Digital Communications I: Modulation and Coding Course. Term Catharina Logothetis Lecture 8
|
|
- Laureen Stokes
- 5 years ago
- Views:
Transcription
1 Digital Communication I: odulation and Coding Coure Term 3-8 Catharina Logotheti Lecture 8
2 Lat time we talked about: Some bandpa modulation cheme -A, -SK, -FSK, -QA How to perform coherent and noncoherent detection Lecture 8
3 xample of two dim. modulation 6QA ψ t SK ψ t QSK 5 ψ t ψ t ψ t ψ t Lecture
4 Today, we are going to talk about: How to calculate the average probability of ymbol error for different modulation cheme that we tudied? How to compare different modulation cheme baed on their error performance? Lecture 8 4
5 rror probability of bandpa modulation Before evaluating the error probability, it i important to remember that: The type of modulation and detection coherent or noncoherent determine the tructure of the deciion circuit and hence the deciion variable, denoted by. The deciion variable,, i compared with - threhold, correponding to deciion region for detection purpoe. ψ t rt ψ t N T T r r N r r N r r Deciion Circuit Compare with threhold. mˆ Lecture 8 5
6 rror probability The matched filter output obervation vector r i the detector input and the deciion variable i a f r function of r, i.e. For A, QA and FSK with coherent detection r For SK with coherent detection r For non-coherent detection -FSK and DSK, r We know that for calculating the average probability of ymbol error, we need to determine r r lie inide Z i i ent r atifie condition C Hence, we need to know the tatitic of, which depend on the modulation cheme and the detection type. i i ent Lecture 8 6
7 rror probability AWGN channel model: r i + The ignal vector i ai, ai,..., ain i determinitic. The element of the noie vector n n, n,..., nn are i.i.d Gauian random variable with ero-mean and variance N /. The noie vector' pdf i n pn n exp N / π N N The element of the oberved vector r r, r,..., r N are independent Gauian random variable. It pdf i r i pr r i exp N / π N N n Lecture 8 7
8 rror probability BSK and BFSK with coherent detection: BSK B ψ t b b b Q ψ t / N / BFSK ψ t b b b ψ t B Q b N B Q b N Lecture 8 8
9 rror probability Non-coherent detection of BFSK / T co ω t T / T in ω t r r r + Deciion variable: Difference of envelope rt / T co ω t T T r r + - Deciion rule: if T >, mˆ if T <, mˆ mˆ / T in ω t r r + T r Lecture 8 9
10 Lecture 8 rror probability cont d Non-coherent detection of BFSK Similarly, non-coherent detection of DBSK [ ] > > > > + >, r, r r r r d p d p d p B exp N b B exp N b B Rayleigh pdf Rician pdf
11 Coherent detection of -A Deciion variable: rror probability. r 4-A 3 g g g g ψ t ψ t rt T r L detector Compare with - threhold mˆ Lecture 8
12 Lecture 8 rror probability. Coherent detection of -A. rror happen if the noie,, exceed in amplitude one-half of the ditance between adjacent ymbol. For ymbol on the border, error can happen only in one direction. Hence: g e g e g m m e r n r n m r n < > < < > r and r ; for r 6 log N Q b g b 3 log m r n Gauian pdf with ero mean and variance / N > < + > + > r r r r N Q dn n p n n n n g n g g g g m m e g
13 rror probability Coherent detection of -QA ψ t ψ t r 6-QA L detector 9 ψ t rt ψ t T r Compare with threhold L detector arallel-to-erial converter mˆ T Compare with threhold Lecture 8 3
14 rror probability Coherent detection of -QA -QA can be viewed a the combination of two modulation on I and Q branche, repectively. No error occur if no error i detected on either the I or the Q branch. Conidering the ymmetry of the ignal pace and the orthogonality of the I and Q branche: A C rno error detected on I and Q branche rno error detected on I and Q branche 4 Q 3log N b rno error on Irno error on Q rno error on I Lecture 8 4 Average probability of ymbol error for A
15 rror probability Coherent detection of SK ψ t SK 5 ψ t ψ t r rt ψ t T r arctan r φˆ Compute φ φˆ i Chooe mallet mˆ T r Deciion variable φˆ r Lecture 8 5
16 Lecture 8 6 rror probability Coherent detection of SK The detector compare the phae of obervation vector to - threhold. Due to the circular ymmetry of the ignal pace, we have: where It can be hown that φ φ π π φ d p c m m c C / / ˆ N Q π in N Q b π in log or ; in exp co ˆ π φ φ φ π φ φ N N p
