Hardware Implementation of the Preprocessing QR-Decomposition for the Soft-Output MIMO Detection with Multiple Tree Traversals

Compared with the single tree detector, the layered orthogonal lattice detector (LORD), developed by Siti et al., is a well-known soft-output multiple input multiple output detector to exploit M parallel tree traversals to deliver data with M times of detection throughput rate. The preprocessing QR-decomposition (QRD) of the M-by-M channel matrix for the single tree detector is of complexity proportional to M3. However, the preprocessing QRD for the LORD needs to compute the M permuted channel matrices that are constructed from the original M-by-M channel matrix through the root conditioning criterion. The original LORD algorithm for this root conditioning QRD (RC-QRD) relies on the Gram-Schmidt orthogonalization and is of complexity proportional to M4 for large M. In this brief, we apply the Givens rotation and take advantage of the relationships among the M permuted matrices to develop an RC-QRD algorithm with complexity proportional to M3. Furthermore, when M is large, our proposed RC-QRD algorithm requires the number of real Givens rotations about 1.8 times necessary for computing a conventional matrix QRD. Also, for M = 4, our proposed RC-QRD hardware architecture requires gate count 2.1 times that required by the conventional triangular systolic array to compute a matrix QRD. Accordingly, with only about two times of complexity for the preprocessing RC-QRD, the LORD is able to perform M tree traversals to deliver data with M times of throughput rate.