ECE559VV Project Report
|
|
- Alan Shaw
- 6 years ago
- Views:
Transcription
1 ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate s one whch only transmts to the user wth best channel recepton []. We now present a smlar result for uplnk (mult-access channels [2]. Consder the sngle-cell multuser uplnk scenaro where the sgnal receved by the base staton s as follows: y = h x + z, = where K s the number of users n the cell, h and x are gan and nformaton for user, respectvely. We assume that the nformaton sources x s are zero-mean, have unt energy, and are mutually uncorrelated. The nose z s a zero-mean Gaussan random varable wth varance N 0. If the channel gans h s are determnstc, then ths s smply a Gaussan mult-access channel whose capacty regon s defned as follows [3]. ( R < 2 log + γ, S {,2,...,K}, S S where R and γ = h 2 /N 0 are the nformaton rate and receved SNR of the user, respectvely. Therefore, the sum-rate s R < ( 2 log + = γ. Now, f we assume frequency flat Raylegh fadng, then h has a Raylegh dstrbuton, and n turn, γ has the followng exponental dstrbuton p γ (x = ( x exp γ s where γ s s the average receved SNR for user. γ s =2 I x 0,
2 2 We would lke to fnd a power control law µ (γ for user, wth γ = [γ,γ 2,...,γ K ], whch takes the nstantaneous receved SNR of other users nto account. Ths can be done by ntroducng some feedback between the base staton and users. The goal s to maxmze the sum-rate C sum = ( log + µ (γγ p(γdγ 2 subject to the constrants that the average power s one unt,.e., µ (γp(γdγ =, ( and µ (γ 0. Ths s a standard convex optmzaton. Introducng the Lagrange multplers, λ, for each constrant, we obtan the followng Lagrangan form: ( max L = log + µ γ p(γdγ s.t. µ 0,. The partal dervatve s = = ( λ = µ p(γdγ Thus, the optmalty condton yelds L µ = γ + K = µ γ λ. γ + K = µ λ γ = 0 f µ > 0, γ + K = µ λ γ < 0 else, and λ s chosen so that the average power condton ( s satsfed. The above optmalty condton can be rewrtten as: Assume that all + = µ j = 0, j and consequently, µ γ γ λ, wth equalty ff µ > 0. (2 γ λ s are dfferent. Then we can see from the condton (2 that f µ > 0, then γ λ > γ j λ j, j. That s, the only user allowed to transmt at any gven tme s the one wth the largest γ λ. Now, suppose that all users have the same average receved power. By symmetry, all λ s are equal. Then the above result can be nterpreted as follows: only the user wth largest nstantaneous receved power s allowed to transmt, and the others must reman quet untl one of them becomes the strongest user.
3 3 The power allocaton for user s a water-fllng soluton wth the form µ (γ = λ γ 0 else where λ s chosen such that the condton ( s satsfed. f γ > λ, γ > λ λ j γ j, j II. MORE ABOUT PROPORTIONAL FAIR SCHEDULING (PFS A. Addtonal property of PFS It has been shown n [4] that, for PFS, f the channel processes have the form h (t = a b (t where a s a constant and the b (t processes are..d, then n the long run the fractons of slots allocated to each user are equal. As a specal case, n the statc envronment, PFS wll become the equal-tme schedulng. B. Proportonal far wth mnmum/maxmum rate constrants Note that the PFS algorthm does not provde any guarantees on the servce rate provded to any user. For some cases, we may need to ntroduce the mnmum as well as maxmum bandwdth to each user. Suppose that for each user we have a mnmum rate T mn average throughput T to satsfy T mn T T max. Therefore, the optmzaton problem becomes and a maxmum rate T max and we want the max log T (3 s.t. T mn T T max, {T } C where C denotes the capacty regon of the system. An algorthm for ths problem has been consdered n [5]. The dea s to mantan a token counter Q (t for each user, and t s updated accordng to the followng rule: where T token = T mn Q (t + = f Q (t 0 and T token s the same as n the orgnal PFS: T (t + = Q (t + T token Q (t + T token = T max R (t f user s served otherwse f Q (t < 0. Note that the update rule of T (t ( W T (t + W R (t f user s served ( W T (t otherwse.
