  This letter proposes the inverse LDM' and LU factorizations of a matrix
partitioned into 2x2 blocks, which include the square-root and division free
version. The proposed squareroot and division free inverse LDM' factorization
is applied to compute the initial estimation error covariance matrix Q for the
recursive V-BLAST algorithm, which can save K-1 divisions (where K is the
number of transmit antennas), and requires about the same computational
complexity as the corresponding algorithm to compute Q in the existing
recursive V-BLAST algorithm [8], [9]. The proposed square-root and division
free inverse LDM' factorization can also be applied to propose the square-root
and division free implementation for the squareroot V-BLAST algorithm in [5],
where the wide-sense Givens rotation in [14] is utilized. With respect to the
existing squareroot V-BLAST algorithms [5], [6], the proposed square-root and
division free V-BLAST algorithm requires about the same computational
complexity, and can avoid the square-root and division operations.
