In this paper novel subspace-based blind schemes are proposed and applied to the sparse channel identification problem. Moreover, adaptive sparse subspace tracking methods are proposed so as to provide efficient real-time implementations. The new algorithms exploit the subspace sparsity either via employing ℓ1-norm relaxation or through greedy-based optimization. The derived schemes have been tested in a Zero-Prefix Orthogonal Frequency Division Multiplexing (ZP-OFDM) system and it turns out that, compared to state-of-art existing schemes, they offer improved performance in terms of convergence rate and steady-state error.