# Capacity Limits of MIMO Channels

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Tutorial and 4G Systems Capacity Limits of MIMO Channels Markku Juntti Contents 1. Introduction. Review of information theory 3. Fixed MIMO channels 4. Fading MIMO channels 5. Summary and Conclusions References Centre for Wireless Communications (CWC) 1

2 1. Introduction The use of multiple antennas can provide gain due to antenna gain more receive antennas more power is collected interference gain interference nulling by beamforming (array gain) interference averaging (to zero) due to independent observations diversity gain against fading receive diversity transmit diversity. Information theoretic model of multi-input multioutput (MIMO) channel is considered. Centre for Wireless Communications (CWC)

3 MIMO Channel Model Assume N T transmit and N R receive antennae called N T N R MIMO system. Fading radio channels modeled as frequency-flat: fixed time-varying known both/either in the transmitter and/or receiver perfect channel state information (CSI) a priori unknown. x 1 ( n) x ( n) x NT M ( n) h h 1, 1 ( n) N R, N T ( n) y 1 ( n) y ( n) y NR MIMO channel model. M ( n) Centre for Wireless Communications (CWC) 3

4 . Review of Information Theory Information theory (IT) has its origins in analyzing the limits communications. Information theory answers two fundamental questions in communication theory: What is the ultimate data compression rate? Answer: entropy. What is the ultimate data transmission rate? Answer: channel capacity. Centre for Wireless Communications (CWC) 4

5 Basic Concepts Assume a discrete valued random variable (RV) X with probability mass function p(x). The average information or entropy of RV X: 1 H ( X ) = p( x ) log[ p( x )] = E[ logp( X )] = E log ( ) x p X Joint entropy of RV s X and Y: [ p( x, y )] = E [ log[ p( X, ) ] Conditional entropy of RV Y given X = x: = p( x ) H ( Y X = x ) = p( x, y )log p( y x ) = x x y Chain rule: H ( X, Y ) = H ( X ) + H ( Y X ). { }. H ( X, Y ) p( x, y )log Y = x y [ ] E log[ p( X, ]. { }. H (Y X ) Y ) Centre for Wireless Communications (CWC) 5

6 Mutual Information Mutual information is the relative entropy between the joint distribution and product distribution: p( x, y ) p( X, Y ) I ( X ; Y ) = p( x, y )log = E log. ( ) ( ) ( ) ( ) p x p y p X p Y I x y ( X ; Y ) = H ( X ) H ( X Y ) = H ( Y ) H ( Y X ) ( ) ( ) ( ) ( ). = H X + H Y H X, Y = I Y ; X Measure of the information one random variable (say, X) contains on the other (Y): If X and Y are independent: I(X;Y) = 0 (also only if ). If Y = X: I(X;X) = H(X). Differential entropy for continuous RV s. Centre for Wireless Communications (CWC) 6

7 Gaussian RV s For multivariate, real-valued Gaussian RV s X 1, X,, X n with mean vector µ and covariance matrix K, the differential entropy is 1 ( ) [( ) ],, n h X1 X K, X n = log πe det( K). Gaussian distribution maximizes the entropy over all distributions with the same covariance: 1 ( ) [( ) ],, n h X1 X K, X n log πe det( K) for any RV s X 1, X,, X n with equality if and only if they are Gaussian. Centre for Wireless Communications (CWC) 7

8 Channel Capacity Message Channel Encoder p(y x) W X n Y n Decoder Information theoretic model of a communication system. Estimate of message Ŵ Channel capacity: C = maxi( X; Y ). p( x) Code rate R is achievable, if there exists a sequence of (nr,n) codes so that P 0, as n. e, max Centre for Wireless Communications (CWC) 8

9 Gaussian Channel X i Channel capacity: C = E Z i S ~ N(0, σ The Gaussian channel. max p( x ) ( ) X σ S I N ). Y i = X i + Z i ( X ; Y ) = log1 ( + γ), Capacity per time unit ((W) samples per second): P C = W log 1 +. N0W 1 γ = σ σ S N. Centre for Wireless Communications (CWC) 9

10 Parallel Gaussian Channels C = Capacity: k σ S,i i = 1 σ N,i 1 log 1 + Optimal transmission: X ~ N 0, diagσ water-filling. = k i = 1 1 ( log1 + γ ). i [ ], σ, K, σ S,1 S, S, k S Z 1 ~ N(0, σ N,1 X Y 1 1 Z ~ N(0, X Y X k S M S Z σ N, k ~ N(0, σ Y k N,k ). ). ). Parallel Gaussian channels. Centre for Wireless Communications (CWC) 10

