A Modified KZ Reduction Algorithm

The Korkine-Zolotareff (KZ) reduction has been used in communications and cryptography. In this paper, we modify a very recent KZ reduction algorithm proposed by Zhang et al., resulting in a new algorithm, which can be much faster and more numerically reliable, especially when the basis matrix is ill conditioned.Comment: has been accepted by IEEE ISIT 201

A Linearithmic Time Algorithm for a Shortest Vector Problem in Compute-and-Forward Design

We propose an algorithm with expected complexity of \bigO(n\log n) arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm is more efficient than the best known algorithms with proved complexity.Comment: It has been submitted to ISIT 201

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

Distributed Cooperative Localization in Wireless Sensor Networks without NLOS Identification

In this paper, a 2-stage robust distributed algorithm is proposed for cooperative sensor network localization using time of arrival (TOA) data without identification of non-line of sight (NLOS) links. In the first stage, to overcome the effect of outliers, a convex relaxation of the Huber loss function is applied so that by using iterative optimization techniques, good estimates of the true sensor locations can be obtained. In the second stage, the original (non-relaxed) Huber cost function is further optimized to obtain refined location estimates based on those obtained in the first stage. In both stages, a simple gradient descent technique is used to carry out the optimization. Through simulations and real data analysis, it is shown that the proposed convex relaxation generally achieves a lower root mean squared error (RMSE) compared to other convex relaxation techniques in the literature. Also by doing the second stage, the position estimates are improved and we can achieve an RMSE close to that of the other distributed algorithms which know \textit{a priori} which links are in NLOS.Comment: Accepted in WPNC 201

On the sensitivity of the SR decomposition

AbstractFirst-order componentwise and normwise perturbation bounds for the SR decomposition are presented. The new normwise bounds are at least as good as previously known results. In particular, for the R factor, the normwise bound can be significantly tighter than the previous result