A quadratic programming problem arising from vector precoding in wireless communications

A quadratic programming problem is studied in the limit of asymptotically large kernel matrices by means of the replica method. It is found that inverse Wishart kernels are - within the validity range of the replica symmetric solution - asymptotically invariant to Cartesian relaxations. In the context of vector precoding for wireless communication systems with dual antenna arrays, so-called MIMO systems, this implies that adding more transmit antennas cannot reduce the minimum required transmit energy per bit significantly. By contrast, a new convex relaxation is proposed and shown to be a practical and useful method.