Infinite Length MMSE Decision Feedback Equalization
|
|
- Roberta Brown
- 6 years ago
- Views:
Transcription
1 Infnte Lengt SE ecson Feedbac Equalzaton FE N * * Y F Z ' Z SS ˆ Y Q N b...
2 Infnte-Lengt ecson Feedbac Equalzer as reoval ^ Y Z Feedforward Flter Feedbac Flter - Input to Slcer - Z Y Assung prevous decsons are correct Error Sequence Z Y E Z Y ^
3 SE-FE revous ecsons are assued correct FFF sapes ISI nto a causal part post-cursor ISI tat can be cancelled by te strctly causal FF tat can be cancelled by te strctly causal FF Error Sequence Analyss Y Z E Y Y Y
4 Optu Flter Coeffcents p Ortogonalty rncple ] [ Y E E YY Y R R R LE SE YY Y R R Q F
5 ole-zero Interpretaton of FE Under deal decsons assupton, transfer functon of FE feedbac loop s / Hence, overall transfer functon of FE s /. erefore, n FE, te flters collaborate to syntesze a pole-zero approxaton of te cannel nverse wc s ore accurate as ore degrees of freedo tan a sngle-flter as n LE 5
6 Error Auto-Correlaton ] [ E E E R ee ] [ ee were Y E E Y LE SE LE SE LE SE *, R n FE SE ee, Q F Intutvely : we sould coose te feedbac flter to wten te error sequence so tat te nput to te slcer s te desred nforaton sybol + wte nose
7 7
8 FE Optzaton Spectral Factorzaton Q F s postve real nuber s canoncal causal, R ee, FESE varance of error onc, r ee, nnu pase n n n Snce / s also a onc polynoal
9 FE Optzaton p wt equalty ff n FE SE Q causal non F Q Note te Feedforward flter coeffcents are not te sae as te LE coeffcents
10 FE Optzaton An Alternatve forula for ln Q e j F ln d e ln j e j proof setc : wrte as rato of products second ter st of order pole - zero sectons etals soon! d
11 FE Optzaton p j ln ln relaton use and d e Q F j j d e Q ln F Q e F FE SE FE SE E SEFE
12 Anoter forula for Zero order ter * Q F g F F g F g
13 Specal Case: Q ISI F Q For no ISI, bas!! F F FE SE F free ISIs snce cannel, F FE U SE S free ISI s
14 FE as Analyss y Y E Z Uncorrelated wt N Q nose F nose nose F nose
15 FE as Analyss e bas ter factor tat ultples s [ ] * * F SEFE SEFE SEFE, U SEFE F SEFE Specal Case ZF FE, set Q ; ZF-FE transfer functon
16 ZF-FE * Q Output of Feedforward Flter : * Q FFF converts cannel Q nto a canoncal flter ISI ll d b t f db flt! q j wose ISI s cancelled by te feedbac flter! ln e d e Q n n FE ZF j not based s FE ZF F FE ZF
17 ZF-FE Feedforward Flter Acton Cannel Ipulse Response Feedforward Flter Ipulse Response - Equvalent Cannel at Feedforward Flter Output 7
18 SE-FE Exaple Note : we get te sae results for =+.9.9 snce we assue analog atced flter so Q F Q γ noncausal realzed wt delay would be te sae! Feedforward Flter Ipulse Response
19 FE Exaple Cont d. 633 Canoncal feedbac tap gven by SEFE n SEFE SE FE, U Loss fro F 8.4.6d d c. f. 4.3d for SE - LE F
20 ZF-FE Exaple Q * * / Loss of.8 ZF FE d.6d fro F One feedbac tap of -.9 etaled roof for Salz Forula ans to forer EE6353 student Saab Sanaye not a recoended bed-te readng!: log Q e Q j F F g g d log * log g e j g e j d
21 Salz Forula R.H.S log j j de γ logge g e πj e j j Contour Integrals! log γ log gg πj d s te unt dsc d logγ logg πj πj logg d Z - d dz Z and - - ZZ
22 Salz Forula Hence : RHS R.H.S log γ j d log g log g πj z dz z z Snce g and g z are bot n pase ence tey are bot analytc R.H.S log log g j log g j but g g ; ence log log Q e j F d
23 nu-ase Cannels Consder -ray ultpat cannel c c were s dfferental pat delay n sybol perods. e zeros of satsfy te relaton / nu pase c c sorter delay pat as larger agntude Effects of fadng, sadowng, and reflectons cause cannel to alternate between nu and non-nu pase nu-pase cannels are easer to equalze! c c c 3
24 Zero-Forcng FE Zero Forcng FE Specal case of SE-FE by lettng Specal case of SE FE by lettng Spectral factorzaton * * * * Q Feedbac flter s and feedforward flter s / * * / Infnte-lengt ZF-FE s unbased For nu-pase cannels : Feedbac flter s 3 Cobned atced flter and feedforward flter s a scalar gan! * * * * / * * * * *