4 4 At tme t, the algorthm serves the user (t = arg max R (t T (t eαq(t, where α s a parameter that determnes the tmescale over whch the rate constrants are satsfed. The basc dea of the token counter s that f the average servce rate to user s less than R mn Q (t s postve and then we are more lkely to serve user. Also, f the average servce rate to user s larger than R max then Q (t s negatve and then we are less lkely to serve user. Fnally, t has been shown n [5] that the algorthm s asymptotcally optmal wth respect to the optmzaton (3 when W goes to nfnty. then C. Other questons What s the ntuton behnd the throughput updatng rule n PFS? We can thnk of T (t as an estmate of the actual throughput for user. The larger the wndow sze W, the more accurate the estmate T (t. Note that we cannot calculate the exact throughput on-the-fly: throughput s a long-term quantty by defnton. So ths s one way to estmate t. h 2 How about the schedulng algorthms based on some functon of h and E[ h 2 ], e.g., to schedule the user only f h s larger than some threshold? Ths s related to the queston I have durng the presentaton: what f we do not fx the power and fnd the optmal power allocaton across tme, e.g., a water-fllng soluton. I do not have an answer for ths queston. 3 What s the rate regon achevable usng the PFS scheme? How does t compare wth max sum-rate mechansm? We have only one rate regon (or capacty regon whch s the regon achevable by any schedulng scheme. The dfference between PFS scheme and max-sum-rate scheme s that they get to dfferent ponts n the capacty regon: the max-sum-rate scheme gves us the pont whch has maxmum total rate T, whle the PFS scheme gves the pont whch maxmzes log T. 4 When s PFS better and when s max-sum-rate s better to use? I guess t depends on the goal of the system operator. In the user s pont of vew, PFS s better because t s farer (at least t asymptotcally acheves the proportonal far allocaton. In the system s pont of vew, max-sum-rate mght be better snce t gves the maxmum total throughput of the system.
5 5 III. OPPORTUNISTIC BEAMFORMING [6] A. Opportunstc beamformng versus space-tme codes The dea of opportunstc beamformng s motvated by the multuser system pont of vew: the larger the dynamc range of channel fluctuatons, the hgher the channel peaks. Hence, n opportunstc beamformng, we use multple transmt antennas to nduce more randomness to channels. On the other hand, the spacetme codes also use multple transmt antennas n the pont-to-pont scenaro. So we would lke to compare between the opportunstc beamformng scheme and the space-tme codes n a multuser system. Let us consder a multuser downlnk system wth two transmt antennas at the base staton. The best known space-tme code for ths scenaro s the Alamout scheme. We assume that the PFS schedulng scheme s used on top of t. Consder the slow fadng scenaro. The Alamout scheme essentally creates a sngle channel wth effectve SNR for user k gven by P( h k 2 + h 2k 2 2N 0 where P s the total transmt power. Ths effectve channel does not change wth tme n a slow fadng envronment, and hence, the PFS schedulng becomes the equal-tme schedulng (see Secton II-A. On the other hand, t has been shown n [6] that under opportunstc beamformng wth PFS, for large number of users, the users are also allocated equal tme wth the followng effectve SNR: P( h k 2 + h 2k 2 N 0. That s, the opportunstc beamformng has 3-dB gan more than the Alamout scheme. Furthermore, both schemes yeld a dversty gan of 2. Thus, n a multuser system wth enough users under PFS, the opportunstc beamformng scheme outperforms the Alamout scheme. Fnally, the Alamout scheme requres separate plots for each transmt antenna and that recevers need to track the channels from both transmt antennas. However, the opportunstc beamformng does not requre any of those. The same sgnal (plot and data goes through both transmt antennas, and the recevers only need to track the overall channel. B. Other questons If perfect CSI s assumed, the BS can beamform to the drecton of the channel of the user to be scheduled, and ths strategy seems to perform better than opportunstc beamformng. So what s the advantage of opportunstc beamformng?
