On overloaded vector precoding for single-user MIMO channels

We address the possibility of overloaded vector precoding in single user MIMO channels, i.e. the number of data streams is larger than the minimum of the number of antennas at transmitter and receiver side.We find that the convex vector precoding introduced in allows for overloading while, with a certain probability, keeping the received signal free of interference. We find that the probability that overloading is not possible decays exponentially with the size of the system as long as the number of data streams is less than twice the minimum number of antennas. We give an explicit formula to calculate this probability for any antenna configuration in presence of correlated Rayleigh fading. Although overloading comes with the need for increased transmitted power, we show by means of the replica method that overloading up to 22% yields better spectral and power efficiency than without overload and spatial matched filter processing at the receiver.