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State-space models and methods for MIMO communication


State-space models are proposed to represent MIMO frequency-selective wireless channels with the motivation of better model approximation and more robust channel equalization performance when the order of the channel model is lower that of the true channel. We study the MIMO channel approximation error as a function of model order and show that state-space models possess improved performance compared to more standard FIR models. We quantify the model approximation error using the upper bound of the minimum H1 norm of the difference between the original channel and the approximated channel model. It is shown that state-space models always maintain lower H1 approximation error than the FIR models with the same model order for either spatially uncorrelated MIMO channels or correlated ones. A recursive algorithm, based on the subspace system identification methods, to estimate the state-space channel model using training data is presented. When compared to the FIR-based Recursive Least Squares algorithm, the state-space based channel estimator shows the ability of providing low-order models of high- quality channel approximation, while preserving comparable convergence rate. We develop a simple framework under which the equalizers for state-space channel models can be designed using the existing methods for designing equalizers for FIR models. In particular, a MIMO MMSE-DFE equalizer is developed for state-space models. When only estimates of the channel are available to the receiver, the equalization performance is affected by the channel estimation accuracy. Because reduced-order state-space models can provide lower H2 channel estimation error than reduced-length FIR models, state-space based equalizers typically exhibit significantly smaller symbol error rate than FIR-based ones. Thus, state-space channel models can be a more robust choice than FIR models in the presence of model order selection error. Numerical simulation also shows that adaptive state-space based receivers have marginally slower but comparable convergence rates compared to FIR based adaptive equalizers. Furthermore, we attempt to design a state-space channel equalizer that is especially suited for blockwise or framed data transmission such as GSM systems. A new state-space equalization scheme is developed based on the theory of fixed-interval smoothing and fixed-interval deconvolution. It is combined with the recursive MOESP channel estimator to form a complete receiver processing procedure

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