Recursive Spatial Multiplexing with a capacity-limited feedback channel

A realistic Recursive Spatial Multiplexing (RSM) scheme for the case of a wireless feedback channel with limited capacity is considered where the identifier for the critical subspaces are encoded using either Grassmannian or vector quantizers. Optimum and suboptimum encoding schemes are proposed and analyzed. The threshold for the eigenvalues of the channel matrix required in the receiver for determining the critical subspaces is chosen based on optimizing channel capacity and uncoded biterror rates within the inner transceiver. It is shown that the limited feedback channel capacity limits the RSM performance, critically determines the achievable bit-error rates and defines the range of signal-to-noise ratio values where RSM outperforms open-loop multiple-input multiple-output transmission schemes.