Algorithmic solutions for pilot design optimization in arbitrarily correlated scenarios

We consider optimized design of training sequences, given knowledge of the channel and noise statistics. Recently, pilot designs considering the end performance of the channel estimate, have been proposed, both optimizing the average performance and the performance at a certain outage level. Unfortunately, these problems, as well as previously proposed designs optimizing the channel estimation MSE, are non-convex for arbitrary channel and noise correlations so additional assumptions have been introduced in the literature to be able to find tractable solutions. Here, we show that arbitrarily correlated scenarios can easily be handled by resorting to alternating optimization, for all the previously mentioned problem formulations. Furthermore, we numerically compare the average and outage performance of the proposed algorithms, to alternative solutions adopted from the literature.