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.

This article proposes an optimal scheduling policy for a system where spatiotemporally dependent sensor observations are broadcast to remote estimators over a resource-limited broadcast channel. We consider a system with a measurement-blind network scheduler that transmits observations, and design scheduling schemes that minimize mean squared error (MSE) by determining a subset of sensor observations to be broadcast based on their information freshness, as measured by their Age of Information (AoI). By modeling the problem as a finite state-space Markov decision process (MDP), we derive an optimal scheduling policy, with AoI as a state variable, minimizing the average MSE for an infinite time horizon. The resulting policy has a periodic pattern that renders an efficient implementation with low data storage. We further show that for any policy that minimizes the overall AoI, the estimation accuracy depends on how the scheduling order relates to the sensor’s intrinsic spatial correlation. Consequently, the estimation accuracy varies from worse than a randomized scheduling approach to near optimal. Thus, we present an additional age-minimizing policy with optimal scheduling order. We also present alternative policies for large state spaces that are attainable with less computational effort. Numerical results validate the presented theory.

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.

We develop a privacy-preserving distributed algorithm to minimize a regularized empirical risk function when the first-order information is not available and data is distributed over a multi-agent network. We employ a zeroth-order method to minimize the associated augmented Lagrangian function in the primal domain using the alternating direction method of multipliers (ADMM). We show that the proposed algorithm, named distributed zeroth-order ADMM (D-ZOA), has intrinsic privacy-preserving properties. Most existing privacy-preserving distributed optimization/estimation algorithms exploit some perturbation mechanism to preserve privacy, which comes at the cost of reduced accuracy. Contrarily, by analyzing the inherent randomness due to the use of a zeroth-order method, we show that D-ZOA is intrinsically endowed with$(\epsilon,\delta)-$differential privacy. In addition, we employ the moments accountant method to show that the total privacy leakage of D-ZOA grows sublinearly with the number of ADMM iterations. D-ZOA outperforms the existing differentially-private approaches in terms of accuracy while yielding similar privacy guarantee. We prove that D-ZOA reaches a neighborhood of the optimal solution whose size depends on the privacy parameter. The convergence analysis also reveals a practically important trade-off between privacy and accuracy. Simulation results verify the desirable privacy-preserving properties of D-ZOA and its superiority over the state-of-the-art algorithms as well as its network-wide convergence.

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.

This paper proposes an optimal scheduling policy for a remote estimation problem, where sensor observations of two spatio-temporally correlated processes are broadcasted to two remote estimators. At each time instant only a single observation can be communicated. For this purpose, a system scheduler determines which sensor measurement is communicated. The scheduler cannot observe measurements, and exploits age-of-information (AoI) to calculate the expected estimation error. We derive an optimal scheduling policy, with AoI as state-variable, that minimizes the average mean squared error for an infinite time horizon. The obtained policy yields a periodic scheduling of the sensor measurements, and we show that the AoI for the process with the largest marginal variance does not exceed one.

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.

We propose a privacy-preserving distributed maximum consensus algorithm where the local state of the agents and identity of the maximum state owner is kept private from adversaries. To that end, we reformulate the maximum consensus problem over a distributed network as a linear program. This optimization problem is solved in a distributed manner using the alternating direction method of multipliers (ADMM) and perturbing the primal update step with Gaussian noise. We define the privacy of an agent as the estimation error of its local state at the adversary and obtain theoretical bounds on the privacy loss for the proposed method. Further, we prove that the proposed algorithm converges to the maximum value at all agents. In addition to the analytical results, we illustrate the convergence speed and privacy-accuracy trade-off through numerical simulations.

We propose a new distributed algorithm to solve the total least-squares (TLS) problem when data are distributed over a multi-agent network. To develop the proposed algorithm, named distributed ADMM TLS (DA-TLS), we reformulate the TLS problem as a parametric semidefinite program and solve it using the alternating direction method of multipliers (ADMM). Unlike the existing consensus-based approaches to distributed TLS estimation, DA-TLS does not require careful tuning of any design parameter. Numerical experiments demonstrate that the DA-TLS converges to the centralized solution significantly faster than the existing consensus-based TLS algorithms.

In this paper, we study energy transmission for decentralized detection in wireless powered sensor networks (WPSN) in which the sensor nodes are powered by harvesting the radio frequency signals transmitted from dedicated energy access points (E-AP). We present a joint design of the transmit covariance matrices at E-APs and sensor precoders to minimize the probability of error. To this end, we maximize the error exponents by employing Dinkelbach's method and semidefinite relaxation. We present an iterative algorithm to solve the relaxed problem and prove that the relaxation is tight. Simulation results demonstrate that the proposed design results in a superior detection performance in comparison to the conventional techniques.

