Recent channel measurement campaigns have revealed that at high carrier frequencies (10GHz and above) MIMO channels exhibit sparsity structure, i.e., a few dominant propagation paths and, in some cases, it can also reduce to a single path, yet very directive, wireless channel. In this work, we leverage the sparsity feature into the development of sparse-MIMO channel estimator and show, how an adaptive l1-optimization method can greatly improve the estimation error.