25 SE-FE vs. ZF-FE 5 ecson ont =+.9^ F Infnte Lengt SE FE Infnte Lengt ZF FE SE-FE s superor to ZF-FE at low ot structures becoe dentcal at g At very low were nose donates ISI, SE-FE converges to a atced flter Input d
26 FE Error ropagaton ost analyses assue correct past decsons for tractablty accurate at g A sngle decson error n FE results n ncorrect estate of post-cursor ISI possbly causng future decson errors Long feedbac flter exacerbates error propagaton On cannels w/ spectral nulls, te perforance advantage of FE over LE far outwegs effects of error propagaton recodng tecnque s used to elnate error propagaton wen cannel s nown at transtter
27 recodng Idea : ove FE feedbac secton to transtter were no decson errors occur Cauton: sple ovng of feedbac loop / to transtter ncreases transtted power degrades FE Soluton : Use odulo artetc to lt te ncrease n transtted power proposed by olnson & Harasa
28 recodng Used to elnate error propagaton n FE by ovng feedbac flter to transtter Requres cannel nowledge at transtter Consder te ZF-FE were and were Q recoded Input Sequence Y Q N 8
29 recodng Analyss g y Feedforward Flter Output Z Y N Q N 9
30 recodng Analyss g y N were N R were Q N R Q n wte! n n 3
31 olnson Harasa recodng roble: ranst ower s boosted Soluton: odulo Operator t d t t d d t s a real nuber wle and d are ntegers unforly-dstrbuted between and Ex :d, 4 4 t t 4 t 8 8 denotes largest nteger less tan or equal to Sawtoot functon t
32 ropertes of Γ x p Y Y recodng at Input Y Y were Input to odulo operator b Output of odulo operator 3 b were
33 recoded ZF-FE Input recoded Output wt Cannel N Q Y d d ZF FE F df d Flt O t t N Y Z * * recoded ZF-FE Feedforward Flter Output N N 33 n b Z
34 After odulo operaton at FFF output n b Z n b b a n b b a n 34 n
35 were a follows fro n ' n sgnal plus nose ' wat s te pdf of n a b a b ranst ower : a a b b Orgnal A sgnal :? - d d d unfor n, d ower ncrease s as 35
36 recodng Suary y ranstter x odulo Operator x odulo Operator x odulo - SE FE SE FE, U x ' odulo o ec. Recever ^ x d x x x d d For -ary constellaton wt dstance d. x denotes largest nteger less tan or equal to x For d nput, precoder output s d and unforly dstrbuted over d, d resultng n slgt power ncrease -
37 recodng Suary Elnates FE error propagaton p Allows us to cobne FE wt codng scees unle conventonal FE wc requres nstantaneous relable decsons wc are only avalable after decoder delay! Requres perfect nowledge of feedbac flter pulse response possble wt te-nvarant nvarant or slowly te varyng cannels. Estated at recever and sent bac va reverse cannel at expense of rate loss recodng slgtly ncreases transtted power by factor of /- for QA
On Pfaff s solution of the Pfaff problem
Zur Pfaff scen Lösung des Pfaff scen Probles Mat. Ann. 7 (880) 53-530. On Pfaff s soluton of te Pfaff proble By A. MAYER n Lepzg Translated by D. H. Delpenc Te way tat Pfaff adopted for te ntegraton of
More informationApplied Mathematics Letters
Appled Matheatcs Letters 2 (2) 46 5 Contents lsts avalable at ScenceDrect Appled Matheatcs Letters journal hoepage: wwwelseverco/locate/al Calculaton of coeffcents of a cardnal B-splne Gradr V Mlovanovć
More informationSystem in Weibull Distribution
Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co
More informationXII.3 The EM (Expectation-Maximization) Algorithm
XII.3 The EM (Expectaton-Maxzaton) Algorth Toshnor Munaata 3/7/06 The EM algorth s a technque to deal wth varous types of ncoplete data or hdden varables. It can be appled to a wde range of learnng probles
More informationStanford University CS254: Computational Complexity Notes 7 Luca Trevisan January 29, Notes for Lecture 7
Stanford Unversty CS54: Computatonal Complexty Notes 7 Luca Trevsan January 9, 014 Notes for Lecture 7 1 Approxmate Countng wt an N oracle We complete te proof of te followng result: Teorem 1 For every
More informationOur focus will be on linear systems. A system is linear if it obeys the principle of superposition and homogenity, i.e.