In this paper, we study vector parameter estimation in multiple-input multiple-output wireless-powered sensor networks (WPSNs) where sensor nodes operate by harvesting the radio frequency signals transmitted from energy access points (E-APs). We investigate a joint design of sensor data precoders, a fusion rule, and energy covariance matrices to minimize the mean square error (MSE) of the parameter estimate based on a non-linear energy harvesting model. First, we propose a centralized algorithm to solve the MSE minimization problem. Next, to reduce the computational complexity at the fusion center (FC) and feedback overhead from the sensors to the FC, we present a distributed algorithm to locally compute the precoders and the energy covariance matrices. We employ the alternating direction method of multipliers technique to minimize the MSE in a distributed manner without any coordination from the FC. In the proposed distributed algorithm, each sensor node calculates its own precoders and determines the local information of the fusion rule, and then messages are broadcast to other sensor nodes and E-APs. Simulation results demonstrate that the distributed algorithm performs close to the centralized algorithm with reduced complexity. Moreover, the proposed methods exhibit superior estimation performance over conventional techniques in WPSNs.

In this paper, we study parameter estimation in multiple-input multiple-output (MIMO) wireless powered sensor networks (WPSN). The sensor nodes are powered exclusively by harvesting the radio frequency signals transmitted from the energy access points. We propose a joint design of the sensor data precoders and energy covariance matrices to minimize the mean square error (MSE) of the parameter estimate. This design also incorporates optimal allocation of the harvested power for data acquisition and data transmission. We employ a zero-forcing precoding based estimation framework and the alternating minimization technique to compute the precoders, power allocation, and energy covariance matrices. Simulation results demonstrate that the proposed method achieves a superior estimation performance in comparison to the conventional energy transfer techniques for estimation in WPSNs.

This letter proposes novel precoding techniques for robust decentralized parameter estimation with only imperfect channel state information (CSI) in a coherent multiple access channel based wireless sensor network. For scalar parameter estimation, the proposed technique minimizes the worst case estimation error arising due to the channel uncertainties while ensuring the maximum gain at each receive antenna. For vector parameter estimation, since the general noisy measurement case is intractable, a robust precoder is developed for noiseless sensor measurements that eliminates the need for postprocessing at the fusion center while simultaneously minimizing the worst case estimation error. Simulation results show that the proposed techniques have a superior performance in comparison to imperfect CSI agnostic estimation techniques.

In this letter, we present a framework for optimal minimum variance distortionless precoder (MVDP) design towards decentralized estimation of a vector parameter in a coherent multiple access channel based multiple-input multiple-output (MIMO) wireless sensor network. The proposed MVDP scheme yields the optimal minimum variance distortionless parameter estimate at the fusion center without the necessity of any receive processing. A closed form expression is derived for the mean square estimation error of the MVDP and it is demonstrated that it asymptotically achieves the centralized minimum mean square error bound. Further, we derive the optimal decentralized estimation schemes with a total network power constraint (MVDP-T) and per-sensor power constraint (MVDP-P). Simulation results demonstrate the performance of the proposed optimal precoding schemes and also support the analytical results derived.

In this paper we propose a novel scheme to jointly determine the optimal transmit/receive beamformers together with multi-user power allocation towards transmission rate maximization in a cooperative MIMO cellular wireless network for unicast/multicast scenarios. For the unicast scenario, we propose a successive constrained eigenbeamforming (SCEB) technique to reduce the inter-user interference and enhance the data rates subject to power constraints. This scheme is further extended to a multicast scenario (SCEB-M) to maximize the sum rate of a user group with group constraints on the transmit power. We also derive optimal schemes to efficiently schedule a subset of users/ groups from the active user set. We employ a practical H.264 scalable video quality model to demonstrate the performance of the presented schemes in realistic video streaming broadband wireless networks. Simulation results show that the proposed SCEB schemes achieve a superior data rate and video quality in comparison to conventional resource allocation schemes in cooperative cellular scenarios.

In this paper, we propose a novel whitening-rotation (WR) based semi-blind (SB) scheme for frequency-selective channel estimation in multiple-input multiple-output (MIMO) multi-carrier (MC) CDMA systems. This scheme is based on a low complexity multi-path multi-carrier decorrelator (MMD) receiver structure developed for the MIMO MC-CDMA system. It is shown that the MMD based receiver naturally enables the formulation of the SB scheme by reducing the frequency-selective MIMO MC-CDMA channel to a flat fading channel matrix of appropriate dimension. Thus, it results in a significant reduction in the computational complexity usually associated with frequency-selective MIMO channel estimation. Further, we derive the Cramer-Rao bound (CRB) to characterize the mean squared error (MSE) performance of the proposed SB scheme. For performance comparison of the proposed SB estimator, we also derive the training estimate and the uncertainty based robust estimate of the frequency-selective MIMO MC-CDMA channel. Simulation results demonstrate that the proposed SB scheme achieves a significantly lower MSE of estimation compared to the competing training and robust estimation schemes.