Non-convex projection algorithms for communication systems

Non-convex projection algorithms are one kind of problem solving method. The purpose of the algorithms is to find a point common to a set of non-convex sets. Depending on the number of non-convex sets involved, the non-convex projection algorithms are categorized as a generalized projection (GP) algorithm when the number of sets are two, and an extended generalized projection (EGP) algorithm when the number of sets are more than two. A performance measure is very important for the non-convex projection algorithms in that it describes the performance of the algorithms.; In this thesis, a new performance measure, summed squared distance error (SSDE), is introduced for the non-convex projection algorithms. Compared to the standard performance measure, summed distance error (SDE), the new performance measure provides more information needed by the algorithms to converge to a point in the intersection of the non-convex sets involved. Therefore, algorithms using the SSDE have better performance than those with the SDE.; As a special case of the EGP algorithm, a parallel generalized projection algorithm (PGPA) is investigated in this thesis. In the PGPA, the SSDE is further proven to be better than the SDE in that it provides an analytical solution of the optimal relaxation parameter. This is an important parameter in the non-convex projection algorithms. The analytical solution of the optimal relaxation parameter liberates the PGPA from a numerical search which requires extensive computational power and time ordinarily required by the SDE, and results in a big calculation time saving. It is also proven that with higher probability, the real distance error to the real signal achieved based the SSDE is smaller than that of the SDE.; In the PGPA, an approximate weight optimization method is also presented to get a weighted summation of the projections onto all involved sets. Since each set is different in size, shape and position, projection of an arbitrary point onto each set has a different distance to the same feasible solution. By choosing appropriate weights, an optimal updating direction could be achieved. Therefore, better performance is obtained. Simulation results from interference suppression problems in direct sequence spread spectrum (DS/SS) communication systems show that the PGPA with the approximate weight optimization method has a significant performance improvement over the PGPA without weight optimization, and is inferior to the theoretical weight optimization method with a tolerable difference.; One application of the non-convex projection algorithms in blind channel equalization problems is discussed in this thesis. The non-convex projection algorithms are compared to some popular blind equalization algorithms such as Sato algorithm and Godard algorithms. Simulation results show that the PGPA has better performance than the Sato and Godard algorithms in terms of a smaller steady state excess mean squared error (MSE) and a faster convergence rate. In the binary case, the PGPA has even a better performance than the least mean square (LMS) algorithm with a training sequence under the same channel condition. Simulation results also show that a theoretical method to find an optimal setting for the PGPA is a key to get a good equalization result. The theoretical method of optimal setting will be mainly the future research direction.