Synchronization and Parameter Estimation in Wireless Communications

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This dissertation is devoted to the design and analysis of synchronization and channel parameter estimation schemes in wireless communications. Intrigued by the observation that the information is conveyed through wireless channels by uniformly spaced pulses that are some kind of "distorted" convolution of data symbols and a shaping pulse, we try to set up a framework to study synchronization and channel parameter estimation problems in the frequency domain.

The dissertation consists of four major parts. Many issues in digital communications and signal processing involve the analysis of the inverse of Toeplitz matrices. In the first part, the convergence of the inverse of Toeplitz matrices and its application are presented. Under the condition that the $z$-transform of the sequence with which the Toeplitz matrices are associated has no zero on the unit circle, we show that the inverse converges to a circular matrix in the weak sense. Furthermore, for the finite boundary quadratic form, a sufficient condition under which the convergence can be strengthened into the strong sense and an upper bound of the approximation residue error are derived. It is well known that a circular matrix can be eigendecomposed by the discrete Fourier transform (DFT) which provides the desired frequency domain approach.

In practical systems, synchronization parameters such as timing and carrier phase offsets, and channel response in fading channels are acquired with the help of a training sequence (TS) that is known to the receiver, which is called the data-aided (DA) estimation. In the second part, the performance limit that is the Cramer-Rao lower Bound (CRB) for the DA joint carrier phase and timing offsets estimation with an arbitrary TS is derived using the properties of Toeplitz matrices. Unlike the CRB derived in the literature, the bound derived in this dissertation reveals the close relation between a TS and its resultant performance limit, therefore it provides a quantitative approach to design TS for the acquisition of synchronization parameters.

Following the estimation theorem, we derive a maximum likelihood (ML) slow frequency-selective fading channel estimator using the frequency domain approach introduced by the properties of Toeplitz matrices in the third part. In the fourth part, a carrier frequency offset estimator and a joint carrier phase and timing offset estimators with moderate complexities are proposed. Their systolic VLSI implementations are also presented. The performance of the proposed estimators approaches their corresponding performance limits.