17 rror probability Coherent detection of -FSK ψ t rt ψ t T T r r r r r r L detector: Chooe the larget element in the oberved vector mˆ Lecture 8 7
18 rror probability Coherent detection of -FSK The dimenion of the ignal pace i. An upper bound for the average ymbol error probability can be obtained by uing the union bound. Hence: or, equivalently Q N Q log N b Lecture 8 8
19 Bit error probability veru ymbol error probability Number of bit per ymbol For orthogonal -ary ignaling -FSK lim k B k B k / For -SK, -A and -QA k log B k for < < Lecture 8 9
20 robability of ymbol error for binary modulation Note! The ame average ymbol energy for different ie of ignal pace b / N db Lecture 8
21 robability of ymbol error for -SK Note! The ame average ymbol energy for different ie of ignal pace b / N db Lecture 8
22 robability of ymbol error for -FSK Note! The ame average ymbol energy for different ie of ignal pace b / N db Lecture 8
23 robability of ymbol error for -A Note! The ame average ymbol energy for different ie of ignal pace b / N db Lecture 8 3
24 robability of ymbol error for - QA Note! The ame average ymbol energy for different ie of ignal pace b / N db Lecture 8 4
25 xample of ample of matched filter output for ome bandpa modulation cheme Lecture 8 5
Chapter 5 Optimum Receivers for the Additive White Gaussian Noise Channel
Chapter 5 Optimum Receiver for the Additive White Gauian Noie Channel Table of Content 5.1 Optimum Receiver for Signal Corrupted by Additive White Noie 5.1.1 Correlation Demodulator 5.1. Matched-Filter
More informationA Study on Simulating Convolutional Codes and Turbo Codes
A Study on Simulating Convolutional Code and Turbo Code Final Report By Daniel Chang July 27, 2001 Advior: Dr. P. Kinman Executive Summary Thi project include the deign of imulation of everal convolutional
More informationPRACTICE FINAL EXAM SOLUTION Jing Liang 12/06/2006
PRACICE FIAL EXAM SOLUIO Jing Liang /6/6 PROBLEM (a) (b) (c) (d) (e) he propagation ignal experience power variation due to the contructive and detructive addition of multi-path ignal component, and therefore
More informationDigital Band-pass Modulation PROF. MICHAEL TSAI 2011/11/10
Digital Band-pass Modulation PROF. MICHAEL TSAI 211/11/1 Band-pass Signal Representation a t g t General form: 2πf c t + φ t g t = a t cos 2πf c t + φ t Envelope Phase Envelope is always non-negative,
More informationSpring 2014 EE 445S Real-Time Digital Signal Processing Laboratory. Homework #0 Solutions on Review of Signals and Systems Material
Spring 4 EE 445S Real-Time Digital Signal Proceing Laboratory Prof. Evan Homework # Solution on Review of Signal and Sytem Material Problem.. Continuou-Time Sinuoidal Generation. In practice, we cannot
More informationOrthogonal Signals With orthogonal signals, we select only one of the orthogonal basis functions for transmission:
4..4 Orthogonal, Biorthogonal and Simplex Signal 4.- In PAM, QAM and PSK, we had only one ai function. For orthogonal, iorthogonal and implex ignal, however, we ue more than one orthogonal ai function,
More informationA Simple Example Binary Hypothesis Testing Optimal Receiver Frontend M-ary Signal Sets Message Sequences. = 4 for QPSK) E b Q 2. 2E b.
Exercie: QPSK I Find the error rate for the ignal et n (t) = p 2E /T co(2pf c t + n p/2 + p/4), for n = 0,, 3 I Anwer: (Recall h P = d min 2 E b = 4 for QPSK) E Pr{e} = 2Q Q 2 = 2Q = 2Q 2E b h P E b 2
More informationLecture 7: Testing Distributions
CSE 5: Sublinear (and Streaming) Algorithm Spring 014 Lecture 7: Teting Ditribution April 1, 014 Lecturer: Paul Beame Scribe: Paul Beame 1 Teting Uniformity of Ditribution We return today to property teting
More informationJul 4, 2005 turbo_code_primer Revision 0.0. Turbo Code Primer
Jul 4, 5 turbo_code_primer Reviion. Turbo Code Primer. Introduction Thi document give a quick tutorial on MAP baed turbo coder. Section develop the background theory. Section work through a imple numerical
More informationFlat Rayleigh fading. Assume a single tap model with G 0,m = G m. Assume G m is circ. symmetric Gaussian with E[ G m 2 ]=1.
