MLE and RBF for AOA Estimation in a Multipath Environment
The problem of estimation of angle-of-arrival (AOA) in multipath environments is addressed in this thesis. In particular, two new estimation techniques are developed. The first technique is based on the maximum likelihood estimation (MLE). This algorithm is unique in that a highly deterministic multipath signal model is used when formulating the likelihood function, which is then maximised with respect to the AOA. The deterministic multipath signal model that has been developed to describe the physics underlying the propogation of signals form a signal radio source to a receiver is much more complete than the general AOA model commonly used in other maximum likelihood formulations. This model makes use of the geometrical information and a priori knowledge of a number of physical parameters. By using the deterministic multipath signal model with the MLE estimator, one is essentially making more information available to the estimation process The Cramer-Rao bounds that apply specifically to this model have been derived to provide a performance measure for the mean-squared errors (MSE) in the estimated AOAs. Although the MLE method is optimum in a statistical sense, the computational load of the nonlinear optimisation procedure inherently required by the MLE method is too heavy for real-time processing. Accordingly, we propose a novel approach to the AOA estimation problem, which is based on the use of an associative memory. The functionality of an associative memory is identical to that of the inverse mapping network. This provides a more comprehensive explanation for the rationale of exploiting the inverse mapping concept in the AOA estimation problem. In particular, the AOA problem is considered as a mapping from the space of AOA to the space of the sensor output. A nonlinear associative memory is used to form the inverse mapping from the space of sensor output the the space of AOA and this memory is realized using the generalised radical basis function (RBF) neural network. In the actual implementation of the RBF network for AOA estimation, the second order statistics of the signals are used as the input vector of the network. The use of second order statistics eliminates the need to deal with the initial phase of the signal. Furthermore, it is suitable for the application to the minimum redundant array. The RBF network is much more efficient in terms of computation than the MLE algorithm. This makes the RBF network attractive for real-time implementation. Simulations are carried out to understand the efficiency of the RBG neural network approach. The learning and estimation performance is inversely proportional to the number of learning samples and the number of hidden units. At relatively low SNR, the estimation performance of the RBF network becomes insensitive to both the number of learning samples and the number of hidden units. The estimation performance of both the MLE technique and the RBF network is also evaluated as functions of the number of snapshots and SNR. The performance of the MLE algorithm is consistent with the Cramer-Rao bound. The MLE method is more efficient in terms of estimation than a RBF, provided that the search resolution used in the MLE method is sufficiently high. For equivalent computational complexity, the RBF network is much less than that produced by the MLE method. In summary, for the same performance, the computational complexity required by the MLE method is much higher than that required by the RBF network. It follows that the advantage to be gained by using a RBF network for AOA estimation is a considerable reduction in computational complexity. Finally, both the MLE technique and the RBF network
are validated using real data, which were collected using a 32-element sampled aperture antenna. The results obtained using the RBF network are very similar to those obtained using the MLE method.