CLLL lattice reduction algorithm

Complex LLL (CLLL) lattice reduction algorithm for complexed-valued lattices

This is the MATLAB code for the complex LLL (CLLL) algorithm:

Ying Hung Gan, Cong Ling, and Wai Ho Mow, “Complex lattice reduction algorithm for low-complexity full-diversity MIMO detection,” IEEE Trans. Signal Processing, vol. 57, pp. 2701-2710, July 2009. (http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4787140)

Function description:
B_reduced = CLLL(B)
Input:
B - Basis matrix with columns being basis vectors
Output:
B_reduced - Reduced basis matrix with columns being basis vectors

Brief introduction of CLLL:
The traditional Lenstra-Lenstra-Lovasz (LLL) reduction algorithm was originally introduced for reducing real lattice bases, while the CLLL algorithm is developed for directly reducing the bases of a complex lattice. When applied in lattice-reduction-aided detectors for multi-input multi-output (MIMO) systems where a complex lattice is naturally defined by a complex-valued channel matrix, the CLLL algorithm can reduce the complexity by nearly 50% compared to the traditional LLL algorithm.