Flat Rayleigh fading Assume a single tap model with G 0,m = G m. Assume G m is circ. symmetric Gaussian with E[ G m 2 ]=1. The magnitude is Rayleigh with f Gm ( g ) =2 g exp{ g 2 } ; g 0 f( g ) g R(G m
More informationChapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog
Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou
More informationLRA DSP. Multi-Rate DSP. Applications: Oversampling, Undersampling, Quadrature Mirror Filters. Professor L R Arnaut 1
ulti-rate Application: Overampling, Underampling, Quadrature irror Filter Profeor L R Arnaut ulti-rate Overampling Profeor L R Arnaut Optimal Sampling v. Overampling Sampling at Nyquit rate F =F B Allow
More informationEfficient Methods of Doppler Processing for Coexisting Land and Weather Clutter
Efficient Method of Doppler Proceing for Coexiting Land and Weather Clutter Ça gatay Candan and A Özgür Yılmaz Middle Eat Technical Univerity METU) Ankara, Turkey ccandan@metuedutr, aoyilmaz@metuedutr
More informationC up (E) C low (E) E 2 E 1 E 0
Spreading in lock-fading hannel. Muriel Médard David N.. Te medardmit.edu Maachuett Intitute of Technoy dteeec.berkeley.edu Univerity of alifornia at erkeley btract We conider wideband fading channel which
More informationCHAPTER 14. Based on the info about the scattering function we know that the multipath spread is T m =1ms, and the Doppler spread is B d =0.2 Hz.
CHAPTER 4 Problem 4. : Based on the info about the scattering function we know that the multipath spread is T m =ms, and the Doppler spread is B d =. Hz. (a) (i) T m = 3 sec (ii) B d =. Hz (iii) ( t) c
More informationWeek 3 Statistics for bioinformatics and escience
Week 3 Statitic for bioinformatic and escience Line Skotte 28. november 2008 2.9.3-4) In thi eercie we conider microrna data from Human and Moue. The data et repreent 685 independent realiation of the
More information4th National Conference on Electrical, Electronics and Computer Engineering (NCEECE 2015)
4th National Conference on Electrical, Electronic and Computer Engineering (NCEECE 25) The Reearch on Anti-interference Performance of Ambiguity Function Baed Digital Communication Sytem Xiaodong Han,
More informationDigital Control System
Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital
More informationImproved Interference Cancellation Scheme for Two-User Detection of Alamouti Code
Improved Interference Cancellation Scheme for Two-Uer Detection of Alamouti Code Manav R hatnagar and Are Hjørungne Abtract In thi correpondence, we propoe an improved interference cancellation method
More informationELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS
EC 32 (CR) Total No. of Questions :09] [Total No. of Pages : 02 III/IV B.Tech. DEGREE EXAMINATIONS, APRIL/MAY- 207 Second Semester ELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS Time: Three Hours
More informationA First Course in Digital Communications
A First Course in Digital Communications Ha H. Nguyen and E. Shwedyk February 9 A First Course in Digital Communications 1/46 Introduction There are benefits to be gained when M-ary (M = 4 signaling methods
More informationSimple Observer Based Synchronization of Lorenz System with Parametric Uncertainty
IOSR Journal of Electrical and Electronic Engineering (IOSR-JEEE) ISSN: 78-676Volume, Iue 6 (Nov. - Dec. 0), PP 4-0 Simple Oberver Baed Synchronization of Lorenz Sytem with Parametric Uncertainty Manih
More informationSignaling over MIMO Multi-Base Systems: Combination of Multi-Access and Broadcast Schemes
Signaling over MIMO Multi-Bae Sytem: Combination of Multi-Acce and Broadcat Scheme Mohammad Ali Maddah-Ali Abolfazl S. Motahari and Amir K. Khandani Coding & Signal Tranmiion Laboratory (www.ct.uwaterloo.ca)
More informationEE 477 Digital Signal Processing. 4 Sampling; Discrete-Time
EE 477 Digital Signal Proceing 4 Sampling; Dicrete-Time Sampling a Continuou Signal Obtain a equence of ignal ample uing a periodic intantaneou ampler: x [ n] = x( nt ) Often plot dicrete ignal a dot or
More informationDigital Modulation 1
Digital Modulation 1 Lecture Notes Ingmar Land and Bernard H. Fleury Navigation and Communications () Department of Electronic Systems Aalborg University, DK Version: February 5, 27 i Contents I Basic
