A general combinatorial sphere decoder and its application

The conventional problem of searching the shortest vector z of a N-dimensional lattice L(H) with generating matrix HisinR
^NtimesM
is considered in a more general setting. There are P generating matrices H
_i
isinR
^NtimesM
(i=1,2,...,P) of the P lattices L(H
_i
). For a (bounded) integer vector bisinZ
^M
, we obtain P lattice points H
_i
b. Let d
_i
be the Euclidean norm of H
_i
b. The problem of interest is how to search for a vector b so that the maximum of d
_i
is minimized. We propose a new sphere decoder called combinatorial sphere decoder (CSD) to solve this problem. One of the applications of the new CSD is presented in detail to show its effectiveness