This paper aims at studying a semi-blind channel estimation scheme based on the subspace method or a carefully weighted linear prediction approach. The corresponding (composite) semi-blind cost functions result from a linear combination of the training-based cost function and a blind cost function. For each blind method, we show how to calculate the asymptotic estimation error. Therefore, by minimizing this error, we can properly tune the K-dimensional regularizing vector introduced in the composite semi-blind criterion (for K active users in the uplink). The asymptotic estimation error minimization is a K-variable minimization problem, which is a complex issue to deal with. We explicitly show under what conditions this problem boils down to K single-variable minimization problems. Our discussion is not limited to theoretical analyses. Simulation results performed in a realistic context (UMTS-TDD mode) are provided. In particular, we conclude about the potential of the proposed approach in real communication systems.