More informationIII.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SUBSTANCES
III.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SBSTANCES. Work purpoe The analyi of the behaviour of a ferroelectric ubtance placed in an eternal electric field; the dependence of the electrical polariation
More informationECE 564/645 - Digital Communications, Spring 2018 Homework #2 Due: March 19 (In Lecture)
ECE 564/645 - Digital Communications, Spring 018 Homework # Due: March 19 (In Lecture) 1. Consider a binary communication system over a 1-dimensional vector channel where message m 1 is sent by signaling
More informationJan Purczyński, Kamila Bednarz-Okrzyńska Estimation of the shape parameter of GED distribution for a small sample size
Jan Purczyńki, Kamila Bednarz-Okrzyńka Etimation of the hape parameter of GED ditribution for a mall ample ize Folia Oeconomica Stetinenia 4()/, 35-46 04 Folia Oeconomica Stetinenia DOI: 0.478/foli-04-003
More informationBASICS OF DETECTION AND ESTIMATION THEORY
BASICS OF DETECTION AND ESTIMATION THEORY 83050E/158 In this chapter we discuss how the transmitted symbols are detected optimally from a noisy received signal (observation). Based on these results, optimal
More informationThis examination consists of 11 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS
THE UNIVERSITY OF BRITISH COLUMBIA Department of Electrical and Computer Engineering EECE 564 Detection and Estimation of Signals in Noise Final Examination 6 December 2006 This examination consists of
More informationÇankaya University ECE Department ECE 376 (MT)
Çankaya Univerity ECE Department ECE 376 (M) Student Name : Date : 13.4.15 Student Number : Open Source Exam Quetion 1. (7 Point) he time waveform of the ignal et, and t t are given in Fig. 1.1. a. Identify
More information6. KALMAN-BUCY FILTER
6. KALMAN-BUCY FILTER 6.1. Motivation and preliminary. A wa hown in Lecture 2, the optimal control i a function of all coordinate of controlled proce. Very often, it i not impoible to oberve a controlled
More informationReview of Doppler Spread The response to exp[2πift] is ĥ(f, t) exp[2πift]. ĥ(f, t) = β j exp[ 2πifτ j (t)] = exp[2πid j t 2πifτ o j ]
Review of Doppler Spread The response to exp[2πift] is ĥ(f, t) exp[2πift]. ĥ(f, t) = β exp[ 2πifτ (t)] = exp[2πid t 2πifτ o ] Define D = max D min D ; The fading at f is ĥ(f, t) = 1 T coh = 2D exp[2πi(d
More informationOutline. Digital Communications. Lecture 12 Performance over Fading Channels and Diversity Techniques. Flat-Flat Fading. Intuition
Digital Counications Lecture 2 Perforance over Fading Channels and Diversity Techniques Pierluigi SALVO ROSSI Outline Noncoherent/Coherent Detection 2 Channel Estiation Departent of Industrial and Inforation
More informationPerformance Analysis of Spread Spectrum CDMA systems
1 Performance Analysis of Spread Spectrum CDMA systems 16:33:546 Wireless Communication Technologies Spring 5 Instructor: Dr. Narayan Mandayam Summary by Liang Xiao lxiao@winlab.rutgers.edu WINLAB, Department
More informationSolutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam
BSc - Sample Examination Digital Control Sytem (5-588-) Prof. L. Guzzella Solution Exam Duration: Number of Quetion: Rating: Permitted aid: minute examination time + 5 minute reading time at the beginning
More informationLecture 10 Filtering: Applied Concepts
Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering
More informationLecture 5 Frequency Response of FIR Systems (III)
EE3054 Signal and Sytem Lecture 5 Frequency Repone of FIR Sytem (III Yao Wang Polytechnic Univerity Mot of the lide included are extracted from lecture preentation prepared by McClellan and Schafer Licene
More informationSource slideplayer.com/fundamentals of Analytical Chemistry, F.J. Holler, S.R.Crouch. Chapter 6: Random Errors in Chemical Analysis
Source lideplayer.com/fundamental of Analytical Chemitry, F.J. Holler, S.R.Crouch Chapter 6: Random Error in Chemical Analyi Random error are preent in every meaurement no matter how careful the experimenter.