11 3. Fixed MIMO Channels Signal x (n) i is transmitted at time interval n from antenna i (i=1,,,n T ). Signal y (n) j is received at time interval n at antenna j (j=1,,,n R ): y j N T ( n) = h ( n) x ( n ) + η ( n), i = 1 where h ij (n) is the complex channel gain with E ij h ij i ( n ) = 1 j x 1 ( n) x ( n) x NT M ( n) h 1, 1 ( n) ( n) Centre for Wireless Communications (CWC) 11 h N R, N T y 1 ( n) y ( n) y NR MIMO channel model. M ( n)

12 Matrix Formulation of MIMO Channel Model The signal received at all antennas: where H ( n) y ( n) = H( n) x( n) + η( n), x ( n ) = x ( n ) x ( n ) L x ( ) N n y h h h N 1,1 R ( n) h ( n) L h ( n) ( n) h ( n) L h ( n),1 1, ( n) h ( n) L h ( n) R, 1, N,1,, N NR N = C M [ ] T T 1, C N T [ y n y n y ] T NR, N n C ( n ) = ( ) ( ) L ( ) 1 N M O R R T M T N, N T T. Centre for Wireless Communications (CWC) 1

13 Noise Model and Power Constraint The noise vector satisfies The transmitted signal satisfies the average power constraint: E η [ ] T C NR, ( n ) = η ( n ) η ( n ) L η ( n ) 1 N ( ( ) ( )) T H T x n x n E x i ( n) = σ σ. = i = 1 N ( n ) ( ~ CN 0, ). η σ N I R N i = 1 S, i S Centre for Wireless Communications (CWC) 13

14 Singular Value Decomposition The MIMO model is a special case of parallel Gaussian channels. The channel transfer matrix has singular value decomposition (SVD): where U C 1 H = UΛ V R R, are unitary matrices, and 1 N R Λ R N T is a diagonal matrix of the singular values of H. H N N N N, V C T T Centre for Wireless Communications (CWC) 14

15 Equivalent Channel Model Let H ~ H x n = V x n, y n = U y n, ~ η n = Since U and V are unitary: ~ H E ~ x n x n σ ~ H ( ) ( ) ( ) ( ) ( ) U η( n). ( ( ) ( )), ~ Equivalent channel model 1 ~ y n = Λ ~ x n + ~ η n Independent parallel Gaussian channels. Capacity achieved with Gaussian input and by water-filling. S ( n ) ( ~ CN 0, ). η σ N I ( ) ( ) ( ). diagonal matrix of sixe N R N T Centre for Wireless Communications (CWC) 15

16 Derivation of Channel Capacity The rank of matrix H is rank(h) min(n R,N T ). The number of positive singular values is rank(h). The capacity of MIMO AWGN channel: rank( H) rank λi σ ( H) ( ) σ S, i C = log 1 = log1 + λ γ, γ = 1 + i i i i = σ N i = 1 σ where the signal powers are solved via water-filling max 0, N µ σ σ =, = 1,, K,rank( H), S, i i λ i and µ is chosen so that the power constraint is satisfied or rank( H) σ σ. i =1 S, i S Centre for Wireless Communications (CWC) 16 S,i N,

17 MIMO Channel Capacity for Full Rank Channel Matrix No CSI at the transmitter (and full rank H): C γ = log det IN + HH R NT H. CSI at the transmitter (and full rank H): γ H C = max log det IN + HQH, R Q N T where Q is the covariance matrix of the input vector x satisfying the power constraint tr(q) σ S. No CSI at the transmitter Q = I. Centre for Wireless Communications (CWC) 17

18 4. Fading MIMO Channels The channels are usually assumed to be ergodic: fading is fast enough and gets all realizations so many times that the sample average equals the theoretical mean the sample covariance equals the theoretical covariance. ergodic (a long observation time) non-ergodic (a short observation time) time Centre for Wireless Communications (CWC) 18

19 Fading Channel Model with Perfect Receiver CSI IN x convolution H y I ( x; y, H) = I ( x; H) + I ( x; yh) = I ( x; yh). OUT = 0 RV conditioned on channel realization The effective channel output: the actual channel output y and the channel realization H. Assuming that the channel is memoryless (independent channel state for each transmission), the capacity equals the mean of the mutual information: γ H C = EH log det IN + HH. R NT Centre for Wireless Communications (CWC) 19

