Challenges to subcarrier MIMO precoding and equalisation with smooth phase responses

Precoding for multiple-input multiple-output orthogonal frequency division multiplexing systems is often based on a per-subcarrier singular value decomposition, where phase smoothing is applied to the singular vectors that form the transmit beamformers. We show that such a smooth solution can ideally be based on an analytic singular value decomposition, but for estimated channel matrices is beset by challenges that deny a smooth or even continuous evolution of singular vectors with frequency. We show how such problems can be bypassed by admitting complex-valued singular values or fractional delays, and by exploiting a method analogous to the analytic eigenvalue decomposition to approximate ground truth analytic singular vectors from estimated channel matrices. We present examples and demonstrate some of the capabilities of a proposed algorithm through simulations.