More informationWhite Rose Research Online URL for this paper: Version: Accepted Version
Thi i a repoitory copy of Identification of nonlinear ytem with non-peritent excitation uing an iterative forward orthogonal leat quare regreion algorithm. White Roe Reearch Online URL for thi paper: http://eprint.whiteroe.ac.uk/107314/
More informationSuggested Answers To Exercises. estimates variability in a sampling distribution of random means. About 68% of means fall
Beyond Significance Teting ( nd Edition), Rex B. Kline Suggeted Anwer To Exercie Chapter. The tatitic meaure variability among core at the cae level. In a normal ditribution, about 68% of the core fall
More informationa) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics.
Digital Modulation and Coding Tutorial-1 1. Consider the signal set shown below in Fig.1 a) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics. b) What is the minimum Euclidean
More informationNetwork based Sensor Localization in Multi-Media Application of Precision Agriculture Part 2: Time of Arrival
Network baed Senor Localization in Multi-Media Application of Preciion Agriculture Part : Time of Arrival Herman Sahota IBM, Silicon Valley Laboratory Email: hahota@u.ibm.com Ratneh Kumar, IEEE Fellow
More informationFading Channels: Capacity, BER and Diversity
Fading Channel: Capacity, BER and Diverity Mater Univeritario en Ingeniería de Telecomunicación I. Santamaría Univeridad de Cantabria Introduction Capacity BER Diverity Concluion Content Introduction Capacity
More informationDetecting Parametric Signals in Noise Having Exactly Known Pdf/Pmf
Detecting Parametric Signals in Noise Having Exactly Known Pdf/Pmf Reading: Ch. 5 in Kay-II. (Part of) Ch. III.B in Poor. EE 527, Detection and Estimation Theory, # 5c Detecting Parametric Signals in Noise
More information9 Lorentz Invariant phase-space
9 Lorentz Invariant phae-space 9. Cro-ection The cattering amplitude M q,q 2,out p, p 2,in i the amplitude for a tate p, p 2 to make a tranition into the tate q,q 2. The tranition probability i the quare
More informationAmplify and Forward Relaying; Channel Model and Outage Behaviour
Amplify and Forward Relaying; Channel Model and Outage Behaviour Mehdi Mortazawi Molu Intitute of Telecommunication Vienna Univerity of Technology Guhautr. 5/E389, 4 Vienna, Autria Email: mmortaza@nt.tuwien.ac.at
More informationSINGLE CARRIER BLOCK TRANSMISSION WITHOUT GUARD INTERVAL
SINGLE CARRIER BLOCK TRANSMISSION WITHOUT GUARD INTERVAL Kazunori Hayahi Hideaki Sakai Graduate School of Informatic, Kyoto Univerity Kyoto, JAPAN ABSTRACT Thi paper propoe a imple detection cheme for
More informationA Genetic Algorithm for Designing Constellations with Low Error Floors
A Genetic Algorithm for Deigning Contellation with Low Error Floor Matthew C. Valenti and Raghu Doppalapudi Wet Virginia Univerity Morgantown, WV Email: {mvalenti,doppala}@cee.wvu.edu Don Torrieri U.S.
More informationGNSS Solutions: What is the carrier phase measurement? How is it generated in GNSS receivers? Simply put, the carrier phase
GNSS Solution: Carrier phae and it meaurement for GNSS GNSS Solution i a regular column featuring quetion and anwer about technical apect of GNSS. Reader are invited to end their quetion to the columnit,
More informationEE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis
EE/ME/AE34: Dynamical Sytem Chapter 8: Tranfer Function Analyi The Sytem Tranfer Function Conider the ytem decribed by the nth-order I/O eqn.: ( n) ( n 1) ( m) y + a y + + a y = b u + + bu n 1 0 m 0 Taking
More informationHOMEWORK ASSIGNMENT #2
Texa A&M Univerity Electrical Engineering Department ELEN Integrated Active Filter Deign Methodologie Alberto Valde-Garcia TAMU ID# 000 17 September 0, 001 HOMEWORK ASSIGNMENT # PROBLEM 1 Obtain at leat
More informationDetermination of the local contrast of interference fringe patterns using continuous wavelet transform
Determination of the local contrat of interference fringe pattern uing continuou wavelet tranform Jong Kwang Hyok, Kim Chol Su Intitute of Optic, Department of Phyic, Kim Il Sung Univerity, Pyongyang,
More information11.5 MAP Estimator MAP avoids this Computational Problem!
