Post-user-selection quantization and estimation of correlated Frobenius and spectral channel norms

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented.