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

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

National records of 3000 European bee and hoverfly species: A contribution to pollinator conservation

Pollinators play a crucial role in ecosystems globally, ensuring the seed production of most flowering plants. They are threatened by global changes and knowledge of their distribution at the national and continental levels is needed to implement efficient conservation actions, but this knowledge is still fragmented and/or difficult to access. As a step forward, we provide an updated list of around 3000 European bee and hoverfly species, reflecting their current distributional status at the national level (in the form of present, absent, regionally extinct, possibly extinct or non-native). This work was attainable by incorporating both published and unpublished data, as well as knowledge from a large set of taxonomists and ecologists in both groups. After providing the first National species lists for bees and hoverflies for many countries, we examine the current distributional patterns of these species and designate the countries with highest levels of species richness. We also show that many species are recorded in a single European country, highlighting the importance of articulating European and national conservation strategies. Finally, we discuss how the data provided here can be combined with future trait and Red List data to implement research that will further advance pollinator conservation