This paper investigates the integration of Internet of Things (IoT) networks with modern massive multiple-input multiple-output (MIMO) wireless systems to enable various new use cases. Given the dynamic nature of parameters monitored by IoT nodes, efficient techniques for tracking these time-varying parameters are required. In a typical IoT networks, each IoT node linearly precodes its observations and transmits them over a coherent multiple access channel to a fusion center (FC). These IoT networks are power and bandwidth constrained in nature. Therefore, designing transmit precoders for the IoT nodes and a combiner for the FC is essential. This work proposes online linear receive combiner and transmit precoder designs that minimize the mean square error (MSE) under transmit power constraints. Using an alternating optimization technique, we derive closed-form solutions for the combiners and transmit precoders. Our numerical results validate the effectiveness of the proposed algorithms.

A scenario with multiple radars connected to a fusion centre and tracking a target endowed with cognitive abilities is considered. The aim of the target is to degrade the performance of the radar network using its cognitive abilities. In the embodiment considered in this paper, the target injects interference that perturbs the measurements at the different radars. The injected interference is designed to maximize the trace of the error covariance matrix in each instance of the extended Kalman filter iterations used at the fusion centre. The optimal interference in such a setting is formulated as a convex problem and its structure reveals a low-rank correlated structure unlike the intuitive additive white noise. Relation to water-filling is drawn and the impact of such an interference is subsequently analysed using numerical simulations.

This work considers an IoT network comprising of several IoT sensor nodes (SNs), a passive intelligent reflecting surface (IRS), and a fusion center (FC). Each IoT SN observes multiple physical phenomena, and transmits its observations to the FC for post processing. This necessitates the need for efficient preprocessing of each SN’s observations to combat wireless fading effects and optimize transmit power utilization. In this context, this paper presents a novel approach that jointly designs the transmit precoding matrix (TPM) for IoT SNs and optimizes the phase reflection matrix (PRM) for the IRS. The resulting non-convex optimization problem is tackled through an alternating optimization framework, where the individual TPM and PRM design subproblems are further addressed using the majorization minimization (MM) framework. Notably, the proposed solution yields closed-form expressions for TPM and PRM in each MM iteration, making it particularly suitable for low-cost IoT SNs. Numerical results demonstrate the efficacy of the proposed approach by showcasing significant enhancements in estimation performance compared to IoT networks lacking an IRS component.

peer reviewed

Hybrid precoder and combiner designs are conceived for decentralized parameter estimation in millimeter wave (mmWave) multiple-input–multiple-output (MIMO) wireless sensor networks (WSNs). More explicitly, efficient pre- and post-processing of the sensor observations and received signal are proposed for the minimum mean square error (MMSE) estimation of a parameter vector. The proposed techniques exploit the limited scattering nature of the mmWave MIMO channel for formulating the hybrid transceiver design framework as a multiple measurement vectors (MMVs)-based sparse signal recovery problem. This is then solved using the iterative appealingly low-complexity simultaneous orthogonal matching pursuit (SOMP). Tailor-made designs are presented for WSNs operating under both total and per-sensor power constraints, while considering ideal noiseless as well as realistic noisy sensors. Furthermore, both the Bayesian Cramer–Rao lower bound and the centralized MMSE bound are derived for benchmarking the proposed decentralized estimation schemes. Our simulation results demonstrate the efficiency of the designs advocated and verify the analytical findings.

Hybrid transceivers are designed for linear decentralized estimation (LDE) in a mmWave multiple-input–multiple-output (MIMO) IoT network (IoTNe). For a noiseless fusion center (FC), it is demonstrated that the mean squared error (MSE) performance is determined by the number of RF chains used at each IoT node (IoTNo). Next, the minimum-MSE RF transmit precoders (TPCs) and receiver combiner (RC) matrices are designed for this setup using the dominant array response vectors, and subsequently, a closed-form expression is obtained for the baseband (BB) TPC at each IoTNo using Cauchy’s interlacing theorem. For a realistic noisy FC, it is shown that the resultant MSE minimization problem is nonconvex. To address this challenge, a block-coordinate descent-based iterative scheme is proposed to obtain the fully digital TPC and RC matrices followed by the simultaneous orthogonal matching pursuit (SOMP) technique for decomposing the fully digital transceiver into its corresponding RF and BB components. A theoretical proof of the convergence is also presented for the proposed iterative design procedure. Furthermore, robust hybrid transceiver designs are also derived for a practical scenario in the face of channel state information (CSI) uncertainty. The centralized MMSE lower bound has also been derived that benchmarks the performance of the proposed LDE schemes. Finally, our numerical results characterize the performance of the proposed transceivers as well as corroborate our various analytical propositions.

