Abstract
Various efficient generalized sphere decoding (GSD) algorithms have been proposed to approach optimal ML performance for underdetermined linear systems, by transforming the original problem into the full-column-rank one so that standard SD can be fully applied. However, their design parameters are heuristically set based on observation or the possibility of an ill-conditioned transformed matrix can affect their searching efficiency. This paper presents a better transformation to alleviate the ill-conditioned structure and provides a systematic approach to select design parameters for various GSD algorithms in order to high efficiency. Simulation results on the searching performance confirm that the proposed techniques can provide significant improvement.
Highlights
Sphere decoding (SD) is an efficient searching method to obtain maximum-likelihood (ML) solution for NP-hard integer least-square (ILS) problems
This paper presents a better transformation to alleviate the ill-conditioned structure and provides a systematic approach to select design parameters for various generalized sphere decoding (GSD) algorithms in order to high efficiency
An improved version of λ-GSD algorithm was first proposed for underdetermined linear systems by transforming the original problem into a full-column-rank one with better structure, so that standard SD can be efficiently applied
Summary
Sphere decoding (SD) is an efficient searching method to obtain maximum-likelihood (ML) solution for NP-hard integer least-square (ILS) problems. When the problem is underdetermined, zero elements appear in the diagonal terms of the upper-triangular matrix generated by QR or Cholesky decomposition before searching, and the standard SD searching cannot apply Such underdetermined ILS problems arise in many areas, e.g., MIMO detection with the number of transmit antennas larger than that of receiver antennas; MIMO detection with strongly correlated channel gains [5] or MUD for overloaded CDMArelated systems [8]. For non-constantmodulus ones, e.g., 16/64QAM, they have to be transformed into multiple QPSKs, leading to larger dimension and increased complexity To avoid this problem and obtain better efficiency, the λ-GSD algorithm proposed in [8], performs transformation without expanding the size of M-ary QAMs. Unlike the GSD algorithms in [6,7], the design parameter can be is upper-bounded [8,13] to guarantee near-ML performance for high QAMs and has little effect on the efficiency of λ-GSD [14].
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