On the design of real and complex fir filters with flatness and peak error constraints using semidefinite programming

This paper studies the problem of designing digital finite duration impulse response (FIR) filters with prescribed flatness and peak error constraints using semidefinite programming (SDP). SDP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. This property is utilized for the optimal minimax and least squares (LS) design of linear-phase and low-delay FIR filters with prescribed magnitude flatness and peak design error, which are formulated as a set of linear equality and convex quadratic inequality constraints, respectively. A method for structurally imposing these equality constraints in the SDP formulation is also proposed. Using these results, the design approach is further extended to the design of constrained complex coefficient FIR filters and variable digital filters (VDFs). Design examples are given to demonstrate the effectiveness of the approach.published_or_final_versio

Optimal design of all-pass variable fractional-delay digital filters

This paper presents a computational method for the optimal design of all-pass variable fractional-delay (VFD) filters aiming to minimize the squared error of the fractional group delay subject to a low level of squared error in the phase response. The constrained optimization problem thus formulated is converted to an unconstrained least-squares (LS) optimization problem which is highly nonlinear. However, it can be approximated by a linear LS optimization problem which in turn simply requires the solution of a linear system. The proposed method can efficiently minimize the total error energy of the fractional group delay while maintaining constraints on the level of the error energy of the phase response. To make the error distribution as flat as possible, a weighted LS (WLS) design method is also developed. An error weighting function is obtained according to the solution of the previous constrained LS design. The maximum peak error is then further reduced by an iterative updating of the error weighting function. Numerical examples are included in order to compare the performance of the filters designed using the proposed methods with those designed by several existing methods

Online Learning Models for Content Popularity Prediction In Wireless Edge Caching

Caching popular contents in advance is an important technique to achieve the low latency requirement and to reduce the backhaul costs in future wireless communications. Considering a network with base stations distributed as a Poisson point process (PPP), optimal content placement caching probabilities are derived for known popularity profile, which is unknown in practice. In this paper, online prediction (OP) and online learning (OL) methods are presented based on popularity prediction model (PPM) and Grassmannian prediction model (GPM), to predict the content profile for future time slots for time-varying popularities. In OP, the problem of finding the coefficients is modeled as a constrained non-negative least squares (NNLS) problem which is solved with a modified NNLS algorithm. In addition, these two models are compared with log-request prediction model (RPM), information prediction model (IPM) and average success probability (ASP) based model. Next, in OL methods for the time-varying case, the cumulative mean squared error (MSE) is minimized and the MSE regret is analyzed for each of the models. Moreover, for quasi-time varying case where the popularity changes block-wise, KWIK (know what it knows) learning method is modified for these models to improve the prediction MSE and ASP performance. Simulation results show that for OP, PPM and GPM provides the best ASP among these models, concluding that minimum mean squared error based models do not necessarily result in optimal ASP. OL based models yield approximately similar ASP and MSE, while for quasi-time varying case, KWIK methods provide better performance, which has been verified with MovieLens dataset.Comment: 9 figure, 29 page

Mapping prior information onto LMI eigenvalue-regions for discrete-time subspace identification

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constraint the possible locations of the eigenvalues of the discrete-time model. Then, we show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.Comment: Under revie

A Comparison of Optimization Techniques for Power Patterns with Low Sidelobes Generated by Linear Arrays with Efficient Excitation Distributions

This is the peer reviewed version of the following article: S. Kyle Smith; Julio C. Brégains; Kathleen L. Melde; Francisco Ares " comparison of optimization techniques for power patterns with low sidelobes generated by linear arrays with efficient excitation distributions", Microwave and Optical Technology Letters, 57 - 60 Volume: 45, Issue: 1, Apr. 2005, which has been published in final form at DOI: 10.1002/mop.20722. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[Abstract] Equispaced linear arrays that have uniformly excited central elements and monotonically decreasing flanking segments have been shown to yield low-sidelobe patterns with specified constraints on the effective radiated voltage (ERV). An analytical method for generating these distributions using a constrained least-squares (CLS) method, with restrictions on both the peak amplitude of the elements and the ERV, has been discussed in a previous work. Simulated annealing (SA) is a versatile global-optimization technique that can be effectively used for similar purposes, but can also provide additional control over some other design parameters. In this paper, we inspect both methods—indicating some of their advantages and drawbacks—through some numerical results

A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations for the GJ581 exoplanetary system. Today this system is controversial due to choices that can be done in the orbital determination. The main ones are the ocurrence of aliases and the additional bodies - the planets f and g - announced in Vogt et al. 2010. Any dynamical study of exoplanets requires the good knowledge of the orbital elements and the investigations involving the planet g are particularly interesting, since this body would lie in the Habitable Zone (HZ) of the star GJ581. This region,for this system, is very attractive of the dynamical point of view due to several resonances of two and three bodies present there. In this work, we investigate the conditions under which the planet g may exist. We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period $\approx 450$ days, but we are judicious about any affirmation concernig this body because its signal is in the threshold of detection and the high period is in a spectral region where the ocorruence of aliases is very common. Besides, we outline some dynamical features of the habitable zone with the dynamical map and point out the role played by some resonances laying there.Comment: 12 pages, 9 figure

Minimax passband group delay nonlinear FIR filter design without imposing desired phase response

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a nonsmooth functional ine-quality constrained optimization problem. To tackle this problem, first, the one norm functional inequality constraint of the optimization problem is approximated by a smooth function so that the nonsmooth functional inequality con-strained optimization problem is approximated as a noncon-vex functional inequality constrained optimization problem. Then, a modified filled function method is applied for find-ing the global minimum of the nonconvex optimization prob-lem. Computer numerical simulation results show that our designed nonlinear phase peak constrained FIR filter could achieve lower minimum passband group delay than those of existing designs