20 Capacity Evaluation The evaluation of the fading MIMO channel capacity is complicated: Wishart distribution Laguerre polynomials [Telatar 1999] bounds [Foschini & Gans 1998] Monte Carlo computer simulations random matrix theory mutual information tends to Gaussian under development. Centre for Wireless Communications (CWC) 0

21 Example: N N MIMO System 10 R-CSI fading channel with N R =N T SNR = 0 db SNR = 10 db SNR = 0 db R-CSI fading channel with N R =N T Capacity [bits per symbol] antennae 16 antennae 8 antennae 4 antennae antennae 1 antenna SNR [db] Capacity [bits per symbol] Number of antennae The capacity curves are sifted upwards by introducing more antennae. The capacity increases linearly vs. the number of antennae. Centre for Wireless Communications (CWC) 1

22 Non-Ergodic Channels The channels are not always ergodic: fading can be so slow that it undergoes only some realizations. The random process becomes non-ergodic. ergodic non-ergodic time Centre for Wireless Communications (CWC)

23 Example AWGN 1 bit / use IN random switch AWGN bits / use OUT Select one of the channels with equal probability, and keep then fixed. Average mutual information is 1.5 bits / channel use. However, with probability 0.5 it is not supported. The achievable rate 1 bits / channel use. Channel capacity the average maximum mutual information. Centre for Wireless Communications (CWC) 3

24 Example: Random and Fixed Channel A simple example: generate a channel realization, and keep it fixed during the whole transmission. There is a positive probability of an arbitrarily bad channel realization. However small a rate, the channel realization may not be able to support it regardless the length of the code word. The Shannon capacity of this non-ergodic channel is zero. The Shannon capacity is again not equal to the average mutual information. Centre for Wireless Communications (CWC) 4

25 Outage Probability In non-ergodic channels, the capacity is measured by the probability of outage for a given rate R: Pout( R) = inf Pr[ I( x; y ) < R] Q: Q 0,tr( Q) σ = Q: Q 0,tr inf ( Q) σ S γ Pr log det I N + HQH R NT Often called capacity versus outage. S The set-up is encountered in real time applications with transmission delay constraints. Similar approach is applicable also for delay constrained communications in ergodic channels. H < R. Centre for Wireless Communications (CWC) 5

26 5. Summary and Conclusions AWGN MIMO channels are an extension of parallel Gaussian channels. Another example of parallel channels: channels on different frequencies. Introducing both multiple transmit and receive antennae is equivalent to increase in bandwidth. The linear capacity increase becomes natural. C γ = log det IN + HQH R NT H. Centre for Wireless Communications (CWC) 6

27 Fading AWGN MIMO Channel Ergodic channels: Channel experiences all its states several times. No delay constraints and/or fast fading. Capacity equals the average mutual information: C γ = EH log det IN + HH R NT H. Capacity increases linearly with N R =N T. Non-ergodic channels: Capacity does not equal the average mutual information. Capacity versus outage probability. Centre for Wireless Communications (CWC) 7

28 Research Challenges Capacity of selective channels time-selective frequency-selective with no or imperfect channel state information in the transmitter and the receiver. Optimal signal structures (coding and modulation) for real use with issues like amount of training vs. non-coherent detection transceiver complexity constraints limited bandwidth of a non-ideal feedback channel. Centre for Wireless Communications (CWC) 8

29 References 1. T. M. Cover & J. A. Thomas, Elements of Information Theory. John Wiley & Sons, ISBN: E. Telatar, Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, vol. 10, no. 6, pp , Nov.-Dec G. J. Foschini & M. J. Gans, On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications, vol. 6, pp , Nov.-Dec T. L. Marzetta & B. M. Hochwald, Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading. IEEE Transactions on Information Theory, vol. 45, no. 1, pp , Jan I. E. Telatar & D. N C. Tse, Capacity and mutual information of wideband multipath fading channels. IEEE Transactions on Information Theory, vol. 46, no. 4, pp , July M. Medard, The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel. IEEE Transactions on Information Theory, vol. 46, no. 3, pp , May M. Medard & R. G. Gallager, Bandwidth scaling for fading multipath channels. IEEE Transactions on Information Theory, vol. 48, no. 4, pp , April V. G. Subramanian & B. Hajek, Broad-band fading channels: signal burstiness and capacity. IEEE Transactions on Information Theory, vol. 48, no. 4, pp , April 00. Centre for Wireless Communications (CWC) 9

