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Table Of Integrals Series And Products

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Sphere Packings, Lattices and Groups

Tables of integrals

This document provides updates to IEEE Std 802.16's MIB for the MAC, PHY and asso- ciated management procedures in order to accommodate recent extensions to the standard.

IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems Draft Amendment: Management Information Base Extensions

We derive in closed-form the outage probability for different statistical models of PDL and evaluate their accuracy. From the resulting expressions, we quantify its impact on optical transmissions as an SNR penalty.

http://biblio.telecom-paristech.fr/cgi-bin/download.cgi?id=12643

Outage Probability derivations for PDL-disturbed Coherent Optical Communication

Cooperative detection without fusion center has many applications such as spectrum sensing in cognitive radio or intrusion detection in ad hoc network. In this paper, we propose a new asynchronous fully-distributed cooperative algorithm which does not require any knowledge on the underlying nodes network. Discussion about the threshold choice and the respective duration of the sensing step and the gossip step is conducted.

Fully distributed signal detection: Application to cognitive radio

In a companion paper (see Resource Allocation for Downlink Cellular OFDMA Systems: Part I— Optimal Allocation), we characterized the optimal resource allocation in terms of power control and sub-carrier assignment, for a downlink OFDMA system impaired by multicell interference. In our model, the network is assumed to be one dimensional (linear) for the sake of analysis. We also assume that a certain part of the available bandwidth is likely to be reused by different base stations and that the other part of the bandwidth is shared in an orthogonal way between the different base stations. The optimal resource allocation characterized in Part I is obtained by minimizing the total power spent by the network under the constraint that all users’ rate requirements in nats/s/Hz are satisfied. It is worth noting that when optimal resource allocation is used, any user receives data either in the reused bandwidth or in the protected bandwidth, but not in both (except for at most one pivot user in each cell). In the present paper, we study the asymptotic behavior of the optimal resource allocation as the number of users in each cell tends to infinity. Our analysis allows to characterize the performance of the optimal resource allocation algorithm and to determine the asymptotically optimal pivot-position. As a byproduct of our analysis, we propose a decentralized suboptimal resource allocation algorithm with low complexity and prove that the proposed algorithm is asymptotically optimal when the number of users tends to infinity. Finally, we characterize the optimal value of the frequency reuse factor. Simulations sustain our claims and show that substantial performance improvements are obtained when the optimal value of the frequency reuse factor is used.

Resource Allocation for Downlink Cellular OFDMA Systems: Part II - Asymptotic Analysis and Applications

The paper deals with power and subcarrier allocation in a Frequency Hopping - Orthogonal Frequency Division Multiple Access (FH-OFDMA) based system. The problem is solved for the downlink of a cellular wireless transmission and the performance of the solution applied in two different frequency reuse schemes are compared. The proposed allocation strategy aims at minimizing the total power emitted by the base station (BS) and only requires the knowledge of the users' mean Signal to Interference plus Noise Ratios and rate requirements. We prove that in a universal frequency reuse scheme, the algorithm converges if the users' mean rate requirement is below a threshold which can be determined by the network designer. Moreover, numerical results show that this scheme outperforms the partial frequency reuse one under some cell size limit.

Performance of a Resource Allocation Strategy for an FH-OFDMA Based System in a Multi-Cell Environment

This paper introduces a novel family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of the carrier phase and frequency offset of quadrature amplitude modulations (QAM). An optimal or "matched" nonlinear estimator that exhibits the smallest asymptotic variance within the family of envisaged NLS-estimators is developed. A class of computationally efficient monomial estimators is also proposed. The asymptotic performance of these estimators is established in closed-form expression and compared with the Cramer-Rao lower bound corresponding to an unmodulated carrier. Finally, computer simulations are presented to corroborate the theoretical performance analysis.

http://ieeexplore.ieee.org/iel5/7744/21273/00987738.pdf

Philippe Ciblat

Papers

Outage Probability derivations for PDL-disturbed Coherent Optical Communication

Fully distributed signal detection: Application to cognitive radio

Resource Allocation for Downlink Cellular OFDMA Systems: Part II - Asymptotic Analysis and Applications

Performance of a Resource Allocation Strategy for an FH-OFDMA Based System in a Multi-Cell Environment

Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for burst QAM modulations