A low-complexity Generalized Sphere Decoding Approach for Underdetermined MIMO Systems

For underdetermined MIMO systems, sphere decoding (SD) fails due to zero diagonal elements in the upper-triangular matrix of the QR or Cholesky factorization of the underdetermined channel matrix. This paper presents a low-complexity generalized sphere decoding (GSD) approach by transforming the original underdetermined problem into the full-column-rank one so that standard SD can be directly applied on the transformed problem. As the introduced transformation maintains the original problem dimension, the proposed GSD algorithm provides significant reduction in complexity as compared to other GSD schemes, especially for M-QAM with large signaling constellation. Performance analysis shows that the proposed GSD algorithm can achieve or approach the optimum maximum-likelihood decoding (MLD) performance by proper selection of design parameters.