.5 MAP timator ecall that the hit-or-mi cot function gave the MAP etimator it maimize the a oteriori PDF Q: Given that the MMS etimator i the mot natural one why would we conider the MAP etimator? A: If
More informationConfusion matrices. True / False positives / negatives. INF 4300 Classification III Anne Solberg The agenda today: E.g., testing for cancer
INF 4300 Claification III Anne Solberg 29.10.14 The agenda today: More on etimating claifier accuracy Cure of dimenionality knn-claification K-mean clutering x i feature vector for pixel i i- The cla label
More informationDigital Transmission Methods S
Digital ransmission ethods S-7.5 Second Exercise Session Hypothesis esting Decision aking Gram-Schmidt method Detection.K.K. Communication Laboratory 5//6 Konstantinos.koufos@tkk.fi Exercise We assume
More informationLecture 4 Topic 3: General linear models (GLMs), the fundamentals of the analysis of variance (ANOVA), and completely randomized designs (CRDs)
Lecture 4 Topic 3: General linear model (GLM), the fundamental of the analyi of variance (ANOVA), and completely randomized deign (CRD) The general linear model One population: An obervation i explained
More informationDesign By Emulation (Indirect Method)
Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal
More informationPilot Assisted SNR Estimation in a Non-Coherent M-FSK Receiver with a Carrier Frequency Offset
IEEE ICC 0 - Signal Processing for Communications Symposium Pilot Assisted SNR Estimation in a Non-Coherent -FSK Receiver with a Carrier Frequency Offset Syed Ali Hassan School of EECS National University
More informationBogoliubov Transformation in Classical Mechanics
Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How
More informationEE6604 Personal & Mobile Communications. Week 13. Multi-antenna Techniques
EE6604 Personal & Mobile Communications Week 13 Multi-antenna Techniques 1 Diversity Methods Diversity combats fading by providing the receiver with multiple uncorrelated replicas of the same information
More informationAssignment for Mathematics for Economists Fall 2016
Due date: Mon. Nov. 1. Reading: CSZ, Ch. 5, Ch. 8.1 Aignment for Mathematic for Economit Fall 016 We now turn to finihing our coverage of concavity/convexity. There are two part: Jenen inequality for concave/convex
More informationMath 273 Solutions to Review Problems for Exam 1
Math 7 Solution to Review Problem for Exam True or Fale? Circle ONE anwer for each Hint: For effective tudy, explain why if true and give a counterexample if fale (a) T or F : If a b and b c, then a c
More informationWolfgang Hofle. CERN CAS Darmstadt, October W. Hofle feedback systems
Wolfgang Hofle Wolfgang.Hofle@cern.ch CERN CAS Darmtadt, October 9 Feedback i a mechanim that influence a ytem by looping back an output to the input a concept which i found in abundance in nature and
More informationProblem 7.7 : We assume that P (x i )=1/3, i =1, 2, 3. Then P (y 1 )= 1 ((1 p)+p) = P (y j )=1/3, j=2, 3. Hence : and similarly.
