MMSE Based Preprocessing and Its Variations for Closest Point Search

The sphere decoding (SD) is a category of algorithms finding the closest lattice point and known to have the expected complexity approximately cubic in the dimension of the lattice point to be searched for a medium-to-high range of signal-to-noise ratios (SNRs). But the expected complexity depends highly on SNR and the portion of high-ordered terms (higher ordered terms than cubic) of it increases rapidly as SNR decreases for low SNRs. The number of points visited by SD is influenced by the processing done before starting to search a closest point. In this paper the minimum mean square error (MMSE) sorted QR-decomposition (SQRD) is proposed as a preprocessing for SD algorithm. By mathematical investigation of MMSE extended matrix we find out that MMSE extension can be generalized and suggest variations of MMSE-SQRD as candidates of the preprocessing for SD. MMSE-SQRD and its variations reduce considerably the dependency of the complexity of SD on SNR.