Development and analysis of signal copy and blind equalization algorithms
The process of signal waveform estimation using an antenna array in non-dispersive and dispersive channels is often referred to as signal copy and equalization, respectively. This thesis centers on these two applications.
The signal copy algorithms developed up to the present include conventional direction-finding (DF) based algorithms which estimate the signals by forming a weighted linear combination of the array outputs, and blind copy algorithms that exploit certain known properties of the signals such as cyclostationarity and the constant modulus property. In DF-based signal copy applications, the weight vector computation involves knowledge of both the array response and the directions-of-arrival (DOA) of the signals. Any errors in the array model not only affect the array response, but also the accuracy of the DOA estimates. The perturbed array response and the resulting imprecise DOA estimates can lead to serious degradation in signal copy performance. To provide some insight into choosing an appropriate algorithm for a practical application, several commonly used signal copy algorithms are studied in this thesis. Effects of the array calibration errors, DOA estimation errors, and noise are considered. Two performance metrics, mean squared error (MSE) and signal to interference plus noise ratio (SINR), are used to evaluate the algorithms. Analytical MSE and SINR expressions are provided, and performance orderings of some of the algorithms are established. The analysis is verified by simulation examples.
This thesis also presents two new algorithms to improve signal copy performance. The first technique combines information about both the spatial and temporal structure of the signals. It uses an initial blind estimate of the signals to compute a least-squares estimate of the array response, which in turn is used to update the signal estimates. The second technique is a decision directed approach for extracting digital signals from antenna array data. This algorithm alternates between (1) estimating and demodulating the received signals, and (2) using the resulting bit decisions to regenerate the signal waveforms and recompute the signal copy weight vectors. An analysis of the (asymptotic) bit-error rate performance of the algorithm for the case of BPSK signals is included.
The problem of equalizing a (narrowband) multipath channel using data from an array of sensors is also addressed in this thesis. Two equalization algorithms are presented, both based on a frequency domain representation of the data and the possible availability of array calibration data. The performance of these algorithms is compared with that of several other recently developed equalization techniques, and is shown to be superior provided the calibration data is reasonably accurate. Some heuristic methods are also presented for handling cases involving multiple sources with differing multipath structure.