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Passive Wi-Fi-based radars (PWRs) are devices that enable the localization of targets using Wi-Fi signals of opportunity transmitted by an access point. Unlike active radars that optimize their transmitted waveform for localization, PWRs align with the 802.11 amendments. Specifically, during the channel sounding session preceding a multi-user multiple-input multiple-output downlink transmission, an access point isotropically transmits a null data packet (NDP) with a known preamble. From these known symbols, client user equipments derive their channel state information and transmit an unencrypted beamforming feedback (BFF) back to the access point. The BFF comprises the right singular matrix of the channel and the corresponding stream gain for each subcarrier, which allows the computation of a beamforming matrix at the access point. In a classical PWR processing, only the preamble symbols from the NDP are exploited during the channel sounding session. In this study, we investigate multiple target localization by a PWR exploiting hybrid information sources. On one hand, the joint angle-of-departure and angle-of-arrival evaluated from the NDP. On another hand, the line-of-sight angle-of-departures inferred from the BFFs. The processing steps at the PWR are defined and an optimal hybrid fusion rule is derived in the maximum likelihood framework. Monte-Carlo simulations assess the enhanced accuracy of the proposed combination method compared to classical PWR processing based solely on the NDP, and compare the localisation performance between client and non-client targets., Comment: 5 pages, 3 figures, under review for SPAWC24

Recent advancements in Wi-Fi sensing have sparked interest in exploiting OFDM modulated communication signals for target detection and tracking. In this study, we address the angle-based localization of multiple targets using a multistatic OFDM radar. While the maximum likelihood approach optimally merges data from each radar pair comprised by the system, it entails a complex multi-dimensional search process. Leveraging pre-estimation of the targets' parameters obtained via the MUSIC algorithm, our method decouples this multi-dimensional search into a single two-dimensional estimator per target. The proposed alternating summation method allows the computation of a combined likelihood map aggregating contributions from each radar pair, enabling target detection via peak selection. Besides reducing computational complexity, the method effectively captures target interactions and accommodates varying radar pair localization abilities. Also, it requires transmitting only the estimated channel covariance matrices of each radar pair to the central processor. Numerical simulations demonstrate superior performance over existing approaches., Comment: 5 Pages, 3 figures, submitted to EUSIPCO2024. arXiv admin note: text overlap with arXiv:2402.13118

This study proposes a novel stochastic geometry framework analyzing power control strategies in spatially correlated network topologies. Heterogeneous networks are studied, with users modeled via the superposition of homogeneous and Poisson cluster processes. First, a new expression approaching the distribution of the number of users per base station is provided. This distribution defines the load associated with each Vorono\"i cell, capturing non-uniformities in user locations and correlation to BSs positions. The power allocation is adjusted based on this load, allowing BSs to enter sleep mode when their activity falls below a defined threshold. Furthermore, the propagation model features millimeter wave transmission characteristics and directional beamforming. Considering these aspects, revisited definitions of coverage probability, spectral efficiency, and energy efficiency are proposed. Tractable expressions for these metrics are derived and validated using Monte-Carlo simulations. Asymptotic expressions are also proposed, providing further understanding on the influence of the system parameters. Our numerical results finally analyze the impact of the sleep control on the performance and display the optimal strategies in terms of energy efficiency., Comment: 15 pages, 9 figures

This study investigates the problem of angle-based localization of multiple targets using a multistatic OFDM radar. Although the maximum likelihood (ML) approach can be employed to merge data from different radar pairs, this method requires a high complexity multi-dimensional search process. The multiple signal classification (MUSIC) algorithm simplifies the complexity to a two-dimensional search, but no framework is derived for combining MUSIC pseudo-spectrums in a multistatic configuration. This paper exploits the relationship between MUSIC and ML estimators to approximate the multidimensional ML parameter estimation with a weighted combination of MUSIC pseudo-spectrum. This enables the computation of a likelihood map on which a peak selection is applied for target detection. In addition to reducing the computational complexity, the proposed method relies only on transmitting the estimated channel covariance matrices of each radar pair to the central processor. A numerical analysis is conducted to assess the benefits of the proposed fusion., Comment: 5 pages, 3 figures, 1 table; accepted to EuCAP2024 conference