SSTEM MODELLIN In order to solve a control syste proble, the descrptons of the syste and ts coponents ust be put nto a for sutable for analyss and evaluaton. The followng ethods can be used to odel physcal
More informationElastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy.
Elastc Collsons Defnton: to pont asses on hch no external forces act collde thout losng any energy v Prerequstes: θ θ collsons n one denson conservaton of oentu and energy occurs frequently n everyday
More informationWhat is LP? LP is an optimization technique that allocates limited resources among competing activities in the best possible manner.
(C) 998 Gerald B Sheblé, all rghts reserved Lnear Prograng Introducton Contents I. What s LP? II. LP Theor III. The Splex Method IV. Refneents to the Splex Method What s LP? LP s an optzaton technque that
More informationError Probability for M Signals
Chapter 3 rror Probablty for M Sgnals In ths chapter we dscuss the error probablty n decdng whch of M sgnals was transmtted over an arbtrary channel. We assume the sgnals are represented by a set of orthonormal
More informationDenote the function derivatives f(x) in given points. x a b. Using relationships (1.2), polynomials (1.1) are written in the form
SET OF METHODS FO SOUTION THE AUHY POBEM FO STIFF SYSTEMS OF ODINAY DIFFEENTIA EUATIONS AF atypov and YuV Nulchev Insttute of Theoretcal and Appled Mechancs SB AS 639 Novosbrs ussa Introducton A constructon
More informationFermi-Dirac statistics
UCC/Physcs/MK/EM/October 8, 205 Fer-Drac statstcs Fer-Drac dstrbuton Matter partcles that are eleentary ostly have a type of angular oentu called spn. hese partcles are known to have a agnetc oent whch
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 informationPHYS 1443 Section 002 Lecture #20
PHYS 1443 Secton 002 Lecture #20 Dr. Jae Condtons for Equlbru & Mechancal Equlbru How to Solve Equlbru Probles? A ew Exaples of Mechancal Equlbru Elastc Propertes of Solds Densty and Specfc Gravty lud
More informationOutline. Review Numerical Approach. Schedule for April and May. Review Simple Methods. Review Notation and Order
Sstes of Ordnar Dfferental Equatons Aprl, Solvng Sstes of Ordnar Dfferental Equatons Larr Caretto Mecancal Engneerng 9 Nuercal Analss of Engneerng Sstes Aprl, Outlne Revew bascs of nuercal solutons of
More informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationDigital Signal Processing
Dgtal Sgnal Processng Dscrete-tme System Analyss Manar Mohasen Offce: F8 Emal: manar.subh@ut.ac.r School of IT Engneerng Revew of Precedent Class Contnuous Sgnal The value of the sgnal s avalable over
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 informationLecture 4: Universal Hash Functions/Streaming Cont d
CSE 5: Desgn and Analyss of Algorthms I Sprng 06 Lecture 4: Unversal Hash Functons/Streamng Cont d Lecturer: Shayan Oves Gharan Aprl 6th Scrbe: Jacob Schreber Dsclamer: These notes have not been subjected
More informationLossy Compression. Compromise accuracy of reconstruction for increased compression.
Lossy Compresson Compromse accuracy of reconstructon for ncreased compresson. The reconstructon s usually vsbly ndstngushable from the orgnal mage. Typcally, one can get up to 0:1 compresson wth almost
More informationSolutions for Homework #9
Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural
More informationx i1 =1 for all i (the constant ).
Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by
More informationChapter 8: Fast Convolution. Keshab K. Parhi
Cater 8: Fat Convoluton Keab K. Par Cater 8 Fat Convoluton Introducton Cook-Too Algort and Modfed Cook-Too Algort Wnograd Algort and Modfed Wnograd Algort Iterated Convoluton Cyclc Convoluton Degn of Fat
More informationChapter One Mixture of Ideal Gases
herodynacs II AA Chapter One Mxture of Ideal Gases. Coposton of a Gas Mxture: Mass and Mole Fractons o deterne the propertes of a xture, we need to now the coposton of the xture as well as the propertes
More informationChapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A.
