier block at the center frequency, resulting in overlap and coherent summation of the blocks. Proposed architecture enables fully digital beamforming over a single block while requiring only a single digital-to-analog converter. The system's performance and tradeoffs are investigated in the context of joint communication and sensing.

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arXiv2025

Frequency Diverse Array OFDM System for Joint Communication and Sensing

The frequency-diverse array (FDA) offers a time-varying beamforming capability without the use of phase shifters. The autoscanning property is achieved by applying a frequency offset between the antennas. This paper analyzes the performance of an FDA joint communication and sensing system with the orthogonal frequency-division multiplexing (OFDM) modulation. The performance of the system is evaluated against the scanning frequency, number of antennas and number of subcarriers. The utilized metrics; integrated sidelobe level (ISL) and error vector magnitude (EVM) allow for straightforward comparison with a standard single-input single-output (SISO) OFDM system.

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arXiv2025

Beamforming with Oversampled Time-Modulated Arrays

The time-modulated array (TMA) is a simple array architecture in which each antenna is connected via a multi-throw switch. The switch acts as a modulator switching state faster than the symbol rate. The phase shifting and beamforming is achieved by a cyclic shift of the periodical modulating signal across antennas. In this paper, the TMA mode of operation is proposed to improve the resolution of a conventional phase shifter. The TMAs are analyzed under constrained switching frequency being a small multiple of the symbol rate. The presented generic signal model gives insight into the magnitude, phase and spacing of the harmonic components generated by the quantized modulating sequence. It is shown that the effective phase-shifting resolution can be improved multiplicatively by the oversampling factor ($O$) at the cost of introducing harmonics. Finally, the array tapering with an oversampled modulating signal is proposed. The oversampling provides $O+1$ uniformly distributed tapering amplitudes.

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arXiv2024

Distributed PMCW Radar Network in Presence of Phase Noise

In Frequency Modulated Continuous Waveform (FMCW) radar systems, the phase noise from the Phase-Locked Loop (PLL) can increase the noise floor in the Range-Doppler map. The adverse effects of phase noise on close targets can be mitigated if the transmitter (Tx) and receiver (Rx) employ the same chirp, a phenomenon known as the range correlation effect. In the context of a multi-static radar network, sharing the chirp between distant radars becomes challenging. Each radar generates its own chirp, leading to uncorrelated phase noise. Consequently, the system performance cannot benefit from the range correlation effect. Previous studies show that selecting a suitable code sequence for a Phase Modulated Continuous Waveform (PMCW) radar can reduce the impact of uncorrelated phase noise in the range dimension. In this paper, we demonstrate how to leverage this property to exploit both the mono- and multi-static signals of each radar in the network without having to share any signal at the carrier frequency. The paper introduces a detailed signal model for PMCW radar networks, analyzing both correlated and uncorrelated phase noise effects in the Doppler dimension. Additionally, a solution for compensating uncorrelated phase noise in Doppler is presented and supported by numerical results.

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arXiv2023

Active Inference in Hebbian Learning Networks

This work studies how brain-inspired neural ensembles equipped with local Hebbian plasticity can perform active inference (AIF) in order to control dynamical agents. A generative model capturing the environment dynamics is learned by a network composed of two distinct Hebbian ensembles: a posterior network, which infers latent states given the observations, and a state transition network, which predicts the next expected latent state given current state-action pairs. Experimental studies are conducted using the Mountain Car environment from the OpenAI gym suite, to study the effect of the various Hebbian network parameters on the task performance. It is shown that the proposed Hebbian AIF approach outperforms the use of Q-learning, while not requiring any replay buffer, as in typical reinforcement learning systems. These results motivate further investigations of Hebbian learning for the design of AIF networks that can learn environment dynamics without the need for revisiting past buffered experiences.

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arXiv2023

FMCW Radar Sensing for Indoor Drones Using Learned Representations

Frequency-modulated continuous-wave (FMCW) radar is a promising sensor technology for indoor drones as it provides range, angular as well as Doppler-velocity information about obstacles in the environment. Recently, deep learning approaches have been proposed for processing FMCW data, outperforming traditional detection techniques on range-Doppler or range-azimuth maps. However, these techniques come at a cost; for each novel task a deep neural network architecture has to be trained on high-dimensional input data, stressing both data bandwidth and processing budget. In this paper, we investigate unsupervised learning techniques that generate low-dimensional representations from FMCW radar data, and evaluate to what extent these representations can be reused for multiple downstream tasks. To this end, we introduce a novel dataset of raw radar ADC data recorded from a radar mounted on a flying drone platform in an indoor environment, together with ground truth detection targets. We show with real radar data that, utilizing our learned representations, we match the performance of conventional radar processing techniques and that our model can be trained on different input modalities such as raw ADC samples of only two consecutively transmitted chirps.