Emerging Internet-of-Things sensing applications rely on ultra low-power (ULP) microcontroller units (MCUs) that wirelessly transmit data to the cloud. Typical MCUs nowadays consist of generic blocks, except for the protocol-specific radios implemented in hardware. Hardware radios however slow down the evolution of wireless protocols due to retrocompatiblity concerns. In this work, we explore a software-defined radio architecture by demonstrating a LoRa transceiver running on custom ULP MCU codenamed SleepRider with an ARM Cortex-M4 CPU. In SleepRider MCU, we offload the generic baseband operations (e.g., low-pass filtering) to a reconfigurable digital front-end block and use the Cortex-M4 CPU to perform the protocol-specific computations. Our software implementation of the LoRa physical layer only uses the native SIMD instructions of the Cortex-M4 to achieve real-time transmission and reception of LoRa packets. SleepRider MCU has been fabricated in a 28nm FDSOI CMOS technology and is used in a testbed to experimentally validate the software implementation. Experimental results show that the proposed software-defined radio requires only a CPU frequency of 20 MHz to correctly receive a LoRa packet, with an ultra-low power consumption of 0.42 mW on average.

Physical-layer security (PLS) has the potential to strongly enhance the overall system security as an alternative to or in combination with conventional cryptographic primitives usually implemented at higher network layers. Secret-key generation relying on wireless channel reciprocity is an interesting solution as it can be efficiently implemented at the physical layer of emerging wireless communication networks, while providing information-theoretic security guarantees. In this paper, we investigate and compare the secret-key capacity based on the sampling of the entire complex channel state information (CSI) or only its envelope, the received signal strength (RSS). Moreover, as opposed to previous works, we take into account the fact that the eavesdropper's observations might be correlated and we consider the high signal-to-noise ratio (SNR) regime where we can find simple analytical expressions for the secret-key capacity. As already found in previous works, we find that RSS-based secret-key generation is heavily penalized as compared to CSI-based systems. At high SNR, we are able to precisely and simply quantify this penalty: a halved pre-log factor and a constant penalty of about 0.69 bit, which disappears as Eve's channel gets highly correlated.

This paper studies the information-theoretic secrecy capacity of an Offset-QAM-based filterbank multicarrier (FBMC-OQAM) communication over a wiretap frequency selective channel. The secrecy capacity is formulated as an optimization problem which has a closed-form solution in the high signal-to-noise ratio (SNR) regime. Two of the most common equalization strategies in FBMC-OQAM are considered, namely, single-tap and multi-tap equalization. For the sake of comparison, we also consider the secrecy capacity of a generic modulation and a cyclic prefix-orthogonal frequency division multiplexing (CP-OFDM) modulation. As a result, we find that FBMC-OQAM is particularly competitive for medium-to-long burst transmissions.

Secret-key generation exploiting the channel reciprocity between two legitimate parties is an interesting alternative solution to cryptographic primitives for key distribution in wireless systems as it does not rely on an access infrastructure and provides information-theoretic security. The large majority of works in the literature generally assumes that the eavesdropper gets no side information about the key from her observations provided that (i) it is spaced more than a wavelength away from a legitimate party and (ii) the channel is rich enough in scattering. In this paper, we show that this condition is not always verified in practice and we analyze the secret-key capacity under realistic propagation conditions.