### MIMO CHANNEL CAPACITY

MIMO CHANNEL CAPACITY Ochi Laboratory Nguyen Dang Khoa (D1) 1 Contents Introduction Review of information theory Fixed MIMO channel Fading MIMO channel Summary and Conclusions 2 1. Introduction The use

### Multiuser Communications in Wireless Networks

Multiuser Communications in Wireless Networks Instructor Antti Tölli Centre for Wireless Communications (CWC), University of Oulu Contact e-mail: antti.tolli@ee.oulu.fi, tel. +358445000180 Course period

### Capacity Limits of MIMO Systems

1 Capacity Limits of MIMO Systems Andrea Goldsmith, Syed Ali Jafar, Nihar Jindal, and Sriram Vishwanath 2 I. INTRODUCTION In this chapter we consider the Shannon capacity limits of single-user and multi-user

### 8 MIMO II: capacity and multiplexing

CHAPTER 8 MIMO II: capacity and multiplexing architectures In this chapter, we will look at the capacity of MIMO fading channels and discuss transceiver architectures that extract the promised multiplexing

### Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 2, FEBRUARY 2002 359 Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel Lizhong Zheng, Student

### 5. Capacity of Wireless Channels

5. Capacity of Wireless Channels 1 Information Theory So far we have only looked at specific communication schemes. Information theory provides a fundamental limit to (coded) performance. It succinctly

### PHASE ESTIMATION ALGORITHM FOR FREQUENCY HOPPED BINARY PSK AND DPSK WAVEFORMS WITH SMALL NUMBER OF REFERENCE SYMBOLS

PHASE ESTIMATION ALGORITHM FOR FREQUENCY HOPPED BINARY PSK AND DPSK WAVEFORMS WITH SMALL NUM OF REFERENCE SYMBOLS Benjamin R. Wiederholt The MITRE Corporation Bedford, MA and Mario A. Blanco The MITRE

### MIMO: What shall we do with all these degrees of freedom?

MIMO: What shall we do with all these degrees of freedom? Helmut Bölcskei Communication Technology Laboratory, ETH Zurich June 4, 2003 c H. Bölcskei, Communication Theory Group 1 Attributes of Future Broadband

### The Multiple-Input Multiple-Output Systems in Slow and Fast Varying Radio Channels

AGH University of Science and Technology Faculty of Electrical Engineering, Automatics, Computer Science and Electronics Ph.D. Thesis Paweł Kułakowski The Multiple-Input Multiple-Output Systems in Slow

### THE downlink of multiuser multiple-input multiple-output

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 7, JULY 2007 3837 Precoding for Multiple Antenna Gaussian Broadcast Channels With Successive Zero-Forcing Amir D. Dabbagh and David J. Love, Member,

### Full- or Half-Duplex? A Capacity Analysis with Bounded Radio Resources

Full- or Half-Duplex? A Capacity Analysis with Bounded Radio Resources Vaneet Aggarwal AT&T Labs - Research, Florham Park, NJ 7932. vaneet@research.att.com Melissa Duarte, Ashutosh Sabharwal Rice University,

### Digital Modulation. David Tipper. Department of Information Science and Telecommunications University of Pittsburgh. Typical Communication System

Digital Modulation David Tipper Associate Professor Department of Information Science and Telecommunications University of Pittsburgh http://www.tele.pitt.edu/tipper.html Typical Communication System Source

### ADVANCED APPLICATIONS OF ELECTRICAL ENGINEERING

Development of a Software Tool for Performance Evaluation of MIMO OFDM Alamouti using a didactical Approach as a Educational and Research support in Wireless Communications JOSE CORDOVA, REBECA ESTRADA

### Capacity of Cognitive Radio Networks

Chapter 2 Capacity of Cognitive Radio Networks Andrea Goldsmith and Ivana Marić 2.1. INTRODUCTION 1 2.1 Introduction This chapter develops the fundamental capacity limits and associated transmission techniques

### Log-Likelihood Ratio-based Relay Selection Algorithm in Wireless Network

Recent Advances in Electrical Engineering and Electronic Devices Log-Likelihood Ratio-based Relay Selection Algorithm in Wireless Network Ahmed El-Mahdy and Ahmed Walid Faculty of Information Engineering