Chapter 3 Gas Mxtures Study Gude n PowerPont to accopany Therodynacs: An Engneerng Approach, 5th edton by Yunus A. Çengel and Mchael A. Boles The dscussons n ths chapter are restrcted to nonreactve deal-gas
More informationAt zero K: All atoms frozen at fixed positions on a periodic lattice.
September, 00 Readng: Chapter Four Homework: None Entropy and The Degree of Dsorder: Consder a sold crystallne materal: At zero K: All atoms frozen at fxed postons on a perodc lattce. Add heat to a fnte
More informationExcess Error, Approximation Error, and Estimation Error
E0 370 Statstcal Learnng Theory Lecture 10 Sep 15, 011 Excess Error, Approxaton Error, and Estaton Error Lecturer: Shvan Agarwal Scrbe: Shvan Agarwal 1 Introducton So far, we have consdered the fnte saple
More informationLimited Dependent Variables
Lmted Dependent Varables. What f the left-hand sde varable s not a contnuous thng spread from mnus nfnty to plus nfnty? That s, gven a model = f (, β, ε, where a. s bounded below at zero, such as wages
More informationRethinking MIMO for Wireless Networks: Linear Throughput Increases with Multiple Receive Antennas
Retnng MIMO for Wreless etwors: Lnear Trougput Increases wt Multple Receve Antennas ar Jndal Unversty of Mnnesota Unverstat Pompeu Fabra Jont wor wt Jeff Andrews & Steven Weber MIMO n Pont-to-Pont Cannels
More informationFinite Vector Space Representations Ross Bannister Data Assimilation Research Centre, Reading, UK Last updated: 2nd August 2003
Fnte Vector Space epresentatons oss Bannster Data Asslaton esearch Centre, eadng, UK ast updated: 2nd August 2003 Contents What s a lnear vector space?......... 1 About ths docuent............ 2 1. Orthogonal
More informationLECTURE :FACTOR ANALYSIS
LCUR :FACOR ANALYSIS Rta Osadchy Based on Lecture Notes by A. Ng Motvaton Dstrbuton coes fro MoG Have suffcent aount of data: >>n denson Use M to ft Mture of Gaussans nu. of tranng ponts If
More information3. Tensor (continued) Definitions
atheatcs Revew. ensor (contnued) Defntons Scalar roduct of two tensors : : : carry out the dot roducts ndcated ( )( ) δ δ becoes becoes atheatcs Revew But, what s a tensor really? tensor s a handy reresentaton
More informationMultipoint Analysis for Sibling Pairs. Biostatistics 666 Lecture 18
Multpont Analyss for Sblng ars Bostatstcs 666 Lecture 8 revously Lnkage analyss wth pars of ndvduals Non-paraetrc BS Methods Maxu Lkelhood BD Based Method ossble Trangle Constrant AS Methods Covered So
More informationComputational and Statistical Learning theory Assignment 4
Coputatonal and Statstcal Learnng theory Assgnent 4 Due: March 2nd Eal solutons to : karthk at ttc dot edu Notatons/Defntons Recall the defnton of saple based Radeacher coplexty : [ ] R S F) := E ɛ {±}
More informationDirect Methods for Solving Macromolecular Structures Ed. by S. Fortier Kluwer Academic Publishes, The Netherlands, 1998, pp
Drect Metods for Solvng Macromolecular Structures Ed. by S. Forter Kluwer Academc Publses, Te Neterlands, 998, pp. 79-85. SAYRE EQUATION, TANGENT FORMULA AND SAYTAN FAN HAI-FU Insttute of Pyscs, Cnese
More informationINDEX NUMBER THEORY AND MEASUREMENT ECONOMICS. By W.E. Diewert. February CHAPTER 9: Two Stage Aggregation and Homogeneous Weak Separability
IDEX UMBER THEORY AD MEASUREMET ECOOMICS By W.E. Dewert. February 05. CHAPTER 9: Two Stage Aggregaton and Hoogeneous Weak Separablty. Introducton Most statstcal agences use the Laspeyres forula to aggregate
More informationUniversal communication part II: channels with memory
Unversal councaton part II: channels wth eory Yuval Lontz, Mer Feder Tel Avv Unversty, Dept. of EE-Systes Eal: {yuvall,er@eng.tau.ac.l arxv:202.047v2 [cs.it] 20 Mar 203 Abstract Consder councaton over
More information= z 20 z n. (k 20) + 4 z k = 4
Problem Set #7 solutons 7.2.. (a Fnd the coeffcent of z k n (z + z 5 + z 6 + z 7 + 5, k 20. We use the known seres expanson ( n+l ( z l l z n below: (z + z 5 + z 6 + z 7 + 5 (z 5 ( + z + z 2 + z + 5 5