LoRaWAN is nowadays one of the most popular protocols for low-power Internet-of-Things communications. Although its physical layer, namely LoRa, has been thoroughly studied in the literature, aspects related to the synchronization of LoRa receivers have received little attention so far. The estimation and correction of carrier frequency and sampling time offsets is however crucial to attain the low sensitivity levels offered by the LoRa spread-spectrum modulation. The goal of this paper is to build a low-complexity, yet efficient synchronization algorithm capable of correcting both offsets. To this end, a complete analytical model of a LoRa signal corrupted by these offsets is first derived. Using this model, we propose a new estimator for the sampling time offset. We also show that the estimations of the carrier frequency and the sampling time offsets cannot be performed independently. Therefore, to avoid a complex joint estimation of both offsets, an iterative low-complexity synchronization algorithm is proposed. To reach a packet error rate of 10^-3, performance evaluations show that the proposed receiver requires only 1 or 2 dB higher SNR than a theoretical perfectly synchronized receiver, while incurring a very low computational overhead., Comment: IEEE Internet of Things Journal

Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift keying (\emph{M}-PSK) system. We show that there exist some typos in the computation and we provide the detailed derivation leading to the correct expressions., Comment: 9 pages, 3 figures

Time reversal (TR) recently emerged as an interesting communication technology capable of providing a good spatio-temporal signal focusing effect. New generations of large-bandwidth devices with reduced cost leverage the use of TR wideband communication systems. While TR is usually implemented in the time domain, the same benefit can be obtained in an orthogonal frequency division multiplexing (OFDM) system by precoding the information in the frequency domain. Besides using multiple antennas, the focusing effect of TR also comes from the use of a high rate back-off factor (BOF), which is the signal up-sampling (or down-sampling) rate in the original time-domain TR precoding. However, a frequency-domain TR precoding in the literature has only considered BOF of one, which does not fully exploit the focusing property of TR. In this paper, we discuss how to properly implement different BOFs using frequency-domain TR precoding in the OFDM system. Moreover, we demonstrate that increasing the BOF and/or the number of transmit antennas significantly improves the focusing gain at the intended position. In contrast, the unintended positions receive less useful power. Furthermore, closed-form approximations of the mean-square-errors (MSEs) of equalized received signals at either intended or unintended positions are derived, expressing the focusing gain as a function of the BOF and the number of antennas. Numerical simulations with multi-path channels are carried out to validate the MSE expressions., Comment: 19 pages, 6 figures

In this paper, we investigate a trade-off between the number of radar observations (or measurements) and their resolution in the context of radar range estimation. To this end, we introduce a novel estimation scheme that can deal with strongly quantized received signals, going as low as 1-bit per signal sample. We leverage for this a dithered quantized compressive sensing framework that can be applied to classic radar processing and hardware. This allows us to remove ambiguous scenarios prohibiting correct range estimation from (undithered) quantized base-band radar signal. Two range estimation algorithms are studied: Projected Back Projection (PBP) and Quantized Iterative Hard Thresholding (QIHT). The effectiveness of the reconstruction methods combined with the dithering strategy is shown through Monte Carlo simulations. Furthermore we show that: (i), in dithered quantization, the accuracy of target range estimation improves when the bit-rate (i.e., the total number of measured bits) increases, whereas the accuracy of other undithered schemes saturate in this case; and (ii), for fixed, low bit-rate scenarios, severely quantized dithered schemes exhibit better performances than their full resolution counterparts. These observations are confirmed using real measurements obtained in a controlled environment, demonstrating the feasibility of the method in real ranging applications., Comment: Submitted to RadarConf2019 as an invited paper

Future generations of communications systems will target a very wide range of applications. Each application comes with its own set of requirements in terms of data rate, latency, user density, reliability... Accommodating this large variety of specifications implies the need for a novel physical layer technology. In this regard, the most popular modulation nowadays, namely, the orthogonal frequency division multiplexing modulation, is characterized by a poor time-frequency localization, implying strong limitations. In the light of these limitations, communications using new waveforms, relying on more sophisticated signal processing techniques and providing improved time-frequency localization, have attracted a lot of attention for the last decade. At the same time, the higher complexity of these new waveforms, not only in terms of implementation but also conceptually, creates an entrance barrier that slows down their adoption by industries, standardization bodies and more generally in the telecommunication community. The WaveComBox toolbox, freely available at www.wavecombox.com, is a user-friendly, open-source and well documented piece of software aiming at considerably lowering the entrance barrier of recently proposed waveforms. This article first describes the general abstract structure of the toolbox. Secondly, examples are given to illustrate how to use the toolbox and to show some more advanced functionalities.

