In this work, we investigate an efficient numerical approach for solving higher
order statistical methods for blind and semi-blind signal recovery from non-ideal channels.
We develop numerical algorithms based on convex optimization relaxation for minimization of
higher order statistical cost functions. The new formulation through convex relaxation
overcomes the local convergence problem of existing gradient descent based algorithms and
applies to several well-known cost functions for effective blind signal recovery including
blind equalization and blind source separation in both single-input-single-output (SISO)
and multi-input-multi-output (MIMO) systems. We also propose a fourth order pilot based
cost function that benefits from this approach. The simulation results demonstrate that our
approach is suitable for short-length packet data transmission using only a few pilot
symbols.