On the Equivalence Between Eigen and Channel Inversion Based Precoders

Multi-user MIMO precoding is crucial in modern and next generation
wireless communication systems. In this paper the equivalence between two
linear precoding methods using closed form solutions is investigated. The first
one is the regularized zero forcing (RZF) algorithm and the second one is signal to leakage and noise ratio (SLNR). Three studies are presented: 1) comparison between the regularized and non-regularized versions; 2) finding a good regularization factor that can fit with all methods; 3) to present the equivalence of the methods in certain cases and the superiority of SLNR over RZF for user cases with more than a single antenna. A simple mathematical proof of the equivalence between RZF and SLNR beamformer implementations for the single antenna user case in a multi-user transmission scenario is presented: this matches simulation results.