An efficient regularized semi-blind estimator

This paper addresses the issue of the optimization of the regularization constant in semi-blind channel estimation techniques, in which the training sequence-based criterion is combined linearly with the blind subspace criterion. In such semi-blind estimation techniques, the optimization of the regularizing constant with respect to the channel estimation error is mandatory, otherwise, the expected improvement in performance could not be achieved. In this context, recent works proposed numerical methods for the setting of the regularization constant. However, these methods are often sub-optimum and involve high computational complexities. In this paper, we propose to optimize with respect to a regularizing matrix instead of a regularizing scalar. We prove that interestingly in this case, a closed-form expression for the optimum regularizing matrix exists, thereby avoiding iterative algorithms as for the conventional techniques. We also prove that the obtained scheme has slightly better performance in terms of mean square error and bit error rate while ensuring lower complexity.