6 6 The pont of opportunstc beamformng s to ntroduce more randomness to the channels by addng more dumb transmt antennas. Ths addton s transparent to recevers. Comparng to the orgnal system wthout opportunstc beamformng, the effort to get the channel state nformaton wth opportunstc beamformng s the same. But opportunstc beamformng yelds better performance. So the perfect CSI assumpton s for schedulng and beamformng the sgnal before t comes to the dumb antennas. REFERENCES [] D. Tse, Optmal power allocaton over parallel gaussan broadcast channels, n Proceedngs of Internatonal Symposum on Informaton Theory, Ulm, Germany, June 997. [2] R. Knopp and P. Humblet, Informaton capacty and power control n sngle-cell multuser communcatons, n Proceedngs of the IEEE Internatonal Conference on Communcatons (ICC, Seattle, WA, June 995. [3] T. M. Cover and J. A. Thomas, Elements of Informaton Theory. John Wley & Sons, 99. [4] J. Holtzman, CDMA forward lnk water-fllng power control, n Proceedngs of the IEEE Semannual Vehcular Technology Conference (VTC2000-Sprng, Tokyo, Japan, May 2000, pp [5] M. Andrews, L. Qan, and A. Stolyar, Optmal utlty based mult-user throughput allocaton subject to throughput constrants, n Proceedngs of IEEE INFOCOM, Mam, IL, March [6] P. Vswanath, D. Tse, and R. Laroa, Opportunstc beamformng usng dumb antennas, IEEE Transactons on Informaton Theory, vol. 48, no. 6, pp , June 2002.
Chapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationEconomics 101. Lecture 4 - Equilibrium and Efficiency
Economcs 0 Lecture 4 - Equlbrum and Effcency Intro As dscussed n the prevous lecture, we wll now move from an envronment where we looed at consumers mang decsons n solaton to analyzng economes full of
More informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationx = x 1 + :::+ x K and the nput covarance matrces are of the form ± = E[x x y ]. 3.2 Dualty Next, we ntroduce the concept of dualty wth the followng t
Sum Power Iteratve Water-fllng for Mult-Antenna Gaussan Broadcast Channels N. Jndal, S. Jafar, S. Vshwanath and A. Goldsmth Dept. of Electrcal Engg. Stanford Unversty, CA, 94305 emal: njndal,syed,srram,andrea@wsl.stanford.edu
More informationThroughput Capacities and Optimal Resource Allocation in Multiaccess Fading Channels
Trougput Capactes and Optmal esource Allocaton n ultaccess Fadng Cannels Hao Zou arc 7, 003 Unversty of Notre Dame Abstract oble wreless envronment would ntroduce specal penomena suc as multpat fadng wc
More informationTHE ARIMOTO-BLAHUT ALGORITHM FOR COMPUTATION OF CHANNEL CAPACITY. William A. Pearlman. References: S. Arimoto - IEEE Trans. Inform. Thy., Jan.
THE ARIMOTO-BLAHUT ALGORITHM FOR COMPUTATION OF CHANNEL CAPACITY Wllam A. Pearlman 2002 References: S. Armoto - IEEE Trans. Inform. Thy., Jan. 1972 R. Blahut - IEEE Trans. Inform. Thy., July 1972 Recall
More informationJoint Scheduling and Power-Allocation for Interference Management in Wireless Networks
Jont Schedulng and Power-Allocaton for Interference Management n Wreless Networks Xn Lu *, Edwn K. P. Chong, and Ness B. Shroff * * School of Electrcal and Computer Engneerng Purdue Unversty West Lafayette,
More informationCognitive Access Algorithms For Multiple Access Channels
203 IEEE 4th Workshop on Sgnal Processng Advances n Wreless Communcatons SPAWC) Cogntve Access Algorthms For Multple Access Channels Ychuan Hu and Alejandro Rbero, Department of Electrcal and Systems Engneerng,
More informationPower Allocation/Beamforming for DF MIMO Two-Way Relaying: Relay and Network Optimization
Power Allocaton/Beamformng for DF MIMO Two-Way Relayng: Relay and Network Optmzaton Je Gao, Janshu Zhang, Sergy A. Vorobyov, Ha Jang, and Martn Haardt Dept. of Electrcal & Computer Engneerng, Unversty
More informationModule 9. Lecture 6. Duality in Assignment Problems
Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept
More information2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification
E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationEURASIP Journal on Wireless Communications and Networking
EURASIP Journal on Wreless Communcatons and Networkng Ths Provsonal PDF corresponds to the artcle as t appeared upon acceptance. Fully formatted PDF and full text (TM) versons wll be made avalable soon.