(b) We note that the above capacity is the same to the capacity of the binary symmetric channel. Indeed, if we considerthe grouping of the output symbols into a = {y 1,y 2 } and b = {y 3,y 4 } we get a
More informationLecture 7: Wireless Channels and Diversity Advanced Digital Communications (EQ2410) 1
Wireless : Wireless Advanced Digital Communications (EQ2410) 1 Thursday, Feb. 11, 2016 10:00-12:00, B24 1 Textbook: U. Madhow, Fundamentals of Digital Communications, 2008 1 / 15 Wireless Lecture 1-6 Equalization
More informationX b s t w t t dt b E ( ) t dt
Consider the following correlator receiver architecture: T dt X si () t S xt () * () t Wt () T dt X Suppose s (t) is sent, then * () t t T T T X s t w t t dt E t t dt w t dt E W t t T T T X s t w t t dt
More informationarxiv: v1 [math.mg] 25 Aug 2011
ABSORBING ANGLES, STEINER MINIMAL TREES, AND ANTIPODALITY HORST MARTINI, KONRAD J. SWANEPOEL, AND P. OLOFF DE WET arxiv:08.5046v [math.mg] 25 Aug 20 Abtract. We give a new proof that a tar {op i : i =,...,
More informationAnalysis of Water Parameters Using Daubechies Wavelet (Level 5) (Db5)
American Journal of Mathematic and Statitic, (3): -3 DOI:.93/j.ajm.3.8 Analyi of Water Parameter Uing Daubechie Wavelet (Level ) (Db) Kulwinder Singh Parmar, Rahmi Bhardwaj * Department of Mathematic,
More informationELEC546 Review of Information Theory
ELEC546 Review of Information Theory Vincent Lau 1/1/004 1 Review of Information Theory Entropy: Measure of uncertainty of a random variable X. The entropy of X, H(X), is given by: If X is a discrete random
More informationFILTERING OF NONLINEAR STOCHASTIC FEEDBACK SYSTEMS
FILTERING OF NONLINEAR STOCHASTIC FEEDBACK SYSTEMS F. CARRAVETTA 1, A. GERMANI 1,2, R. LIPTSER 3, AND C. MANES 1,2 Abtract. Thi paper concern the filtering problem for a cla of tochatic nonlinear ytem
More informationGenerating Functions. STAT253/317 Winter 2013 Lecture 8. More Properties of Generating Functions Random Walk w/ Reflective Boundary at 0
Generating Function STAT253/37 Winter 203 Lecture 8 Yibi Huang January 25, 203 Generating Function For a non-negative-integer-valued random variable T, the generating function of T i the expected value
More informationImpact of channel-state information on coded transmission over fading channels with diversity reception
Impact of channel-state information on coded transmission over fading channels with diversity reception Giorgio Taricco Ezio Biglieri Giuseppe Caire September 4, 1998 Abstract We study the synergy between
More informationDesign of Digital Filters
Deign of Digital Filter Paley-Wiener Theorem [ ] ( ) If h n i a caual energy ignal, then ln H e dω< B where B i a finite upper bound. One implication of the Paley-Wiener theorem i that a tranfer function
More informationSuggestions - Problem Set (a) Show the discriminant condition (1) takes the form. ln ln, # # R R
Suggetion - Problem Set 3 4.2 (a) Show the dicriminant condition (1) take the form x D Ð.. Ñ. D.. D. ln ln, a deired. We then replace the quantitie. 3ß D3 by their etimate to get the proper form for thi
More informationA FUNCTIONAL BAYESIAN METHOD FOR THE SOLUTION OF INVERSE PROBLEMS WITH SPATIO-TEMPORAL PARAMETERS AUTHORS: CORRESPONDENCE: ABSTRACT
A FUNCTIONAL BAYESIAN METHOD FOR THE SOLUTION OF INVERSE PROBLEMS WITH SPATIO-TEMPORAL PARAMETERS AUTHORS: Zenon Medina-Cetina International Centre for Geohazard / Norwegian Geotechnical Intitute Roger
More informationBy Xiaoquan Wen and Matthew Stephens University of Michigan and University of Chicago
Submitted to the Annal of Applied Statitic SUPPLEMENTARY APPENDIX TO BAYESIAN METHODS FOR GENETIC ASSOCIATION ANALYSIS WITH HETEROGENEOUS SUBGROUPS: FROM META-ANALYSES TO GENE-ENVIRONMENT INTERACTIONS
More informationAN ADAPTIVE SIGNAL SEARCH ALGORITHM IN GPS RECEIVER
N PTIVE SIGNL SERH LGORITHM IN GPS REEIVER Item Type text; Proceeding uthor Li, Sun; Yinfeng, Wang; Qihan, Zhang Publiher International Foundation for Telemetering Journal International Telemetering onference
More informationPerformance Degradation due to I/Q Imbalance in Multi-Carrier Direct Conversion Receivers: A Theoretical Analysis
Performance egradation due to I/Q Imbalance in Multi-Carrier irect Converion Receiver: A Theoretical Analyi Marcu Windich, Gerhard Fettwei reden Univerity of Technology, Vodafone Chair Mobile Communication
More informationEE4304 C-term 2007: Lecture 17 Supplemental Slides
EE434 C-term 27: Lecture 17 Supplemental Slides D. Richard Brown III Worcester Polytechnic Institute, Department of Electrical and Computer Engineering February 5, 27 Geometric Representation: Optimal
More informationDetection and Estimation Theory
ESE 524 Detection and Etimation Theory Joeph A. O Sullivan Samuel C. Sach Profeor Electronic Sytem and Signal Reearch Laboratory Electrical l and Sytem Engineering Wahington Univerity 2 Urbauer Hall 34-935-473
More informationDirect-Sequence Spread-Spectrum
Chapter 3 Direct-Sequence Spread-Spectrum In this chapter we consider direct-sequence spread-spectrum systems. Unlike frequency-hopping, a direct-sequence signal occupies the entire bandwidth continuously.