Linear hybrid beamformer designs are conceived for the decentralized estimation of a vector parameter in a millimeter-wave (mmWave) multiple-input–multiple-output (MIMO) Internet of Things Network (IoTNe). The proposed designs incorporate both total IoTNe and individual IoT node power constraints, while also eliminating the need for a baseband receiver combiner at the fusion center (FC). To circumvent the nonconvexity of the hybrid beamformer design problem, the proposed approach initially determines the minimum mean-square error (MMSE) digital transmit precoder (TPC) weights followed by a simultaneous orthogonal matching pursuit (SOMP)-based framework for obtaining the analog RF and digital baseband TPCs. Robust hybrid beamformers are also derived for the realistic imperfect channel state information (CSI) scenario, utilizing both the stochastic and norm ball CSI uncertainty frameworks. The centralized MMSE bound derived in this work serves as a lower bound for the estimation performance of the proposed hybrid TPC designs. Finally, our simulation results quantify the benefits of the various designs developed.

Robust linear decentralized tracking of a time-varying sparse parameter is studied in a multiple-input–multiple-output (MIMO) wireless sensor network (WSN) under channel state information (CSI) uncertainty. Initially, assuming perfect CSI availability, a novel sparse Bayesian learning-based Kalman filtering (SBL-KF) framework is developed in order to track the time-varying sparse parameter. Subsequently, an optimization problem is formulated to minimize the mean-square error (MSE) in each time slot (TS), followed by the design of a fast block coordinate descent (FBCD)-based iterative algorithm. A unique aspect of the proposed technique is that it requires only a single iteration per TS to obtain the transmit precoder (TPC) matrices for all the sensor nodes (SNs) and the receiver combiner (RC) matrix for the fusion center (FC) in an online fashion. The recursive Bayesian Cramer–Rao bound (BCRB) is also derived for benchmarking the performance of the proposed linear decentralized estimation (LDE) scheme. Furthermore, for considering a practical scenario having CSI uncertainty, a robust SBL-KF (RSBL-KF) is derived for tracking the unknown parameter vector of interest followed by the conception of a robust transceiver design. Our simulation results show that the schemes designed outperform both the traditional sparsity-agnostic Kalman filter and the state-of-the-art sparse reconstruction methods. Furthermore, as compared to the uncertainty-agnostic design, the robust transceiver architecture conceived is shown to provide improved estimation performance, making it eminently suitable for practical applications.

Wireless sensor networks (WSNs) are vulnerable to eavesdropping as the sensor nodes (SNs) communicate over an open radio channel. Intelligent reflecting surface (IRS) technology can be leveraged for physical layer security in WSNs. In this letter, we propose a joint transmit and reflective beamformer (JTRB) design for secure parameter estimation at the fusion center (FC) in the presence of an eavesdropper (ED) in a WSN. We develop a semidefinite relaxation (SDR)-based iterative algorithm, which alternately yields the transmit beamformer at each SN and the corresponding reflection phases at the IRS, to achieve the minimum mean-squared error (MSE) parameter estimate at the FC, subject to transmit power and ED signal-to-noise ratio constraints. Our simulation results demonstrate robust MSE and security performance of the proposed IRS-based JTRB technique.

An optimal precoder design is conceived for the decentralized estimation of an unknown spatially as well as temporally correlated parameter vector in a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) based wireless sensor network (WSN). Furthermore, exploiting the temporal correlation present in the parameter vector, a rate-distortion theory based framework is developed for the optimal quantization of the sensor observations so that the resultant distortion is minimized for a given bit-budget. Subsequently, optimal precoders are also developed that minimize the sum-MSE (SMSE) for the scenario of transmitting quantized observations. In order to reduce the computational complexity of the decentralized framework, distributed precoder design algorithms are also developed which design precoders using the consensus based alternating direction method of multipliers (ADMM), wherein each SN determines its precoders without any central coordination by the fusion center. Finally, new robust MIMO precoder designs are proposed for practical scenarios operating in the face of channel state information (CSI) uncertainty. Our simulation results demonstrate the improved performance of the proposed schemes and corroborate our analytical formulations.

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relying on realistic imperfect channel estimates over the benchmarks.

This work considers the design of linear minimum mean square error (MMSE) precoders and combiners for the estimation of an unknown vector parameter in a coherent multiple access channel (MAC)-based multiple-input multiple-output (MIMO) wireless sensor network. The proposed designs that minimize the mean squared error (MSE) of the parameter estimate at the fusion center are based on majorization theory, which leads to non-iterative closed-form solutions for the precoders and combiners. Various scenarios are considered for parameter estimation such as networks with ideal high precision sensors as well as noisy non-ideal sensors. Moreover, inter parameter correlation is also incorporated, which makes the analysis comprehensive. The Bayesian Cramer-Rao bound (BCRB) and centralized MMSE bound are determined to characterize the estimation performance. Simulation results demonstrate the improved performance and also corroborate our analytical formulations.