Intrinsic Subspace Convergence in TDD MIMO Communication

In numerical linear algebra, students encounter early the iterative power method, which finds eigenvectors of a matrix from an arbitrary starting point through repeated normalization and multiplications by the matrix itself. In practice, more sophisticated methods are used nowadays, threatening to make the power method a historical and pedagogic footnote. However, in the context of communication over a time-division duplex (TDD) multiple-input multiple-output (MIMO) channel, the power method takes a special position. It can be viewed as an intrinsic part of the uplink and downlink communication switching, enabling estimation of the eigenmodes of the channel without extra overhead. Generalizing the method to vector subspaces, communication in the subspaces with the best receive and transmit signal-to-noise ratio (SNR) is made possible. In exploring this intrinsic subspace convergence (ISC), we show that several published and new schemes can be cast into a common framework where all members benefit from the ISC.