Institute for Systems Research Technical Reports

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.

Furthermore, the Cramer-Rao lower bound (CRLB) for DA case is investigated. The performance of the estimator is shown through simulation to meet the CRLB even at low signal-to-noise ratios (SNR). Compared with theoretical solutions, the proposed estimator is less computationally intensive and is therefore easier to implement using current VLSI technology. IEEE Wireless Communications and Networking Conference: WCNC'99

In this paper we present an approximated maximum likelihood (ML) carrier frequency offset estimator, ML joint carrier phase and timing offsets estimator and their systolic VLSI implementations for PSK burst modems. The performances are close to the Cramer-Rao lower bounds (CRLB) at low SNRs.

Compared with theoretical solutions, the estimators proposed here are much simpler and easier to implement by the current VLSI technology. The CRLB for DA estimations is discussed in some depth, some issues on training sequence design is also addressed in this work.

Globecomm99

3-D wavelet decomposition can remove spatial and temporal redundancy and provide scalability of video quality. In order to conceal the errors occurring under bad channel conditions, a novel slicing method and a joint source channel coding scenario that combines RCPC with CRC and utilizes the distortion information to allocate convolutional coding rates are presented. A new performance index based on JND is proposed and used to evaluate the overall performance at different signal-to-noise ratios (SNR). Our system uses the OQPSK modulation scheme.

VTC 1999

In this paper we present an approximated maximum likelihood (ML) carrier frequency offset estimator, ML joint carrier phase and timing offsets estimator and their systolic VLSI implementations for PSK burst modems. The performances are close to the Cramer-Rao lower bounds (CRLB) at low SNRs. Compared with theoretical solutions the estimators proposed here are much simpler and easier to implement by the current VLSI technology.

VTC'99

In order to conceal errors occurring under bad channel conditions, a novel slicing method and a joint source channel coding scenario that combines RCPC with CRC and utilizes the distortion information to allocate convolutional coding rates are proposed. A new performance index based on JND is proposed and used to evaluate the overall performance at different signal-to-noise ratios (SNR). Our system uses OQPSK modulation scheme.

This paper has been submitted to Globecomm99, Rio de Janeiro, Brazil, December 5-9, 1999.

In order to conceal errors occurring under bad channel conditions, a novel slicing method and a joint source channel coding scenario that combines RCPC with CRC and utilizes the distortion information to allocate convolutional coding rates are proposed. A new performance index based on JND is proposed and used to evaluate the overall performance at different signal-to-noise ratios (SNR). Our system uses OQPSK modulation scheme.