In this paper, we focus on the adaptive identification of sparse SIMO channels in a blind context. More specifically, we propose different adaptive implementations of the sparse cross relation (SCR) method then we compare and analyse their performances in terms of convergence rate, estimation accuracy and robustness. The SCR method proceeds as follows: at first a blind approach based on the cross-relation criterion is derived for channel estimation. Secondly, to take into account the channel sparsity, the criterion is penalized by adding an extra lp norm term in order to enforce the sparsity of the desired solution. The corresponding algorithm (i.e. SCR) is shown to outperform the original CR method in terms of estimation accuracy and robustness to channel order over-estimation errors. The adaptive versions of the SCR proposed in this paper are shown to preserve the main advantages of the batch technique but suffer from low convergence rate for large dimensional systems.