More informationScattering by a perfectly conducting infinite cylinder
Scatterng by a perfectly conductng nfnte cylnder Reeber that ths s the full soluton everywhere. We are actually nterested n the scatterng n the far feld lt. We agan use the asyptotc relatonshp exp exp
More informationPreference and Demand Examples
Dvson of the Huantes and Socal Scences Preference and Deand Exaples KC Border October, 2002 Revsed Noveber 206 These notes show how to use the Lagrange Karush Kuhn Tucker ultpler theores to solve the proble
More informationThe Parity of the Number of Irreducible Factors for Some Pentanomials
The Party of the Nuber of Irreducble Factors for Soe Pentanoals Wolfra Koepf 1, Ryul K 1 Departent of Matheatcs Unversty of Kassel, Kassel, F. R. Gerany Faculty of Matheatcs and Mechancs K Il Sung Unversty,
More informationOn the number of regions in an m-dimensional space cut by n hyperplanes
6 On the nuber of regons n an -densonal space cut by n hyperplanes Chungwu Ho and Seth Zeran Abstract In ths note we provde a unfor approach for the nuber of bounded regons cut by n hyperplanes n general
More informationFeb 14: Spatial analysis of data fields
Feb 4: Spatal analyss of data felds Mappng rregularly sampled data onto a regular grd Many analyss technques for geophyscal data requre the data be located at regular ntervals n space and/or tme. hs s
More information1 Definition of Rademacher Complexity
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #9 Scrbe: Josh Chen March 5, 2013 We ve spent the past few classes provng bounds on the generalzaton error of PAClearnng algorths for the
More informationNot-for-Publication Appendix to Optimal Asymptotic Least Aquares Estimation in a Singular Set-up
Not-for-Publcaton Aendx to Otmal Asymtotc Least Aquares Estmaton n a Sngular Set-u Antono Dez de los Ros Bank of Canada dezbankofcanada.ca December 214 A Proof of Proostons A.1 Proof of Prooston 1 Ts roof
More informationarxiv: v2 [math.co] 3 Sep 2017
On the Approxate Asyptotc Statstcal Independence of the Peranents of 0- Matrces arxv:705.0868v2 ath.co 3 Sep 207 Paul Federbush Departent of Matheatcs Unversty of Mchgan Ann Arbor, MI, 4809-043 Septeber
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 information1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys
More information,..., k N. , k 2. ,..., k i. The derivative with respect to temperature T is calculated by using the chain rule: & ( (5) dj j dt = "J j. k i.
Suppleentary Materal Dervaton of Eq. 1a. Assue j s a functon of the rate constants for the N coponent reactons: j j (k 1,,..., k,..., k N ( The dervatve wth respect to teperature T s calculated by usng
More informationAssuming that the transmission delay is negligible, we have
Baseband Transmsson of Bnary Sgnals Let g(t), =,, be a sgnal transmtted over an AWG channel. Consder the followng recever g (t) + + Σ x(t) LTI flter h(t) y(t) t = nt y(nt) threshold comparator Decson ˆ
More informationSource-Channel-Sink Some questions
Source-Channel-Snk Soe questons Source Channel Snk Aount of Inforaton avalable Source Entro Generall nos and a be te varng Introduces error and lts the rate at whch data can be transferred ow uch nforaton
More informationPHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University
PHYS 45 Sprng semester 7 Lecture : Dealng wth Expermental Uncertantes Ron Refenberger Brck anotechnology Center Purdue Unversty Lecture Introductory Comments Expermental errors (really expermental uncertantes)
More informationFall 2012 Analysis of Experimental Measurements B. Eisenstein/rev. S. Errede
Fall 0 Analyss of Expermental easurements B. Esensten/rev. S. Errede We now reformulate the lnear Least Squares ethod n more general terms, sutable for (eventually extendng to the non-lnear case, and also
More informationComposite Hypotheses testing
Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter
More informationCHAPTER 6 CONSTRAINED OPTIMIZATION 1: K-T CONDITIONS
