Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random steering vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Performance analysis for a class of robust adaptive beamformers

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. Recently, worst-case approaches which consist of protecting the array's response in an ellipsoid centered around the nominal steering vector have been proposed. They amount to generalized (i.e. non necessarily diagonal) loading of the covariance matrix. In this paper, we present a theoretical analysis of the signal to interference plus noise ratio (SINR) for this class of robust beamformers, in the presence of random steering vector errors. A closed-form expression for the SINR is derived which is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Steering vector errors and diagonal loading

Diagonal loading is one of the most widely used and effective methods to improve robustness of adaptive beamformers. In this paper, we consider its application to the case of steering vector errors, i.e. when there exists a mismatch between the actual steering vector of interest and the presumed one. More precisely, we address the problem of optimally selecting the loading level with a view to maximise the signal to interference plus noise ratio in the presence of random steering vector errors. First, we derive an expression for the optimal loading for a given steering vector error and we show that this loading is negative. Next, this optimal loading is averaged with respect to the probability density function of the steering vector errors, yielding a very simple expression for the average optimal loading. Numerical simulations attest to the validity of the analysis and show that diagonal loading with the optimal loading factor derived herein provides a performance close to optimum

Computing price trends in sequential auctions

This paper compares various methods used for measuring price trends in sequential auctions and draws on index number theory. Data from wine auctions are used to show that different methods applied to the same data may lead to significantly différent conclusions. Moreover the same method can even lead to opposite results depending on the way pairs are selected within the set of similar objects sold sequentially. Finally, the number of identical objects being sold also influences the price trend.Sequential auctions, Price aggregation, Price indices

A Characterization of Stochastically Stable Networks

Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance that may be quite complex. When a 1/2-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2-pairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust network. We also show that the 1/2-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network.Network formation, Pairwise stability, Stochastic stability

The geography of innovation in the Luxembourg metropolitan region: an intra-regional approach

The main objective of the paper is to analyse the local determinants of innovation in the Luxembourg metropolitan region. We are particularly interested in the impact of the local milieu and characteristics of firms. Our paper addresses two specific research questions. Firstly, we examine the extent to which geographic space is a determinant of innovation for five intra-regional units based on an aggregation of municipalities. Secondly, we investigate whether innovation is dependent on accessibility to the mean centre. In both cases, we examine innovation propensity and innovation output using microdata from the Community Innovation Survey (CIS 2006) carried out in Luxembourg. The paper shows that space matters both in terms of spatial units and accessibility within the intra-regional context of Luxembourg. It provides, in particular, first evidence of a close link between the effects on innovation at the intra-regional level of firms? profiles and agglomeration externalities. Both favour innovation for firms from Luxembourg-City and, to a lesser extent, from the Suburban Area.intra-regional innovation; firms' profile; location factors; local polynomial regression; Luxembourg metropolitan region

Financing Higher Education with Students Loans - The crucial role of income-contingency and risk pooling

There are many economic and philosophical arguments supporting the introduction of student loans as a way to complement public financing and secure adequate resources for higher education, particularly in Europe. These arguments are briefly reviewed in this paper. But the case in favour of student loans largely rests on the capability to provide loans that are income-contingent. Indeed, income-contingent repayments are critical to both efficiendy (students and lenders should not be deterred due to excessive risk) and equity (contributions should be tailored to ex post ability to pay). But income-contingency comes at a cost that can be expressed as a risk premium that should be supported and shared between graduates and/or taxpayers. The central aim of this paper is to produce realistic estiamtes of such a risk, identifying the conditions for the implementation of an income-contingent loan scheme in order to channel additional private funding to higher education systems. How does low lifetime income and/or unemployment spells among higher education graduates translates into risk premia ? Results, derived from the analysis of Belgian earnings data, suggest that the risk premium ranges from 13% for university (ISCED 6-7) graduates to 26% for non-university (ISCED 5) ones. The paper further investigates the various ways of pooling and shifting this risk, while addressing the danger of public debt classification (ie, student loans classified as public) and adverse selection (ie, unsustainable pooling of high and low risk loans).Higher Education Finance; Income-contingent Loans; Risk premium; Risk poolong