More informationprinceton univ. F 17 cos 521: Advanced Algorithm Design Lecture 7: LP Duality Lecturer: Matt Weinberg
prnceton unv. F 17 cos 521: Advanced Algorthm Desgn Lecture 7: LP Dualty Lecturer: Matt Wenberg Scrbe: LP Dualty s an extremely useful tool for analyzng structural propertes of lnear programs. Whle there
More informationProblem Set 9 Solutions
Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem
More informationTwo-Way and Multiple-Access Energy Harvesting Systems with Energy Cooperation
Two-Way and Multple-Access Energy Harvestng Systems wth Energy Cooperaton Berk Gurakan, Omur Ozel, Jng Yang 2, and Sennur Ulukus Department of Electrcal and Computer Engneerng, Unversty of Maryland, College
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationSolutions to exam in SF1811 Optimization, Jan 14, 2015
Solutons to exam n SF8 Optmzaton, Jan 4, 25 3 3 O------O -4 \ / \ / The network: \/ where all lnks go from left to rght. /\ / \ / \ 6 O------O -5 2 4.(a) Let x = ( x 3, x 4, x 23, x 24 ) T, where the varable
More informationWhich Separator? Spring 1
Whch Separator? 6.034 - Sprng 1 Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng 3 Margn of a pont " # y (w $ + b) proportonal
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationU.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017
U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that
More informationJoint Scheduling of Rate-guaranteed and Best-effort Services over a Wireless Channel
Jont Schedulng of Rate-guaranteed and Best-effort Servces over a Wreless Channel Murtaza Zafer and Eytan Modano Abstract We consder mult-user schedulng over the downln channel n wreless data systems. Specfcally,
More informationThe Study of Teaching-learning-based Optimization Algorithm
Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute
More informationGeneralized Linear Methods
Generalzed Lnear Methods 1 Introducton In the Ensemble Methods the general dea s that usng a combnaton of several weak learner one could make a better learner. More formally, assume that we have a set
More informationPerfect Competition and the Nash Bargaining Solution
Perfect Competton and the Nash Barganng Soluton Renhard John Department of Economcs Unversty of Bonn Adenauerallee 24-42 53113 Bonn, Germany emal: rohn@un-bonn.de May 2005 Abstract For a lnear exchange
More informationExternalities in wireless communication: A public goods solution approach to power allocation. by Shrutivandana Sharma
Externaltes n wreless communcaton: A publc goods soluton approach to power allocaton by Shrutvandana Sharma SI 786 Tuesday, Feb 2, 2006 Outlne Externaltes: Introducton Plannng wth externaltes Power allocaton:
More informationThe Second Anti-Mathima on Game Theory
The Second Ant-Mathma on Game Theory Ath. Kehagas December 1 2006 1 Introducton In ths note we wll examne the noton of game equlbrum for three types of games 1. 2-player 2-acton zero-sum games 2. 2-player
More informationECE 534: Elements of Information Theory. Solutions to Midterm Exam (Spring 2006)
ECE 534: Elements of Informaton Theory Solutons to Mdterm Eam (Sprng 6) Problem [ pts.] A dscrete memoryless source has an alphabet of three letters,, =,, 3, wth probabltes.4,.4, and., respectvely. (a)
More informationThe Expectation-Maximization Algorithm
The Expectaton-Maxmaton Algorthm Charles Elan elan@cs.ucsd.edu November 16, 2007 Ths chapter explans the EM algorthm at multple levels of generalty. Secton 1 gves the standard hgh-level verson of the algorthm.