Chapter 6: Constraned Optzaton CHAPER 6 CONSRAINED OPIMIZAION : K- CONDIIONS Introducton We now begn our dscusson of gradent-based constraned optzaton. Recall that n Chapter 3 we looked at gradent-based
More informationGradient Descent Learning and Backpropagation
Artfcal Neural Networks (art 2) Chrstan Jacob Gradent Descent Learnng and Backpropagaton CSC 533 Wnter 200 Learnng by Gradent Descent Defnton of the Learnng roble Let us start wth the sple case of lnear
More informationTLCOM 612 Advanced Telecommunications Engineering II
TLCOM 62 Advanced Telecommuncatons Engneerng II Wnter 2 Outlne Presentatons The moble rado sgnal envronment Combned fadng effects and nose Delay spread and Coherence bandwdth Doppler Shft Fast vs. Slow
More informationPerformance Analysis of V-BLAST with Optimum Power Allocation
Perforance Analyss of V-BLAST wth Optu Power Allocaton Vctora Kostna, Sergey Loyka School of Inforaton Technology and Engneerng, Unversty of Ottawa, 6 Lous Pasteur, Ottawa, Canada, KN 6N5 E-al: sergey.loyka@eee.org
More informationECE 2C, notes set 7: Basic Transistor Circuits; High-Frequency Response
class notes, M. odwell, copyrhted 013 EE, notes set 7: Basc Transstor rcuts; Hh-Frequency esponse Mark odwell Unversty of alforna, Santa Barbara rodwell@ece.ucsb.edu 805-893-344, 805-893-36 fax oals class
More informationLimit Cycle Bifurcations in a Class of Cubic System near a Nilpotent Center *
Appled Mateatcs 77-777 ttp://dxdoorg/6/a75 Publsed Onlne July (ttp://wwwscrporg/journal/a) Lt Cycle Bfurcatons n a Class of Cubc Syste near a Nlpotent Center * Jao Jang Departent of Mateatcs Sanga Marte
More informationCOS 511: Theoretical Machine Learning
COS 5: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #0 Scrbe: José Sões Ferrera March 06, 203 In the last lecture the concept of Radeacher coplexty was ntroduced, wth the goal of showng that
More informationEE513 Audio Signals and Systems. Statistical Pattern Classification Kevin D. Donohue Electrical and Computer Engineering University of Kentucky
EE53 Audo Sgnals and Systes Statstcal Pattern Classfcaton Kevn D. Donohue Electrcal and Couter Engneerng Unversty of Kentucy Interretaton of Audtory Scenes Huan erceton and cognton greatly eceeds any couter-based
More informationFinal Exam Solutions, 1998
58.439 Fnal Exa Solutons, 1998 roble 1 art a: Equlbru eans that the therodynac potental of a consttuent s the sae everywhere n a syste. An exaple s the Nernst potental. If the potental across a ebrane
More informationTests of Single Linear Coefficient Restrictions: t-tests and F-tests. 1. Basic Rules. 2. Testing Single Linear Coefficient Restrictions
ECONOMICS 35* -- NOTE ECON 35* -- NOTE Tests of Sngle Lnear Coeffcent Restrctons: t-tests and -tests Basc Rules Tests of a sngle lnear coeffcent restrcton can be performed usng ether a two-taled t-test
More informationMulti-dimensional Central Limit Argument
Mult-dmensonal Central Lmt Argument Outlne t as Consder d random proceses t, t,. Defne the sum process t t t t () t (); t () t are d to (), t () t 0 () t tme () t () t t t As, ( t) becomes a Gaussan random
More informationChapter 6. Wideband channels. Slides for Wireless Communications Edfors, Molisch, Tufvesson
Chapter 6 Wdeband channels 128 Delay (tme) dsperson A smple case Transmtted mpulse h h a a a 1 1 2 2 3 3 Receved sgnal (channel mpulse response) 1 a 1 2 a 2 a 3 3 129 Delay (tme) dsperson One reflecton/path,
More informationCHAPTER 7 CONSTRAINED OPTIMIZATION 1: THE KARUSH-KUHN-TUCKER CONDITIONS
CHAPER 7 CONSRAINED OPIMIZAION : HE KARUSH-KUHN-UCKER CONDIIONS 7. Introducton We now begn our dscusson of gradent-based constraned optzaton. Recall that n Chapter 3 we looked at gradent-based unconstraned
More informationChapter 12 Lyes KADEM [Thermodynamics II] 2007
Chapter 2 Lyes KDEM [Therodynacs II] 2007 Gas Mxtures In ths chapter we wll develop ethods for deternng therodynac propertes of a xture n order to apply the frst law to systes nvolvng xtures. Ths wll be
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationXiangwen Li. March 8th and March 13th, 2001
