In this paper we address the problem of large dimension decoding in MIMO systems. The complexity of the optimal maximum likelihood detection makes it unfeasible in practice when the number of antennas, the channel impulse response length or the source constellation size become too high. We consider a MIMO system with finite constellation and model it as a system with sparse signal sources. We formulate the decoding problem as an underdetermined sparse source recovering problem and apply the L1-minimization to solve it. The resulting decoding scheme is applied to large MIMO systems and to frequency selective channel . We also review the computational cost of some L1-minimization algorithms. Simulation results show significant improvement compared to other existing receivers.