Robust Linear Hybrid Beamforming Designs Relying on Imperfect CSI in mmWave MIMO IoT Networks

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 IoTNo power constraints, while also eliminating the need for a baseband receiver combiner at the fusion center (FC). To circumvent the non-convexity 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.Comment: 15 pages, 7 figure

Robust linear decentralized tracking of a time-varying sparse parameter relying on imperfect CSI

Robust linear decentralized tracking of a time varying sparse parameter is studied in a multiple-input multipleoutput (MIMO) wireless sensor network (WSN) under channelstate 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, 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 time slot 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 recursiveBayesian 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 KF 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

Bayesian learning-based linear decentralized sparse parameter estimation in MIMO wireless sensor networks relying on imperfect CSI

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 relyingon realistic imperfect channel estimates over the benchmarks

Privacy-preserving distributed beamformer design techniques for correlated parameter estimation

Privacy-preserving distributed beamforming designs are conceived for temporally correlated vector parameter estimation in an orthogonal frequency division multiplexing (OFDM)-based wireless sensor network (WSN). The temporal correlation inherent in the parameter vector is exploited by the rate distortion theorybased bit allocation framework used for the optimal quantization of the sensor measurements. The proposed distributed beamforming designs are derived via fusion of the dual consensus alternating direction method of multipliers (DC-ADMM) technique with a pertinent privacy-preserving framework. This makes it possible for each SN to design its transmit precoders in a distributed fashion, which minimizes the susceptibility of vital information to malicious eavesdropper (Ev) nodes, while simultaneously avoiding the significant communication overhead required by a centralized approach for the transmission of the state information to the fusion center (FC). The Bayesian Cramer Rao Bound (BCRB) is derived for benchmarking the estimation performance of the proposed transmit beamformer and receiver combiner designs, while our simulation results illustrate the performance and explicitly demonstrate the trade-off between the privacy and estimation performance

Robust finite-resolution transceivers for decentralized estimation in energy harvesting aided IoT networks

This paper develop novel approaches for designing robust transceivers and energy covariance in an IoT network powered by energy harvesting. Our goal is to minimize the mean square error (MSE) at the fusion center (FC) while considering the uncertainty of channel state information (CSI). The proposed designs incorporate both Gaussian and bounded CSI uncertainty models to model the uncertainty in the CSI. Furthermore, two different optimal bit allocation scheme have been proposed for quantizing the measurements from each sensor node (SeN). However, solving the resulting MSEoptimization problems with constraints on individual SeN power and total bit rate proves to be challenging due to their non-convex nature under both CSI uncertainty models. To address this challenge, we develop a block coordinate descent (BCD) based iterative framework. This framework leverages the blockconvexity of the optimization objective and provides efficient solutions for both uncertainty paradigms considered. By making use of this analytical tractability, we obtain improved performance compared to the uncertainty-agnostic scheme that disregards CSI uncertainty. We validate our approach through numerical simulations, which not only support ouranalytical findings but also demonstrate the superior performance achieved with our method that accounts for CSI uncertainty

Hybrid precoder and combiner designs for decentralized parameter estimation in mmWave MIMO wireless sensor networks

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 postprocessingof 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 formulatingthe hybrid transceiver design framework as a multiple measurement vectors (MMV)-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 estimationschemes. Our simulation results demonstrate the efficiency of the designs advocated and verify the analytical findings

Robust hybrid transceiver designs for linear decentralized estimation in mmWave MIMO IoT networks in the face of imperfect CSI

Hybrid transceivers are designed for linear decentralized estimation (LDE) in a mmWave multiple-input multipleoutput (MIMO) IoT network (IoTNe). For a noiseless fusion center (FC), it is demonstrated that the 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 mean squared error (MSE) minimization problem is non-convex. 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

Robust decentralized and distributed estimation of a correlated parameter vector in MIMO-OFDM wireless sensor networks

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 bitbudget. 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 precodersusing the consensus based alternating direction method of multipliers(ADMM), wherein each SN determines its precoderswithout any central coordination by the fusion center. Finally,new robust MIMO precoder designs are proposed for practicalscenarios operating in the face of channel state information (CSI)uncertainty. Our simulation results demonstrate the improvedperformance of the proposed schemes and corroborate ouranalytical formulations