CS49I Approxaton Algorths The Vertex-Cover Proble Lecture Notes Xangwen L March 8th and March 3th, 00 Absolute Approxaton Gven an optzaton proble P, an algorth A s an approxaton algorth for P f, for an
More informationOn Syndrome Decoding of Punctured Reed-Solomon and Gabidulin Codes 1
Ffteenth Internatonal Workshop on Algebrac and Cobnatoral Codng Theory June 18-24, 2016, Albena, Bulgara pp. 35 40 On Syndroe Decodng of Punctured Reed-Soloon and Gabduln Codes 1 Hannes Bartz hannes.bartz@tu.de
More informationLINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables
LINEAR REGRESSION ANALYSIS MODULE VIII Lecture - 7 Indcator Varables Dr. Shalabh Department of Maematcs and Statstcs Indan Insttute of Technology Kanpur Indcator varables versus quanttatve explanatory
More informationThe Gaussian classifier. Nuno Vasconcelos ECE Department, UCSD
he Gaussan classfer Nuno Vasconcelos ECE Department, UCSD Bayesan decson theory recall that we have state of the world X observatons g decson functon L[g,y] loss of predctng y wth g Bayes decson rule s
More informationLecture 3. Camera Models 2 & Camera Calibration. Professor Silvio Savarese Computational Vision and Geometry Lab. 13- Jan- 15.
Lecture Caera Models Caera Calbraton rofessor Slvo Savarese Coputatonal Vson and Geoetry Lab Slvo Savarese Lecture - - Jan- 5 Lecture Caera Models Caera Calbraton Recap of caera odels Caera calbraton proble
More informationMultiplicative Functions and Möbius Inversion Formula
Multplcatve Functons and Möbus Inverson Forula Zvezdelna Stanova Bereley Math Crcle Drector Mlls College and UC Bereley 1. Multplcatve Functons. Overvew Defnton 1. A functon f : N C s sad to be arthetc.
More informationChapter 7 Generalized and Weighted Least Squares Estimation. In this method, the deviation between the observed and expected values of
Chapter 7 Generalzed and Weghted Least Squares Estmaton The usual lnear regresson model assumes that all the random error components are dentcally and ndependently dstrbuted wth constant varance. When
More information, rst we solve te PDE's L ad L ad n g g (x) = ; = ; ; ; n () (x) = () Ten, we nd te uncton (x), te lnearzng eedbac and coordnates transormaton are gve
Freedom n Coordnates Transormaton or Exact Lnearzaton and ts Applcaton to Transent Beavor Improvement Kenj Fujmoto and Tosaru Suge Dvson o Appled Systems Scence, Kyoto Unversty, Uj, Kyoto, Japan suge@robotuassyoto-uacjp
More information1.3 Hence, calculate a formula for the force required to break the bond (i.e. the maximum value of F)
EN40: Dynacs and Vbratons Hoework 4: Work, Energy and Lnear Moentu Due Frday March 6 th School of Engneerng Brown Unversty 1. The Rydberg potental s a sple odel of atoc nteractons. It specfes the potental
More informationThe Finite Element Method: A Short Introduction
Te Fnte Element Metod: A Sort ntroducton Wat s FEM? Te Fnte Element Metod (FEM) ntroduced by engneers n late 50 s and 60 s s a numercal tecnque for solvng problems wc are descrbed by Ordnary Dfferental
More informationA Proof of a Conjecture for the Number of Ramified Coverings of the Sphere by the Torus
Journal of Cobnatoral Theory, Seres A 88, 4658 (999) Artcle ID jcta99999, avalable onlne at httpwwwdealbraryco on A Proof of a Conjecture for the Nuber of Rafed Coverngs of the Sphere by the Torus I P
More informationSlobodan Lakić. Communicated by R. Van Keer
Serdca Math. J. 21 (1995), 335-344 AN ITERATIVE METHOD FOR THE MATRIX PRINCIPAL n-th ROOT Slobodan Lakć Councated by R. Van Keer In ths paper we gve an teratve ethod to copute the prncpal n-th root and
More informationAn Optimal Bound for Sum of Square Roots of Special Type of Integers
The Sxth Internatonal Syposu on Operatons Research and Its Applcatons ISORA 06 Xnang, Chna, August 8 12, 2006 Copyrght 2006 ORSC & APORC pp. 206 211 An Optal Bound for Su of Square Roots of Specal Type
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 informationHowever, since P is a symmetric idempotent matrix, of P are either 0 or 1 [Eigen-values
