Robust Linear Transceiver Designs for Vector Parameter Estimation in MIMO Wireless Sensor Networks under CSI Uncertainty
Abstract : This work conceives the robust linear transceivers for the estimation of an unknown vector parameter in a coherent multiple access channel (MAC)-based multiple-input multiple-output (MIMO) multi-sensor network under imperfect channel state information (CSI) at the fusion center (FC). Both the popular stochastic (S-) and norm ball CSI uncertainty (N-CSIU) models are considered for robust design. The proposed techniques are based on two design criterion, the first being, minimizing the mean squared error (MSE) of the estimate at the FC subject to total network power or individual sensor power constraints. Second, minimizing the total power consumption in the network while meeting a predefined level of MSE performance. Furthermore, the framework for precoder and combiner optimization is based on results from majorization theory, which leads to non-iterative closed-form solutions for the transceivers. While the most general scenario with correlated parameters and arbitrary observation SNR is considered to begin with, scenarios with uncorrelated parameters and high observation SNR are also considered as special cases, which makes the analysis comprehensive. Simulation results are presented to demonstrate the efficacy of the proposed schemes.
? We demonstrate our methodology using simulated data, and illustrate the convergence and existence of our solution over different parameter settings.
? This suggests that the robust solution presented here has improved power efficiency with the existence solutions of multiuser beam forming with non-perfect CSI.
? The existence and convergence of our methodology using different system parameters.
? A novel procedure for the design of beamforming vectors in multicell, multigroup, multicasting CRN with non-perfect CSI for both the secondary user network and interference power network.
? The framework considers the design problem where the imperfect CSI consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix.
? The framework developed in the paper for the linear MIMO transceiver design problem is based on majorization theory.
? The whole optimization problem is reduced to a power allocation problem, which depends on the specific cost function.
? In addition to the design problem, which minimizes a cost function of the MSEs with a total transmit power constraint, it is also possible to consider the dual problem that minimizes the total transmit power with a global performance constraint.
• Our proposed solution is more power efficient than the sub-optimal solution proposed in, while the non-robust solution has the best power performance among the three solutions.
• We presented an extensive computational simulation, demonstrating the superior performance of our approach when compared to a non-robust solution that does not account for uncertainty, and a sub-optimal approach proposed.
• All of the solutions proposed by these authors use semidefinite relaxation(SDR).
• Two types of solution are proposed for finding the beamforming vectors: the sub-optimal solution and the robust solution.
? If one has to guarantee certain performance or outage for all the channel realizations, worst case designs or certainty-equivalent margins should be used.
? Such imperfections and taking them into account in the transceiver design, a robust high performance link can be achieved.
? The best spectral efficiency and/or performance is obviously achieved when perfect CSI is available at both sides of the link.
? In a scalar channel, the performance is typically measured in terms of SNR, BER, or MSE.
? In contrast to the perfect CSI case where an arbitrary increasing function of the instantaneous MSEs is considered, the average system performance should be considered.
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