On the Success Probability of the Box-Constrained Rounding and Babai Detectors

In communications, one frequently needs to detect a parameter vector \hbx in a box from a linear model. The box-constrained rounding detector \x^\sBR and Babai detector \x^\sBB are often used to detect \hbx due to their high probability of correct detection, which is referred to as success probability, and their high efficiency of implimentation. It is generally believed that the success probability P^\sBR of \x^\sBR is not larger than the success probability P^\sBB of \x^\sBB. In this paper, we first present formulas for P^\sBR and P^\sBB for two different situations: \hbx is deterministic and \hbx is uniformly distributed over the constraint box. Then, we give a simple example to show that P^\sBR may be strictly larger than P^\sBB if \hbx is deterministic, while we rigorously show that P^\sBR\leq P^\sBB always holds if \hbx is uniformly distributed over the constraint box.Comment: to appear in ISIT 201

Improved Maximum Likelihood Detection through Sphere Decoding combined with Box Optimization

this is the author’s version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing, [VOL 98, may 14] DOI 10.1016/j.sigpro.2013.11.041Sphere Decoding is a popular Maximum Likelihood algorithm that can be used to detect signals coming from multiple-input, multiple-output digital communication systems. It is well known that the complexity required to detect each signal with the Sphere Decoding algorithm may become unacceptable, especially for low signal-to-noise ratios. In this paper, we describe an auxiliary technique that drastically decreases the computation required to decode a signal. This technique was proposed by Stojnic, Hassibi and Vikalo in 2008, and is based on using continuous box-bounded minimization in combination with Sphere Decoding. Their implementation is, however, not competitive due to the box minimization algorithm selected. In this paper we prove that by judiciously selecting the box minimization algorithm and tailoring it to the Sphere Decoding environment, the computational complexity of the resulting algorithm for low signal-to-noise ratios is better (by orders of magnitude) than standard Sphere Decoding implementations. & 2013 Elsevier B.V. All rights reserved.This work has been partially funded by Universitat Politecnica de Valencia through Programa de Apoyo a la Investigacion y Desarrollo de la UPV (PAID-06-11) and (PAID-05-12), by Generalitat Valenciana through projects PROMETEO/2009/013 and Ayudas para la realizacion de proyectos de I+D para grupos de investigacion emergentes GV/2012/039, and by Ministerio Espanol de Economia y Competitividad through project TEC2012-38142-C04.García Mollá, VM.; Vidal Maciá, AM.; González Salvador, A.; Roger Varea, S. (2014). Improved Maximum Likelihood Detection through Sphere Decoding combined with Box Optimization. Signal Processing. 98:284-294. https://doi.org/10.1016/j.sigpro.2013.11.041S2842949

Maximum likelihood soft-output detection through Sphere Decoding combined with box optimization

This is the author’s version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing 125 (2016) 249–260. DOI 10.1016/j.sigpro.2016.02.006.This paper focuses on the improvement of known algorithms for maximum likelihood soft-output detection. These algorithms usually have large computational complexity, that can be reduced by using clipping. Taking two well-known soft-output maximum likelihood algorithms (Repeated Tree Search and Single Tree Search) as a starting point, a number of modifications (based mainly on box optimization techniques) are proposed to improve the efficiency of the search. As a result, two new algorithms are proposed for soft-output maximum likelihood detection. One of them is based on Repeated Tree Search (which can be applied with and without clipping). The other one is based on Single Tree Search, which can only be applied to the case with clipping. The proposed algorithms are compared with the Single Tree Search algorithm, and their efficiency is evaluated in standard detection problems (4 4 16-QAM and 4 4 64-QAM) with and without clipping. The results show that the efficiency of the proposed algorithms is similar to that of the Single Tree Search algorithm in the case 4 4 16-QAM; however, in the case 4 4 64- QAM, the new algorithms are far more efficient than the Single Tree Search algorithm. & 2016 Elsevier B.V. All rights reserved.This work has been partially funded by Generalitat Valenciana through the projects ISIC/2012/006 and PROMETEO II/2014/003, and by Ministerio Espanol de Economia y Competitividad through the project TEC2012-38142-C04 and through the Grant RACHEL TEC2013-47141-C4-4-R.García Mollá, VM.; Simarro Haro, MDLA.; Martínez Zaldívar, FJ.; González Salvador, A.; Vidal Maciá, AM. (2016). Maximum likelihood soft-output detection through Sphere Decoding combined with box optimization. Signal Processing. 125:249-260. https://doi.org/10.1016/j.sigpro.2016.02.006S24926012