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.