The theory of bootstrapped algorithms and their applications to cross polarization interference cancelation

Dual-polarized transmission has become an important method for frequency re-use, particularly in satellite and microwave radio communication. Nevertheless, cross-polarization interference, which is inherent to this method, may cause degradation in system performance. Different canceler [sic] structures have been proposed to mitigate the effect of cross-polarization. Among these are the diagonalizer, the least mean square (LMS) canceler [sic] and the bootstrapped cancelers [sic]. Bootstrapped canceler [sic] schemes have been proposed and implemented in different applications, such as satellites, tactical communications, and quadrature amplitude madulation [sic] (QAM) dual polarized microwave radio. Nevertheless, no attempt was made in the past to quantify the probability of error of dual polarized transmission systems when such cancelers [sic] are used, nor were important issues such as stability and the dynamic behavior of algorithms controlling such cancelers [sic] studied. In this thesis, the error probability performance of dual polarized QAM transmission, for nondispersive fading channels and different configurations of bootstrapped cross-pol cancelers [sic], is derived and compared to the performance for other cancelers [sic]. Stability analyses of different canceler [sic] configurations are investigated, and an application of orthogonal perturbation sequences in controlling the bootstrapped cancelers [sic] is considered. It is shown that the error probability performance of the bootstrapped canceler [sic] is always better than that of other cancellers, such as the LMS canceler [sic]. It is also shown that, when the bootstrapped canceler [sic] is designed to meet certain conditions, it is asymptotically stable in converging to the calculated optimal points. Controlling the cancelers [sic] with adaptive algorithms using orthogonal dithering sequences is shown to be satisfactory; the canceler [sic] converges in the mean to the optimal condition. The results indicate that bootstrapped algorithms are faster than other algorithms. Considering the fact such cancelers [sic] do not require decision feedback for their operation, we can conclude that bootstrapped algorithms are not only advantageous for cross polarization cancelation [sic], but perhaps suitable for other adaptive signal processing applications, as well