Out-sphere decoder for non-coherent ML SIMO detection and its expected complexity

In multi-antenna communication systems, channel information is often not known at the receiver. To fully exploit the bandwidth resources of the system and ensure the practical feasibility of the receiver, the channel parameters are often estimated and then employed in the design of signal detection algorithms. However, sometimes communication can occur in an environment where learning the channel coefficients becomes infeasible. In this paper we consider the problem of maximum-likelihood (ML)-detection in singleinput multiple-output (SIMO) systems when the channel information is completely unavailable at the receiver and when the employed signalling at the transmitter is q-PSK. It is well known that finding the solution to this optimization requires solving an integer maximization of a quadratic form and is, in general, an NP hard problem. To solve it, we propose an exact algorithm based on the combination of branch and bound tree search and semi-definite program (SDP) relaxation. The algorithm resembles the standard sphere decoder except that, since we are maximizing we need to construct an upper bound at each level of the tree search. We derive an analytical upper bound on the expected complexity of the proposed algorithm

Modeling the kinetics of hybridization in microarrays

Conventional fluorescent-based microarrays acquire data after the hybridization phase. In this phase the targets analytes (i.e., DNA fragments) bind to the capturing probes on the array and supposedly reach a steady state. Accordingly, microarray experiments essentially provide only a single, steady-state data point of the hybridization process. On the other hand, a novel technique (i.e., realtime microarrays) capable of recording the kinetics of hybridization in fluorescent-based microarrays has recently been proposed in [5]. The richness of the information obtained therein promises higher signal-to-noise ratio, smaller estimation error, and broader assay detection dynamic range compared to the conventional microarrays. In the current paper, we develop a probabilistic model of the kinetics of hybridization and describe a procedure for the estimation of its parameters which include the binding rate and target concentration. This probabilistic model is an important step towards developing optimal detection algorithms for the microarrays which measure the kinetics of hybridization, and to understanding their fundamental limitations

An H-infinity based lower bound to speed up the sphere decoder

It is well known that maximum-likelihood (ML) decoding in many digital communication schemes reduces to solving an integer least problem, which is NP hard in the worst-case. On the other hand, it has recently been shown that, over a wide range of dimensions and signal-to-noise ratios (SNR), the sphere decoder can be used to find the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity of sphere decoding becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In recent work M. Stonjic et al. (2005), we have targeted these two regimes and attempted to find faster algorithms by employing a branch-and-bound technique based on convex relaxations of the original integer least-squares problem. In this paper, using ideas from H∞ estimation theory, we propose new lower bounds that are generally tighter than the ones obtained in M. Stonjic et al. (2005). Simulation results snow the advantages, in terms of computational complexity, of the new H∞-based branch-and-bound algorithm over the ones based on convex relaxation, as well as the original sphere decoder

A branch and bound approach to speed up the sphere decoder

In many communications applications, maximum-likelihood decoding reduces to solving an integer least-squares problem which is NP hard in the worst-case. However, as has recently been shown, over a wide range of dimensions and SNRs, the sphere decoder can be used to find the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. We target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoder. The search tree is pruned by computing lower bounds on the possible optimal solution as we proceed down the tree. We observe a trade-off between the computational complexity required to compute the lower bound and the size of the pruned tree: the more effort spent computing a tight lower bound, the more branches that can be eliminated in the tree. Thus, even though it is possible to prune the search tree (and hence the number of points visited) by several orders of magnitude, this may be offset by the computations required to perform the pruning. All of which suggests the need for computationally-efficient tight lower bounds. We present three different lower bounds (based on spherical-relaxation, polytope-relaxation and duality), simulate their performances and discuss their relative merits

PEP Analysis of the SDP Based Joint Channel Estimation and Signal Detection

In multi-antenna communication systems, channel information is often not known at the receiver. To fully exploit bandwidth resources of the system and ensure practical feasibility of the receiver, channel parameters are often estimated blindly and then employed in the design of signal detection algorithms. Instead of separating channel estimation from signal detection, in this paper we focus on the joint channel estimation and signal detection problem in a single-input multiple-output (SIMO) system. It is well known that finding solution to this optimization requires solving an integer maximization of a quadratic form and is, in general, an NP hard problem. To solve it, we propose an approximate algorithm based on the semi-definite program (SDP) relaxation. We derive a bound on the pairwise probability of error (PEP) of the proposed algorithm and show that, the algorithm achieves the same diversity as the exact maximum-likelihood (ML) decoder. The computed PEP implies that, over a wide range of system parameters, the proposed algorithm requires moderate increase in the signal-to-noise ratio (SNR) in order to achieve performance comparable to that of the ML decoder but with often significantly lower complexit

Gender Differences in Academic Efficacy across STEM Fields

Cultural processes can reduce self-selection into math and science fields, but it remains unclear how confidence in computer science develops, where women are currently the least represented in STEM (science, technology, engineering, and mathematics). Few studies evaluate both computer skills and self-assessments of skill. In this paper, we evaluate gender differences in efficacy across three STEM fields using a data set of middle schoolers, a particularly consequential period for academic pathways. Even though girls and boys do not significantly differ in terms of math grades and have similar levels of computer skill, the gender gap in computer efficacy is twice as large as the gap for math. We offer support for disaggregation of STEM fields, so the unique meaning making around computing can be addressed

Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

Optimal quantum detectors for unambiguous detection of mixed states

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.Comment: Submitted to Phys. Rev.

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