On the equivalence between SLNR and MMSE precoding schemes with single-antenna receivers

This letter considers transmit precoding schemes based on the maximum signal-to-leakage-and-noise ratio (SLNR) in multiuser MIMO systems with single-antenna receivers. The closed-form solution of SLNR design is generally given in the form of the eigenvector associated to the maximum eigenvalue. In this letter, analytic expressions of SLNR-based solutions and resulting SLNR are derived for a generic power allocation (GPA). The solution is shown to be a function of user-allocated power and an arbitrary phase shift. Under equal power allocation (EPA), the SLNR precoding scheme is shown to be equivalent to the minimum mean square error (MMSE) precoding scheme. Several useful implications in terms of the possible extension of existing algorithms and performance analysis are also discussed.