### 802.11A - OFDM PHY CODING AND INTERLEAVING. Fernando H. Gregorio. Helsinki University of Technology

802.11A - OFDM PHY CODING AND INTERLEAVING Fernando H. Gregorio Helsinki University of Technology Signal Processing Laboratory, POB 3000, FIN-02015 HUT, Finland E-mail:gregorio@wooster.hut.fi 1. INTRODUCTION

### IMPROVED CHANNEL ESTIMATION FOR OFDM SYSTEMS IN QUASI-STATIC CHANNELS

IMPROVED CHANNEL ESTIMATION FOR OFDM SYSTEMS IN QUASI-STATIC CHANNELS Mo Zhu, Adegbenga B. Awoseyila and Barry G. Evans Centre for Communication Systems Research (CCSR) University of Surrey, Guildford,

S-7. POSTGRADUATE COURSE IN RADIO COMMUNICATIONS, AUTUMM BLAST Architectures Eduardo Zacarías B. Signal Processing Laboratory ezacaria@wooster.hut.fi Abstract Multiple Input Multiple Output(MIMO) systems

### Errata Introduction to Wireless Systems P. Mohana Shankar. Page numbers are shown in blue Corrections are shown in red.

Errata Introduction to Wireless Systems P. Mohana Shankar Page numbers are shown in blue Corrections are shown in red February 25 Page 11 below Figure 2.4 The power detected by a typical receiver is shown

### MATLAB in Digital Signal Processing and Communications

MATLAB in Digital Signal Processing and Communications Jan Mietzner (janm@ece.ubc.ca) MATLAB Tutorial October 15, 2008 Objective and Focus Focus Learn how MATLAB can be used efficiently in order to perform

### On the Mobile Wireless Access via MIMO Relays

On the Mobile Wireless Access via MIMO Relays Tae Hyun Kim and Nitin H. Vaidya Dept. of Electrical and Computer Eng. Coordinated Science Laborartory University of Illinois at Urbana-Champaign, IL 6181

### The Degrees of Freedom of Compute-and-Forward

The Degrees of Freedom of Compute-and-Forward Urs Niesen Jointly with Phil Whiting Bell Labs, Alcatel-Lucent Problem Setting m 1 Encoder m 2 Encoder K transmitters, messages m 1,...,m K, power constraint

### Diversity and Multiplexing: A Fundamental Tradeoff in Multiple-Antenna Channels

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 49, NO 5, MAY 2003 1073 Diversity Multiplexing: A Fundamental Tradeoff in Multiple-Antenna Channels Lizhong Zheng, Member, IEEE, David N C Tse, Member, IEEE

### Diversity and Degrees of Freedom in Wireless Communications

1 Diversity and Degrees of Freedom in Wireless Communications Mahesh Godavarti Altra Broadband Inc., godavarti@altrabroadband.com Alfred O. Hero-III Dept. of EECS, University of Michigan hero@eecs.umich.edu

### INTRODUCTION TO CODING THEORY: BASIC CODES AND SHANNON S THEOREM

INTRODUCTION TO CODING THEORY: BASIC CODES AND SHANNON S THEOREM SIDDHARTHA BISWAS Abstract. Coding theory originated in the late 1940 s and took its roots in engineering. However, it has developed and

### Energy Efficiency of Cooperative Jamming Strategies in Secure Wireless Networks

Energy Efficiency of Cooperative Jamming Strategies in Secure Wireless Networks Mostafa Dehghan, Dennis L. Goeckel, Majid Ghaderi, and Zhiguo Ding Department of Electrical and Computer Engineering, University

### OPTIMAL RESOURCE ALLOCATION IN WIRELESS COMMUNICATIONS SUBJECT TO SEVERAL POWER AND ENERGY CONSTRAINTS. A Thesis. Submitted to the Graduate School

OPTIMAL RESOURCE ALLOCATION IN WIRELESS COMMUNICATIONS SUBJECT TO SEVERAL POWER AND ENERGY CONSTRAINTS A Thesis Submitted to the Graduate School of the University of Notre Dame in Partial Fulfillment of

### Mobile Wireless Access via MIMO Relays

Mobile Wireless Access via MIMO Relays Tae Hyun Kim and Nitin H. Vaidya Dept. of Electrical and Computer Eng. Coordinated Science Laborartory University of Illinois at Urbana-Champaign, IL 680 Emails:

### Large random matrices and their application to wireless communication

Large random matrices and their application to wireless communication Jamal Najim, CNRS and Télécom ParisTech French-Chinese Summer Institute - Changchun, China - July 2011 A historical perspective A historical

### Chapter 1 Introduction

Chapter 1 Introduction 1. Shannon s Information Theory 2. Source Coding theorem 3. Channel Coding Theory 4. Information Capacity Theorem 5. Introduction to Error Control Coding Appendix A : Historical

### Capacity of Wireless Communication Systems Employing Antenna Arrays, a Tutorial Study

Wireless Personal Communications 23: 321 352, 2002. 2002 Kluwer Academic Publishers. Printed in the Netherlands. Capacity of Wireless Communication Systems Employing Antenna Arrays, a Tutorial Study MOHAMMAD

### IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 1, JANUARY 2007 341

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 1, JANUARY 2007 341 Multinode Cooperative Communications in Wireless Networks Ahmed K. Sadek, Student Member, IEEE, Weifeng Su, Member, IEEE, and K.

### Distributed Detection Systems. Hamidreza Ahmadi

Channel Estimation Error in Distributed Detection Systems Hamidreza Ahmadi Outline Detection Theory Neyman-Pearson Method Classical l Distributed ib t Detection ti Fusion and local sensor rules Channel

### Joint Optimal Pilot Placement and Space Frequency (SF) Code Design for MIMO-OFDM Systems

Joint Optimal Pilot Placement and Space Frequency (SF) Code Design for MIMO- Systems Saurav K. Bandyopadhyay W&W Communications Inc. 640 W. California Avenue Sunnyvale, CA 94086 USA Srinivas Prasad D.

### SC-FDMA and LTE Uplink Physical Layer Design

Seminar Ausgewählte Kapitel der Nachrichtentechnik, WS 29/21 LTE: Der Mobilfunk der Zukunft SC-FDMA and LTE Uplink Physical Layer Design Burcu Hanta 2. December 29 Abstract The Long Term Evolution (LTE)

### Cross-layer Scheduling and Resource Allocation in Wireless Communication Systems

Cross-layer Scheduling and Resource Allocation in Wireless Communication Systems Srikrishna Bhashyam Department of Electrical Engineering Indian Institute of Technology Madras 21 June 2011 Srikrishna Bhashyam

### Simulation and measurement of a MIMO antenna system

Simulation and measurement of a MIMO antenna system ANDREA FARKASVÖLGYI, ÁKOS NÉMETH, LAJOS NAGY Budapest University of Technology and Economics, Department of Broadband Infocommunications and Electromagnetic

### CS263: Wireless Communications and Sensor Networks

CS263: Wireless Communications and Sensor Networks Matt Welsh Lecture 2: RF Basics and Signal Encoding September 22, 2005 2005 Matt Welsh Harvard University 1 Today's Lecture Basics of wireless communications

### 5 Capacity of wireless channels

CHAPTER 5 Capacity of wireless channels In the previous two chapters, we studied specific techniques for communication over wireless channels. In particular, Chapter 3 is centered on the point-to-point

### MIMO detector algorithms and their implementations for LTE/LTE-A

GIGA seminar 11.01.2010 MIMO detector algorithms and their implementations for LTE/LTE-A Markus Myllylä and Johanna Ketonen 11.01.2010 2 Outline Introduction System model Detection in a MIMO-OFDM system

### MIMO Antenna Systems in WinProp

MIMO Antenna Systems in WinProp AWE Communications GmbH Otto-Lilienthal-Str. 36 D-71034 Böblingen mail@awe-communications.com Issue Date Changes V1.0 Nov. 2010 First version of document V2.0 Feb. 2011

### ECEN 5682 Theory and Practice of Error Control Codes

ECEN 5682 Theory and Practice of Error Control Codes Convolutional Codes University of Colorado Spring 2007 Linear (n, k) block codes take k data symbols at a time and encode them into n code symbols.

