  The problem of choosing the optimal multipath components to be employed at a
minimum mean square error (MMSE) selective Rake receiver is considered for an
impulse radio ultra-wideband system. First, the optimal finger selection
problem is formulated as an integer programming problem with a non-convex
objective function. Then, the objective function is approximated by a convex
function and the integer programming problem is solved by means of constraint
relaxation techniques. The proposed algorithms are suboptimal due to the
approximate objective function and the constraint relaxation steps. However,
they perform better than the conventional finger selection algorithm, which is
suboptimal since it ignores the correlation between multipath components, and
they can get quite close to the optimal scheme that cannot be implemented in
practice due to its complexity. In addition to the convex relaxation
techniques, a genetic algorithm (GA) based approach is proposed, which does not
need any approximations or integer relaxations. This iterative algorithm is
based on the direct evaluation of the objective function, and can achieve
near-optimal performance with a reasonable number of iterations. Simulation
results are presented to compare the performance of the proposed finger
selection algorithms with that of the conventional and the optimal schemes.
