Vector precoding for singular MIMO channels

We propose a method for vector precoding suited to singular multiple-input multiple-output (MIMO) channels were the number of data streams is larger than the number of transmit antennas. We calculate the probability that our method, due to the channel singularity, fails to provide the data without crosstalk to the receiver, analytically, and show that this probability goes to zero exponentially with the size of the MIMO system if the number of QPSK data streams in smaller than twice the number of transmit antennas.