### THE problems of characterizing the fundamental limits

Beamforming and Aligned Interference Neutralization Achieve the Degrees of Freedom Region of the 2 2 2 MIMO Interference Network (Invited Paper) Chinmay S. Vaze and Mahesh K. Varanasi Abstract We study

Power Allocation in Multi-Antenna Wireless Systems Subject to Simultaneous Power Constraints Mostafa Khoshnevisan, Student Member, IEEE, and J. Nicholas Laneman, Senior Member, IEEE Abstract We address

### Hybrid Type-II ARQ Schemes for Rayleigh Fading Channels

Hybrid Type-II ARQ Schemes for Rayleigh Fading Channels Sorour Falahati and Arne Svensson Dept. of Signals and Systems, Communication Systems Group Chalmers University of Technology, E-42 96 Göteborg,

### Degrees of Freedom in Wireless Networks

Degrees of Freedom in Wireless Networks Zhiyu Cheng Department of Electrical and Computer Engineering University of Illinois at Chicago Chicago, IL 60607, USA Email: zcheng3@uic.edu Abstract This paper

### T-79.7001 Postgraduate Course in Theoretical Computer Science T-79.5401 Special Course in Mobility Management: Ad hoc networks (2-10 cr) P V

T-79.7001 Postgraduate Course in Theoretical Computer Science T-79.5401 Special Course in Mobility Management: Ad hoc networks (2-10 cr) P V professor Hannu H. Kari Laboratory for Theoretical Computer

### How Far from Kronecker can a MIMO Channel be? Does it Matter?

How Far from Kronecker can a MIMO Channel be? Does it Matter? Proceedings of European Wireless (EW) 27-29 April, Vienna, Austria, 2011 NAFISEH SHAIATI AND MATS BENGTSSON I-EE-SB 2011:012 Stockholm 2011

### Teaching Convolutional Coding using MATLAB in Communication Systems Course. Abstract

Section T3C2 Teaching Convolutional Coding using MATLAB in Communication Systems Course Davoud Arasteh Department of Electronic Engineering Technology, LA 70813, USA Abstract Convolutional codes are channel

### Adaptive Allocation of Pilot and Data Power for Time-Selective Fading Channels with Feedback

Adaptive Allocation of Pilot and Data Power for Time-Selective Fading Channels with Feedback Manish Agarwal, Michael Honig, and Baris Ata Dept. of EECS and Kellogg School of Management Northwestern University

### Half-Duplex or Full-Duplex Relaying: A Capacity Analysis under Self-Interference

Half-Duplex or Full-Duplex elaying: A Capacity Analysis under Self-Interference Nirmal Shende Department of ECE, Polytechnic Institute of NYU Brooklyn, NY 0 Email: nvs5@students.poly.edu Ozgur Gurbuz Faculty

### Capacity of the Multiple Access Channel in Energy Harvesting Wireless Networks

Capacity of the Multiple Access Channel in Energy Harvesting Wireless Networks R.A. Raghuvir, Dinesh Rajan and M.D. Srinath Department of Electrical Engineering Southern Methodist University Dallas, TX

### White Paper FADING BASICS. Narrow Band, Wide Band, and Spatial Channels White Paper 101. Rev. X mm/08

White Paper FADING BASICS Narrow Band, Wide Band, and Spatial Channels White Paper 101 Rev. X mm/08 SPIRENT 1325 Borregas Avenue Sunnyvale, CA 94089 USA Email: Web: sales@spirent.com http://www.spirent.com

### Total Inter-Carrier Interference Cancellation for MC-CDMA System in Mobile Environment

Total Inter-Carrier Interference Cancellation for MC-CDMA System in Mobile Environment Xue Li 1, Ruolin Zhou 1, Steven Hong 2, and Zhiqiang Wu 1 Dept of EE, Wright State University 1, Dept of EE, Stanford

### EE4367 Telecom. Switching & Transmission. Prof. Murat Torlak

Path Loss Radio Wave Propagation The wireless radio channel puts fundamental limitations to the performance of wireless communications systems Radio channels are extremely random, and are not easily analyzed

### Division algebras for coding in multiple antenna channels and wireless networks

Division algebras for coding in multiple antenna channels and wireless networks Frédérique Oggier frederique@systems.caltech.edu California Institute of Technology Cornell University, School of Electrical

### Enhancing Wireless Security with Physical Layer Network Cooperation

Enhancing Wireless Security with Physical Layer Network Cooperation Amitav Mukherjee, Ali Fakoorian, A. Lee Swindlehurst University of California Irvine The Physical Layer Outline Background Game Theory