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arXiv2022

Fusing Event-based Camera and Radar for SLAM Using Spiking Neural Networks with Continual STDP Learning

This work proposes a first-of-its-kind SLAM architecture fusing an event-based camera and a Frequency Modulated Continuous Wave (FMCW) radar for drone navigation. Each sensor is processed by a bio-inspired Spiking Neural Network (SNN) with continual Spike-Timing-Dependent Plasticity (STDP) learning, as observed in the brain. In contrast to most learning-based SLAM systems%, which a) require the acquisition of a representative dataset of the environment in which navigation must be performed and b) require an off-line training phase, our method does not require any offline training phase, but rather the SNN continuously learns features from the input data on the fly via STDP. At the same time, the SNN outputs are used as feature descriptors for loop closure detection and map correction. We conduct numerous experiments to benchmark our system against state-of-the-art RGB methods and we demonstrate the robustness of our DVS-Radar SLAM approach under strong lighting variations.

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arXiv2022

Learning to SLAM on the Fly in Unknown Environments: A Continual Learning Approach for Drones in Visually Ambiguous Scenes

Learning to safely navigate in unknown environments is an important task for autonomous drones used in surveillance and rescue operations. In recent years, a number of learning-based Simultaneous Localisation and Mapping (SLAM) systems relying on deep neural networks (DNNs) have been proposed for applications where conventional feature descriptors do not perform well. However, such learning-based SLAM systems rely on DNN feature encoders trained offline in typical deep learning settings. This makes them less suited for drones deployed in environments unseen during training, where continual adaptation is paramount. In this paper, we present a new method for learning to SLAM on the fly in unknown environments, by modulating a low-complexity Dictionary Learning and Sparse Coding (DLSC) pipeline with a newly proposed Quadratic Bayesian Surprise (QBS) factor. We experimentally validate our approach with data collected by a drone in a challenging warehouse scenario, where the high number of ambiguous scenes makes visual disambiguation hard.

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arXiv2022

A New Look at Spike-Timing-Dependent Plasticity Networks for Spatio-Temporal Feature Learning

We present new theoretical foundations for unsupervised Spike-Timing-Dependent Plasticity (STDP) learning in spiking neural networks (SNNs). In contrast to empirical parameter search used in most previous works, we provide novel theoretical grounds for SNN and STDP parameter tuning which considerably reduces design time. Using our generic framework, we propose a class of global, action-based and convolutional SNN-STDP architectures for learning spatio-temporal features from event-based cameras. We assess our methods on the N-MNIST, the CIFAR10-DVS and the IBM DVS128 Gesture datasets, all acquired with a real-world event camera. Using our framework, we report significant improvements in classification accuracy compared to both conventional state-of-the-art event-based feature descriptors (+8.2% on CIFAR10-DVS), and compared to state-of-the-art STDP-based systems (+9.3% on N-MNIST, +7.74% on IBM DVS128 Gesture). Our work contributes to both ultra-low-power learning in neuromorphic edge devices, and towards a biologically-plausible, optimization-based theory of cortical vision.

cs.CV↗

arXiv2022

Continuously Learning to Detect People on the Fly: A Bio-inspired Visual System for Drones

This paper demonstrates for the first time that a biologically-plausible spiking neural network (SNN) equipped with Spike-Timing-Dependent Plasticity (STDP) can continuously learn to detect walking people on the fly using retina-inspired, event-based cameras. Our pipeline works as follows. First, a short sequence of event data ($<2$ minutes), capturing a walking human by a flying drone, is forwarded to a convolutional SNNSTDP system which also receives teacher spiking signals from a readout (forming a semi-supervised system). Then, STDP adaptation is stopped and the learned system is assessed on testing sequences. We conduct several experiments to study the effect of key parameters in our system and to compare it against conventionally-trained CNNs. We show that our system reaches a higher peak $F_1$ score (+19%) compared to CNNs with event-based camera frames, while enabling on-line adaptation.

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