Design and analysis of estimators for multicarrier modulation and ultrasonic imaging
Abstract: This thesis deals with two areas: multicarrier modulation and ultrasonic imaging. Although different in application, these fields have a lot in common. For instance, synchronization and channel estimation in communication systems correspond to time-delay estimation and system identification in ultrasonic imaging. This thesis concentrates on these estimation problems. Three tasks in orthogonal frequency-division multiplexing (OFDM), a type of multicarrier system, are considered: synchornization, channel estimation and coding. The cyclic prefix, a preamble within OFDM symbols used to avoid intersymbol and intercarrier interference, is composed of redundant data and is shown to contain sufficient information. Channel estimation in OFDM systems is usually done with pilot-symbol assisted modulation, i.e. pilots are multiplexed into the transmitted symbol stream. Estimation of the channel with finite-impulse response (FIR) filters has been estimators based on optimal rank reduction can give better performance with the same complexity. These novel estimators are presented and evaluated, both in terms of mean-squared error and coded bit-error rate. The mean-squared error is obtained from analytical expressions and the coded bit-error rate from both simulations and analytical expressions. The analytical method we employ for these evaluations is itself investigated as a part of this thesis. This method of estimating coded bit-error rates, presented in the literature a few years ago, is in this thesis extended to OFDM systems. Showing a high potential for analyzing coded systems, it can be very useful in the design of an OFDM system, since it does not require lengthy simulations. This makes it possible to vary several parameters and obtain bit-error rates more promptly. The problems considered in ultrasonic imaging are system identification and time-delay estimation. The former seeks to obtain the spatial impulse response of an ultrasonic transducer, i.e., the echo from a (idealized) point reflector. This can be veryuseful, since the echo from an arbitrary surface can be modelled as a sum of the echoes from the individual points making up the surface. The spatial impulse response can be measured directly, but this poses some practical problems. The reflector must be made small enough to resemble a point, increasing the reflected echo's susceptibility to measurement noise. We propose a novel method of estimating the spatial impulse response indirectly by measuring the echoes from sliding halfplanes and inverting them. Working with this method, we found a need for estimating small time-delay differences in the received echoes. Hence, a fast and simple method was developed which is based on the correlation with Hilbert-transformed echoes.
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