The Effect of Preprocessing to the Complexity of List Sphere Detector Algorithms

A list sphere detector (LSD) is an enhancement of a sphere detector (SD) that can be used to approximate the soft output MAP detector used in the detection of the multiple-input multiple-output (MIMO) signals. The LSD algorithm executes a tree search on the given lattice and returns a candidate list. The LSD algorithm complexity, i.e., the number of visited nodes in the search tree, can be decreased by applying proper ordering of the transmitted spatial streams in the detection. In this paper, we study the effect of two sophisticated preprocessing methods, the channel matrix column ordering based on Euclidean norm and the sorted QR decomposition (SQRD), to the performance and complexity of the LSD algorithms and compare them to the traditional QR decomposition (QRD). We show that the SQRD preprocessing is a simple way to decrease complexity of the LSD and it decreases the number of visited nodes approximately 20− 30% compared to the QRD which results in significant number of saved arithmetic operations in the LSD. We also show that the plain channel matrix column ordering is not feasible preprocessing method to be used with LSD in highly correlated channel realization.