Multi-resolution broadcasting over the Grassmann and stiefel manifolds

We consider the design of space-time codes for multi-resolution multiple-input multiple-output (MIMO) broadcast communication systems. Two classes of receivers are considered: high-resolution (HR) receivers, which have access to reliable channel state information (CSI) and can perform coherent detection, and low-resolution (LR) receivers which do not have access to CSI and can only perform non-coherent detection. We propose a layered encoding structure, whereby, for the LR receivers, the transmitted codewords are chosen to be points on the Grassmann manifold whereas, for the HR receivers, incremental information is encoded in the particular bases of the transmitted codewords, thereby representing points on the Stiefel manifold. For the HR receivers, we develop a computationally-efficient two-step detector. Using this detector, we show that the proposed structure enables reliable coherent communication of the incremental HR information without compromising the reliability with which the basic LR information is non-coherently communicated. We also show that this structure enables full diversity to be achieved for both LR and HR receivers. Finally, we show that this structure achieves the maximum number of degrees of freedom for non-coherent LR channels and coherent HR channels with unitarily-constrained input signals.