More informationDistributed Non-Autonomous Power Control through Distributed Convex Optimization
Dstrbuted Non-Autonomous Power Control through Dstrbuted Convex Optmzaton S. Sundhar Ram and V. V. Veeravall ECE Department and Coordnated Scence Lab Unversty of Illnos at Urbana-Champagn Emal: {ssrnv5,vvv}@llnos.edu
More informationA Feedback Reduction Technique for MIMO Broadcast Channels
A Feedback Reducton Technque for MIMO Broadcast Channels Nhar Jndal Department of Electrcal and Computer Engneerng Unversty of Mnnesota Mnneapols, MN 55455, USA Emal: nhar@umn.edu Abstract A multple antenna
More informationCollege of Computer & Information Science Fall 2009 Northeastern University 20 October 2009
College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:
More informationPower Allocation for Distributed BLUE Estimation with Full and Limited Feedback of CSI
Power Allocaton for Dstrbuted BLUE Estmaton wth Full and Lmted Feedback of CSI Mohammad Fanae, Matthew C. Valent, and Natala A. Schmd Lane Department of Computer Scence and Electrcal Engneerng West Vrgna
More information3.1 ML and Empirical Distribution
67577 Intro. to Machne Learnng Fall semester, 2008/9 Lecture 3: Maxmum Lkelhood/ Maxmum Entropy Dualty Lecturer: Amnon Shashua Scrbe: Amnon Shashua 1 In the prevous lecture we defned the prncple of Maxmum
More informationBook Title: Orthogonal Frequency Division Multiple Access. Editors
Book Ttle: Orthogonal Frequency Dvson Multple Access Edtors August 18, 2009 Contents 1 Schedulng and Resource Allocaton n OFDMA 1 1.1 Introducton.................................... 2 1.2 Related Work
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationNP-Completeness : Proofs
NP-Completeness : Proofs Proof Methods A method to show a decson problem Π NP-complete s as follows. (1) Show Π NP. (2) Choose an NP-complete problem Π. (3) Show Π Π. A method to show an optmzaton problem
More informationCalculation of time complexity (3%)
Problem 1. (30%) Calculaton of tme complexty (3%) Gven n ctes, usng exhaust search to see every result takes O(n!). Calculaton of tme needed to solve the problem (2%) 40 ctes:40! dfferent tours 40 add
More informationMMA and GCMMA two methods for nonlinear optimization
MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons
More informationThe Concept of Beamforming
ELG513 Smart Antennas S.Loyka he Concept of Beamformng Generc representaton of the array output sgnal, 1 where w y N 1 * = 1 = w x = w x (4.1) complex weghts, control the array pattern; y and x - narrowband
More informationA Game Theoretic Approach to Distributed Opportunistic Scheduling
A Game Theoretc Approach to Dstrbuted Opportunstc Schedulng Albert Banchs, Senor Member, IEEE, Andres Garca-Saavedra, Pablo Serrano, Member, IEEE, and Joerg Wdmer, Senor Member, IEEE. Banchs et al.: A
More informationResource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud
Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal
More informationAn Upper Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control
An Upper Bound on SINR Threshold for Call Admsson Control n Multple-Class CDMA Systems wth Imperfect ower-control Mahmoud El-Sayes MacDonald, Dettwler and Assocates td. (MDA) Toronto, Canada melsayes@hotmal.com
More informationAn Admission Control Algorithm in Cloud Computing Systems
An Admsson Control Algorthm n Cloud Computng Systems Authors: Frank Yeong-Sung Ln Department of Informaton Management Natonal Tawan Unversty Tape, Tawan, R.O.C. ysln@m.ntu.edu.tw Yngje Lan Management Scence
More informationJoint Scheduling and Resource Allocation in CDMA Systems
TO APPEAR IEEE TRANSACTIONS ON INFORMATION THEORY Jont Schedulng and Resource Allocaton n CDMA Systems Vjay G. Subramanan, Randall A. Berry, and Rajeev Agrawal Abstract In ths paper, the schedulng and
More informationMulti-beam multiplexing using multiuser diversity and random beams in wireless systems
Mult-eam multplexng usng multuser dversty and random eams n reless systems Sung-Soo ang Telecommuncaton R&D center Samsung electroncs co.ltd. Suon-cty Korea sungsoo.hang@samsung.com Yong-an Lee School
More informationJoint Scheduling and Resource Allocation in CDMA Systems
TECHNICAL REPORT - JUNE 2009 1 Jont Schedulng and Resource Allocaton n CDMA Systems Vjay G. Subramanan, Randall A. Berry, and Rajeev Agrawal Expanded Techncal Report: A shorter verson of ths paper wll
More informationMIMO Systems and Channel Capacity
MIMO Systems and Channel Capacty Consder a MIMO system wth m Tx and n Rx antennas. x y = Hx ξ Tx H Rx The power constrant: the total Tx power s x = P t. Component-wse representaton of the system model,
More informationChapter 7 Channel Capacity and Coding
Chapter 7 Channel Capacty and Codng Contents 7. Channel models and channel capacty 7.. Channel models Bnary symmetrc channel Dscrete memoryless channels Dscrete-nput, contnuous-output channel Waveform
More informationWinter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan
Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments
More informationSum Capacity of Multiuser MIMO Broadcast Channels with Block Diagonalization
Sum Capacty of Multuser MIMO Broadcast Channels wth Block Dagonalzaton Zukang Shen, Runhua Chen, Jeffrey G. Andrews, Robert W. Heath, Jr., and Bran L. Evans The Unversty of Texas at Austn, Austn, Texas
More informationOnline Appendix. t=1 (p t w)q t. Then the first order condition shows that
Artcle forthcomng to ; manuscrpt no (Please, provde the manuscrpt number!) 1 Onlne Appendx Appendx E: Proofs Proof of Proposton 1 Frst we derve the equlbrum when the manufacturer does not vertcally ntegrate
More informationSome modelling aspects for the Matlab implementation of MMA
Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton
More informationEnergy Efficient Resource Allocation for Quantity of Information Delivery in Parallel Channels
TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES Trans. Emergng Tel. Tech. 0000; 00: 6 RESEARCH ARTICLE Energy Effcent Resource Allocaton for Quantty of Informaton Delvery n Parallel Channels Jean-Yves
More informationJoint Scheduling and Resource Allocation in CDMA Systems
ACCEPTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 1 Jont Schedulng and Resource Allocaton n CDMA Systems Vjay G. Subramanan, Randall A. Berry, and Rajeev Agrawal Abstract We consder schedulng and resource
More informationCOGNITIVE RADIO NETWORKS BASED ON OPPORTUNISTIC BEAMFORMING WITH QUANTIZED FEEDBACK
COGNITIVE RADIO NETWORKS BASED ON OPPORTUNISTIC BEAMFORMING WITH QUANTIZED FEEDBACK Ayman MASSAOUDI, Noura SELLAMI 2, Mohamed SIALA MEDIATRON Lab., Sup Com Unversty of Carthage 283 El Ghazala Arana, Tunsa
More informationOutline. Communication. Bellman Ford Algorithm. Bellman Ford Example. Bellman Ford Shortest Path [1]
DYNAMIC SHORTEST PATH SEARCH AND SYNCHRONIZED TASK SWITCHING Jay Wagenpfel, Adran Trachte 2 Outlne Shortest Communcaton Path Searchng Bellmann Ford algorthm Algorthm for dynamc case Modfcatons to our algorthm
More informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationDownlink Throughput Maximization: TDMA versus CDMA
00 Conference on Informaton Scences and Systems, The Johns Hopkns Unversty, March, 00 Downlnk Throughput Maxmzaton: TDMA versus CDMA Changyoon Oh and Ayln Yener Department of Electrcal Engneerng The Pennsylvana
More informationCIS526: Machine Learning Lecture 3 (Sept 16, 2003) Linear Regression. Preparation help: Xiaoying Huang. x 1 θ 1 output... θ M x M
CIS56: achne Learnng Lecture 3 (Sept 6, 003) Preparaton help: Xaoyng Huang Lnear Regresson Lnear regresson can be represented by a functonal form: f(; θ) = θ 0 0 +θ + + θ = θ = 0 ote: 0 s a dummy attrbute
More informationJoint Scheduling of Rate-guaranteed and Best-effort Users over a Wireless Fading Channel
Jont Schedulng of Rate-guaranteed and Best-effort Users over a Wreless Fadng Channel Murtaza Zafer and Eytan Modano Massachusetts Insttute of Technology Cambrdge, MA 239, USA Emal:{murtaza@mt.edu, modano@mt.edu}
More informationAssignment 2. Tyler Shendruk February 19, 2010
Assgnment yler Shendruk February 9, 00 Kadar Ch. Problem 8 We have an N N symmetrc matrx, M. he symmetry means M M and we ll say the elements of the matrx are m j. he elements are pulled from a probablty
More informationJoint Scheduling and Resource Allocation in CDMA Systems
SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 1 Jont Schedulng and Resource Allocaton n CDMA Systems Vjay Subramanan, Randall A. Berry, and Rajeev Agrawal Abstract We consder schedulng and resource
More informationOrder Optimal Delay for Opportunistic Scheduling in Multi-User Wireless Uplinks and Downlinks
IEEE TRANSACTIONS ON NETWORKING, VOL. 16, NO. 5, PP. 1188-1199, OCT. 008 1 Order Optmal Delay for Opportunstc Schedulng n Mult-User Wreless Uplnks and Downlnks Mchael J. Neely Unversty of Southern Calforna
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More informationEstimation: Part 2. Chapter GREG estimation
Chapter 9 Estmaton: Part 2 9. GREG estmaton In Chapter 8, we have seen that the regresson estmator s an effcent estmator when there s a lnear relatonshp between y and x. In ths chapter, we generalzed the
More informationInteractive Bi-Level Multi-Objective Integer. Non-linear Programming Problem
Appled Mathematcal Scences Vol 5 0 no 65 3 33 Interactve B-Level Mult-Objectve Integer Non-lnear Programmng Problem O E Emam Department of Informaton Systems aculty of Computer Scence and nformaton Helwan
More informationExplicit and Implicit Temperature Constraints in Energy Harvesting Communications
Explct and Implct Temperature Constrants n Energy Harvestng Communcatons Abdulrahman Baknna, Omur Ozel 2, and Sennur Ulukus Department of Electrcal and Computer Engneerng, Unversty of Maryland, College
More informationOPTIMUM BEAMFORMING USING TRANSMIT ANTENNA ARRAYS. feasible points with monotonically decreasing costs).