The design of linear precoders or decoders for multiuser (MU) multiple-input multiple-output (MIMO) filterbank multicarrier (FBMC) modulations in the case of strong channel frequency selectivity is presented. The users and the base station (BS) communicate using space division multiple access (SDMA). The low complexity proposed solution is based on a single tap per-subcarrier precoding/decoding matrix at the base station (BS) in the downlink/uplink. As opposed to classical approaches that assume flat channel frequency selectivity at the subcarrier level, the BS does not make this assumption and takes into account the distortion caused by channel frequency selectivity. The expression of the FBMC asymptotic mean squared error (MSE) in the case of strong channel selectivity derived in earlier works is developed and extended. The linear precoders and decoders are found by optimizing the MSE formula under two design criteria, namely zero forcing (ZF) or minimum mean squared error (MMSE). Finally, simulation results demonstrate the performance of the optimized design. As long as the number of BS antennas is larger than the number of users, it is shown that those extra degrees of freedom can be used to compensate for the channel frequency selectivity.

The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner product of any atom of a suitable dictionary and the current signal residual, which is formed by the subtraction of previously selected atoms. This inner product, or correlation, is a key metric to determine the best atom to pick at each iteration. This paper provides, for each iteration of SOMP, a novel lower bound of the aforementioned metric for the atoms belonging to the correct and common joint support of the multiple signals. Although the bound is obtained for the noiseless case, its main purpose is to intervene in noisy analyses of SOMP. Finally, it is shown for specific signal patterns that the proposed bound outperforms state-of-the-art results for SOMP, and orthogonal matching pursuit (OMP) as a special case.

In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analysed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results.

Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the associated restricted isometry constant (RIC) and sometimes the restricted orthogonality constant (ROC). In this paper, three of the most recent ERC for OMP are examined. The contribution is to show that these ERC remain valid for a generalization of OMP, entitled simultaneous orthogonal matching pursuit (SOMP), that is capable to process several measurement vectors simultaneously and return a common support estimate for the underlying sparse vectors. The sharpness of the bounds is also briefly discussed in light of previous works focusing on OMP.

This paper addresses a weighted sum rate (WSR) maximization problem for downlink OFDMA aided by a decode-and-forward (DF) relay under a total power constraint. A novel subcarrier-pair based opportunistic DF relaying protocol is proposed. Specifically, user message bits are transmitted in two time slots. A subcarrier in the first slot can be paired with a subcarrier in the second slot for the DF relay-aided transmission to a user. In particular, the source and the relay can transmit simultaneously to implement beamforming at the subcarrier in the second slot. Each unpaired subcarrier in either the first or second slot is used for the source's direct transmission to a user. A benchmark protocol, same as the proposed one except that the transmit beamforming is not used for the relay-aided transmission, is also considered. For each protocol, a polynomial-complexity algorithm is developed to find at least an approximately optimum resource allocation (RA), by using continuous relaxation, the dual method, and Hungarian algorithm. Instrumental to the algorithm design is an elegant definition of optimization variables, motivated by the idea of regarding the unpaired subcarriers as virtual subcarrier pairs in the direct transmission mode. The effectiveness of the RA algorithm and the impact of relay position and total power on the protocols' performance are illustrated by numerical experiments. The proposed protocol always leads to a maximum WSR equal to or greater than that for the benchmark one, and the performance gain of using the proposed one is significant especially when the relay is in close proximity to the source and the total power is low. Theoretical analysis is presented to interpret these observations., Comment: 8 figures, accepted and to be published in IEEE Transactions on Signal Processing. arXiv admin note: text overlap with arXiv:1301.2935