  We propose a low complexity complex valued Sphere Decoding (CV-SD) algorithm,
referred to as Circular Sphere Decoding (CSD) which is applicable to
multiple-input multiple-output (MIMO) systems with arbitrary two dimensional
(2D) constellations. CSD provides a new constraint test. This constraint test
is carefully designed so that the element-wise dependency is removed in the
metric computation for the test. As a result, the constraint test becomes
simple to perform without restriction on its constellation structure. By
additionally employing this simple test as a prescreening test, CSD reduces the
complexity of the CV-SD search. We show that the complexity reduction is
significant while its maximum-likelihood (ML) performance is not compromised.
We also provide a powerful tool to estimate the pruning capacity of any
particular search tree. Using this tool, we propose the Predict-And-Change
strategy which leads to a further complexity reduction in CSD. Extension of the
proposed methods to soft output SD is also presented.