OPTIMUM BEAMFORMING USING TRANSMIT ANTENNA ARRAYS Eugene Vsotsky Upamanyu Madhow Abstract - Transmt beamformng s a powerful means of ncreasng capacty n systems n whch the transmtter s eupped wth an antenna
More informationAntenna Combining for the MIMO Downlink Channel
Antenna Combnng for the IO Downlnk Channel arxv:0704.308v [cs.it] 0 Apr 2007 Nhar Jndal Department of Electrcal and Computer Engneerng Unversty of nnesota nneapols, N 55455, USA Emal: nhar@umn.edu Abstract
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationPROBLEM SET 7 GENERAL EQUILIBRIUM
PROBLEM SET 7 GENERAL EQUILIBRIUM Queston a Defnton: An Arrow-Debreu Compettve Equlbrum s a vector of prces {p t } and allocatons {c t, c 2 t } whch satsfes ( Gven {p t }, c t maxmzes βt ln c t subject
More informationA Lower Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control
A ower Bound on SIR Threshold for Call Admsson Control n Multple-Class CDMA Systems w Imperfect ower-control Mohamed H. Ahmed Faculty of Engneerng and Appled Scence Memoral Unversty of ewfoundland St.
More informationClosed form solutions for water-filling problems in optimization and game frameworks
Closed form solutons for water-fllng problems n optmzaton and game frameworks Etan Altman INRIA BP93 24 route des Lucoles 692 Sopha Antpols FRANCE altman@sopha.nra.fr Konstantn Avrachenkov INRIA BP93 24
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationMaximizing the number of nonnegative subsets
Maxmzng the number of nonnegatve subsets Noga Alon Hao Huang December 1, 213 Abstract Gven a set of n real numbers, f the sum of elements of every subset of sze larger than k s negatve, what s the maxmum
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationSimultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals
Smultaneous Optmzaton of Berth Allocaton, Quay Crane Assgnment and Quay Crane Schedulng Problems n Contaner Termnals Necat Aras, Yavuz Türkoğulları, Z. Caner Taşkın, Kuban Altınel Abstract In ths work,
More informationNatural Language Processing and Information Retrieval
Natural Language Processng and Informaton Retreval Support Vector Machnes Alessandro Moschtt Department of nformaton and communcaton technology Unversty of Trento Emal: moschtt@ds.untn.t Summary Support
More informationReport on Image warping
Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.
