Statistical prefilter design for MIMO ZF and MMSE receivers based on majorization theory

Recently, the authors proposed statistical prefilters for MMSE and ZF receivers that minimize SER (Kiessling, M. et al., IEEE WCNC, 2003; IEEE VTC, 2003). We now give a general derivation of their structure based on majorization theory. For both receiver types, it is shown that the optimal prefilter essentially transmits on the strongest long-term eigenmodes of the channel with proper power allocation. Moreover, simple closed-form power allocation schemes are presented for Rayleigh and Ricean fading environments. Interestingly, while the statistical prefilters exhibit the same basic mathematical structure as their short-term counterparts, they require only statistical information of the correlation properties and the Ricean component of the channel. Monte-Carlo simulations show that the proposed filters can achieve a considerable performance gain. Specifically, it is demonstrated that they can completely counteract the SER degradation due to a Ricean channel component.