Minimum Mean Square Error Vector Precoding

We derive the minimum mean square error (MMSE) solution to vector precoding for frequency flat multiuser scenarios with a centralized multi-antenna transmitter. The receivers employ a modulo operation, giving the transmitter the additional degree of freedom to choose a perturbation vector. Similar to existing vector precoding techniques, the optimum perturbation vector is found with a closest point search in a lattice. The proposed MMSE vector precoder does not, however, search for the perturbation vector resulting in the lowest transmit energy, as proposed in all previous contributions on vector precoding, but finds an optimum compromise between noise enhancement and residual interference. We present simulation results showing that the proposed technique outperforms existing vector precoders, as well as the MMSE Tomlinson-Harashima precoder.