More information6.854J / J Advanced Algorithms Fall 2008
MIT OpenCourseWare http://ocw.mt.edu 6.854J / 18.415J Advanced Algorthms Fall 2008 For nformaton about ctng these materals or our Terms of Use, vst: http://ocw.mt.edu/terms. 18.415/6.854 Advanced Algorthms
More informationChapter 7 Channel Capacity and Coding
Wreless Informaton Transmsson System Lab. Chapter 7 Channel Capacty and Codng Insttute of Communcatons Engneerng atonal Sun Yat-sen Unversty Contents 7. Channel models and channel capacty 7.. Channel models
More informationPricing and Resource Allocation Game Theoretic Models
Prcng and Resource Allocaton Game Theoretc Models Zhy Huang Changbn Lu Q Zhang Computer and Informaton Scence December 8, 2009 Z. Huang, C. Lu, and Q. Zhang (CIS) Game Theoretc Models December 8, 2009
More informationLogistic Regression. CAP 5610: Machine Learning Instructor: Guo-Jun QI
Logstc Regresson CAP 561: achne Learnng Instructor: Guo-Jun QI Bayes Classfer: A Generatve model odel the posteror dstrbuton P(Y X) Estmate class-condtonal dstrbuton P(X Y) for each Y Estmate pror dstrbuton
More informationOptimal information storage in noisy synapses under resource constraints
Optmal nformaton storage n nosy synapses under resource constrants Lav arshney MIT Jesper Sjöström Brandes, UCL London Dmtr Mtya Chklovsk Cold Sprng Harbor Laboratory Modfcatons of synaptc connectons store
More informationFlexible Allocation of Capacity in Multi-Cell CDMA Networks
Flexble Allocaton of Capacty n Mult-Cell CDMA Networs Robert Al, Manu Hegde, Mort Naragh-Pour*, Paul Mn Washngton Unversty, St. Lous, MO *Lousana State Unversty, Baton Rouge, LA Outlne Capacty and Probablty
More informationLecture 4: November 17, Part 1 Single Buffer Management
Lecturer: Ad Rosén Algorthms for the anagement of Networs Fall 2003-2004 Lecture 4: November 7, 2003 Scrbe: Guy Grebla Part Sngle Buffer anagement In the prevous lecture we taled about the Combned Input
More informationI + HH H N 0 M T H = UΣV H = [U 1 U 2 ] 0 0 E S. X if X 0 0 if X < 0 (X) + = = M T 1 + N 0. r p + 1
Homework 4 Problem Capacty wth CSI only at Recever: C = log det I + E )) s HH H N M T R SS = I) SVD of the Channel Matrx: H = UΣV H = [U 1 U ] [ Σr ] [V 1 V ] H Capacty wth CSI at both transmtter and
More information4884 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 61, NO. 12, DECEMBER Energy Cooperation in Energy Harvesting Communications
4884 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO., DECEMBER 3 Energy Cooperaton n Energy Harvestng Communcatons Ber Guraan, Student Member, IEEE, Omur Ozel, Student Member, IEEE, Jng Yang, Member,
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationOptimum Association of Mobile Wireless Devices with a WLAN 3G Access Network
Optmum Assocaton of Moble Wreless Devces wth a WLAN 3G Access Network K. Premkumar Appled Research Group Satyam Computer Servces Lmted, Bangalore 560 012 Emal: kprem@ece.sc.ernet.n Anurag Kumar Dept. of
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #16 Scribe: Yannan Wang April 3, 2014
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #16 Scrbe: Yannan Wang Aprl 3, 014 1 Introducton The goal of our onlne learnng scenaro from last class s C comparng wth best expert and
More informationAn Interactive Optimisation Tool for Allocation Problems
An Interactve Optmsaton ool for Allocaton Problems Fredr Bonäs, Joam Westerlund and apo Westerlund Process Desgn Laboratory, Faculty of echnology, Åbo Aadem Unversty, uru 20500, Fnland hs paper presents
More informationTornado and Luby Transform Codes. Ashish Khisti Presentation October 22, 2003
Tornado and Luby Transform Codes Ashsh Khst 6.454 Presentaton October 22, 2003 Background: Erasure Channel Elas[956] studed the Erasure Channel β x x β β x 2 m x 2 k? Capacty of Noseless Erasure Channel
More informationThe Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationAPPENDIX A Some Linear Algebra
APPENDIX A Some Lnear Algebra The collecton of m, n matrces A.1 Matrces a 1,1,..., a 1,n A = a m,1,..., a m,n wth real elements a,j s denoted by R m,n. If n = 1 then A s called a column vector. Smlarly,
More informationOptimal Resource Allocation in Full-Duplex Wireless-Powered Communication Network
1 Optmal Resource Allocaton n Full-Duplex Wreless-owered Communcaton Network Hyungsk Ju and Ru Zhang, Member, IEEE arxv:143.58v3 [cs.it] 15 Sep 14 Abstract Ths paper studes optmal resource allocaton n
More information