More informationNotes on Phase Space Fall 2007, Physics 233B, Hitoshi Murayama
Note on Phae Space Fall 007, Phyic 33B, Hitohi Murayama Two-Body Phae Space The two-body phae i the bai of computing higher body phae pace. We compute it in the ret frame of the two-body ytem, P p + p
More informationLecture 8: Period Finding: Simon s Problem over Z N
Quantum Computation (CMU 8-859BB, Fall 205) Lecture 8: Period Finding: Simon Problem over Z October 5, 205 Lecturer: John Wright Scribe: icola Rech Problem A mentioned previouly, period finding i a rephraing
More informationEE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject
EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Flat Paband/Stopband Filter T j T j Lowpa Bandpa T j T j Highpa Bandreject Review from Lat
More informationEE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject
EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation
More information5.5 Application of Frequency Response: Signal Filters
44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to
More informationDiversity Combining Techniques
Diversity Combining Techniques When the required signal is a combination of several plane waves (multipath), the total signal amplitude may experience deep fades (Rayleigh fading), over time or space.
More informationCONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. VIII Decoupling Control - M. Fikar
DECOUPLING CONTROL M. Fikar Department of Proce Control, Faculty of Chemical and Food Technology, Slovak Univerity of Technology in Bratilava, Radlinkého 9, SK-812 37 Bratilava, Slovakia Keyword: Decoupling:
More informationEE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject
EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation
More informationThe statistical properties of the primordial fluctuations
The tatitical propertie of the primordial fluctuation Lecturer: Prof. Paolo Creminelli Trancriber: Alexander Chen July 5, 0 Content Lecture Lecture 4 3 Lecture 3 6 Primordial Fluctuation Lecture Lecture
More informationBeta Burr XII OR Five Parameter Beta Lomax Distribution: Remarks and Characterizations
Marquette Univerity e-publication@marquette Mathematic, Statitic and Computer Science Faculty Reearch and Publication Mathematic, Statitic and Computer Science, Department of 6-1-2014 Beta Burr XII OR
More informationMassless fermions living in a non-abelian QCD vortex based on arxiv: [hep-ph]
Male fermion living in a non-abelian QCD vortex baed on arxiv:1001.3730 [hep-ph] Collaborator : S.Yaui KEK and M. Nitta Keio U. K. Itakura KEK Theory Center, IPNS, KEK New frontier in QCD @ Kyoto March
More informationCHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS
CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 REDUCED ORDER MODEL DESIGN FOR LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.3
More informationFundamental Physics of Force and Energy/Work:
Fundamental Phyic of Force and Energy/Work: Energy and Work: o In general: o The work i given by: dw = F dr (5) (One can argue that Eqn. 4 and 5 are really one in the ame.) o Work or Energy are calar potential
More informationEnd-to-End BER Analysis of Space Shift Keying in Decode-and-Forward Cooperative Relaying
3 IEEE Wirele Communication and Networking Conference (WCNC: PHY End-to-End BER Analyi of Space Shift Keying in Decode-and-Forwa Cooperative Relaying Pritam Som and A. Chockalingam Department of ECE, Indian
More informationLecture #9 Continuous time filter
Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................
More informationA Thresholding-Based Antenna Switching in SWIPT-Enabled MIMO Cognitive Radio Networks with Co-Channel Interference
A Threholding-Baed Antenna Switching in SWIPT-Enabled MIMO Cognitive Radio Network wi Co-Channel Interference Fatma Benkhelifa, and Mohamed-Slim Alouini Computer, Electrical and Maematical Science and
More informationON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION. Xiaoqun Wang
Proceeding of the 2008 Winter Simulation Conference S. J. Maon, R. R. Hill, L. Mönch, O. Roe, T. Jefferon, J. W. Fowler ed. ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION Xiaoqun Wang
More information