Fall 007 Soluton to Mdterm Examnaton STAT 7 Dr. Goel. [0 ponts] For the general lnear model = X + ε, wth uncorrelated errors havng mean zero and varance σ, suppose that the desgn matrx X s not necessarly
More information1 GSW Iterative Techniques for y = Ax
1 for y = A I m gong to cheat here. here are a lot of teratve technques that can be used to solve the general case of a set of smultaneous equatons (wrtten n the matr form as y = A), but ths chapter sn
More informationLecture 19 of 42. MAP and MLE continued, Minimum Description Length (MDL)
Lecture 19 of 4 MA and MLE contnued, Mnu Descrpton Length (MDL) Wednesday, 8 February 007 Wlla H. Hsu, KSU http://www.kddresearch.org Readngs for next class: Chapter 5, Mtchell Lecture Outlne Read Sectons
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 informationDiscrete Memoryless Channels
Dscrete Meorless Channels Source Channel Snk Aount of Inforaton avalable Source Entro Generall nos, dstorted and a be te varng ow uch nforaton s receved? ow uch s lost? Introduces error and lts the rate
More informationPubH 7405: REGRESSION ANALYSIS. SLR: INFERENCES, Part II
PubH 7405: REGRESSION ANALSIS SLR: INFERENCES, Part II We cover te topc of nference n two sessons; te frst sesson focused on nferences concernng te slope and te ntercept; ts s a contnuaton on estmatng
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have
More informationLeast Squares Fitting of Data
Least Squares Fttng of Data Davd Eberly Geoetrc Tools, LLC http://www.geoetrctools.co/ Copyrght c 1998-2014. All Rghts Reserved. Created: July 15, 1999 Last Modfed: February 9, 2008 Contents 1 Lnear Fttng
More informationScatter Plot x
Construct a scatter plot usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent
More informationStatistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation
Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 13 The Smple Lnear Regresson Model and Correlaton 1999 Prentce-Hall, Inc. Chap. 13-1 Chapter Topcs Types of Regresson Models Determnng the Smple Lnear
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not
More informationEconomics 130. Lecture 4 Simple Linear Regression Continued
Economcs 130 Lecture 4 Contnued Readngs for Week 4 Text, Chapter and 3. We contnue wth addressng our second ssue + add n how we evaluate these relatonshps: Where do we get data to do ths analyss? How do
More informationCOMP th April, 2007 Clement Pang
COMP 540 12 th Aprl, 2007 Cleent Pang Boostng Cobnng weak classers Fts an Addtve Model Is essentally Forward Stagewse Addtve Modelng wth Exponental Loss Loss Functons Classcaton: Msclasscaton, Exponental,
More informationFeasibility Conditions of Interference Alignment via Two Orthogonal Subcarriers
Feasblty Condtons of Interference Algnment va Two Ortogonal Subcarrers Stefan Ders and Gerard Kramer Insttute for Communcatons Engneerng Tecnsce Unverstät Müncen, Munc, Germany Emal: {stefan.ders, gerard.ramer}@tum.de
More informationFinite Fields and Their Applications
Fnte Felds and Ther Applcatons 5 009 796 807 Contents lsts avalable at ScenceDrect Fnte Felds and Ther Applcatons www.elsever.co/locate/ffa Typcal prtve polynoals over nteger resdue rngs Tan Tan a, Wen-Feng
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More informationAverage SIR of the desired user ([7]) β=0.99. β= Average NSE of the desired user (BADD) β=0.95. µ= β=0.9
A Blnd Adaptve Decorrelatng Detector for CDMA Systems Sennur Ulukus Roy D. Yates Department of lectrcal and Computer ngneerng Wreless Informaton Networks Laboratory (WINLAB) Rutgers Unversty, PO Box 909,
More informationtotal If no external forces act, the total linear momentum of the system is conserved. This occurs in collisions and explosions.
Lesson 0: Collsons, Rotatonal netc Energy, Torque, Center o Graty (Sectons 7.8 Last te we used ewton s second law to deelop the pulse-oentu theore. In words, the theore states that the change n lnear oentu
More information