Optimisation of test signals for channel identification

Channel estimation is required in virtually all communication systems: wireless, optical, and electrical systems. Modern mobile wireless devices undertake channel estimation repeatedly and audio communication systems of all varieties repeatedly estimate the echo-path channel so that echos can be cancelled. The channel estimation must be carried out repeatedly because the channel will vary while communication is taking place. This dissertation examines channel estimation in both acoustic and wireless cases. Echo cancellation has become ubiquitous because it is superior to other echo management techniques whenever the echo channel can successfully be estimated. Echo cancellation relies on the correct estimation and modelling of the echo channel. Despite much research into advanced echo cancellation techniques, there remains acoustic applications where the channel is too dynamic for existing echo channel estimation techniques to succeed. An echo cancellation simulation environment has been developed to facilitate the simulation of dynamic echo environments and the monitoring of the results and the internal state of echo cancellation algorithms. This environment enables the monitoring of the overall result and the internal state of the echo cancellation algorithms. Object oriented programming techniques are used to achieve the flexibility needed to do this for different algorithms, different stimulus or test signals, different background noise and different channels. While most acoustic echo channels are essentially linear, speakers can introduce non linearity to an echo channel, depending on their quality. A simplified non linear echo channel model of this situation is used, and a non linear algorithm for echo cancellation developed that estimates the parameters of this model. Second order statistics are used in techniques for channel estimation in wireless systems. Their use is necessary, given the dynamic nature of wireless channels. To date, however, there have been few attempts to fully utilise second order statistics as part of channel estimation for acoustic systems. The optimal linear estimator of the channel is identified that fully takes the second-order statistics of the channel variation into account. Test signals are often used in the estimation of wireless channels. They are also used in the estimation of acoustic channels. Equations characterising the optimal (in the sense of least-squares estimation error for fixed power) test signal based on the second order statistics of the channel and of the noise are developed. The power advantage of an optimal test signal over white noise as a signal is unbounded as the channel statistics vary. Channel autocovariances may be represented by covariance matrices. The model offered by a covariance matrix is often too complicated for use in practice, however. A model of intermediate complexity has been developed that remains sufficiently flexible to encapsulate desirable features of a channel autocovariance while being significantly simpler to use. The simplified model of a channel autocovariance has been used to randomly generate autocovariance matrices that are suitable for use in the testing the method for finding optimal test signals.