### Wireless Channel Models 8-1

Wireless Channel Models 8-1 Why do we need models? Help analyze the performance of large systems Ask fundamental questions about a system E.g. what is the best I can do with a given system? Allows comparison

### EFFECTIVE CHANNEL STATE INFORMATION (CSI) FEEDBACK FOR MIMO SYSTEMS IN WIRELESS BROADBAND COMMUNICATIONS

EFFECTIVE CHANNEL STATE INFORMATION (CSI) FEEDBACK FOR MIMO SYSTEMS IN WIRELESS BROADBAND COMMUNICATIONS Maneesha Sharma Bachelor of Engineering Principal Supervisor: Dr. Karla Ziri-Castro Associate Supervisor:

### Statistical Machine Learning

Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes

### Cooperative Diversity in Wireless Relay Networks with. Multiple-Antenna Nodes

Cooperative Diversity in Wireless Relay Networks with Multiple-Antenna Nodes YINDI JING AND BABAK HASSIBI Department of Electrical Engineering California Institute of Technology asadena, CA 95 Abstract

### Cloud Radios with Limited Feedback

Cloud Radios with Limited Feedback Dr. Kiran Kuchi Indian Institute of Technology, Hyderabad Dr. Kiran Kuchi (IIT Hyderabad) Cloud Radios with Limited Feedback 1 / 18 Overview 1 Introduction 2 Downlink

### I. Wireless Channel Modeling

I. Wireless Channel Modeling April 29, 2008 Qinghai Yang School of Telecom. Engineering qhyang@xidian.edu.cn Qinghai Yang Wireless Communication Series 1 Contents Free space signal propagation Pass-Loss

### Coding and decoding with convolutional codes. The Viterbi Algor

Coding and decoding with convolutional codes. The Viterbi Algorithm. 8 Block codes: main ideas Principles st point of view: infinite length block code nd point of view: convolutions Some examples Repetition

### Ergodic Capacity of Continuous-Time, Frequency-Selective Rayleigh Fading Channels with Correlated Scattering

Ergodic Capacity of Continuous-Time, Frequency-Selective Rayleigh Fading Channels with Correlated Scattering IEEE Information Theory Winter School 2009, Loen, Norway Christian Scheunert, Martin Mittelbach,

### Designing Wireless Broadband Access for Energy Efficiency

Designing Wireless Broadband Access for Energy Efficiency Are Small Cells the Only Answer? Emil Björnson 1, Luca Sanguinetti 2,3, Marios Kountouris 3,4 1 Linköping University, Linköping, Sweden 2 University

### ISI Mitigation in Image Data for Wireless Wideband Communications Receivers using Adjustment of Estimated Flat Fading Errors

International Journal of Engineering and Management Research, Volume-3, Issue-3, June 2013 ISSN No.: 2250-0758 Pages: 24-29 www.ijemr.net ISI Mitigation in Image Data for Wireless Wideband Communications

### Multiuser Wireless Communication Systems

Multiuser Wireless Communication Systems Ashutosh Sabharwal and Behnaam Aazhang Department of Electrical and Computer Engineering Rice University Houston TX 77005 Abstract Wireless cellular systems have

Direct Sequence Spreading Gene W. Marsh I. A General Description of Direct Sequence Spreading A. The standard view of a communication syste m Channel Encoder Modulator Channel Demodulator Channel Decoder

### Power and Bandwidth Allocation in Cooperative Dirty Paper Coding

Power and Bandwidth Allocation in Cooperative Dirty Paper Coding Chris T. K. Ng, Nihar Jindal, Andrea J. Goldsmith and Urbashi Mitra Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305

### WiMAX Performance Analysis under the Effect of Doppler s Shift

WiMAX Performance Analysis under the Effect of Doppler s Shift Navgeet Singh 1, Amita Soni 2 1, 2 Department of Electronics and Electrical Engineering, PEC University of Technology, Chandigarh, India Abstract:

### MULTIPLE-INPUT MULTIPLE-OUTPUT WIRELESS SYSTEM DESIGNS WITH IMPERFECT CHANNEL KNOWLEDGE

MULTIPLE-INPUT MULTIPLE-OUTPUT WIRELESS SYSTEM DESIGNS WITH IMPERFECT CHANNEL KNOWLEDGE by Minhua Ding A thesis submitted to the Department of Electrical and Computer Engineering in conformity with the

### FUNDAMENTALS OF WIRELESS COMMUNICATIONS

Objectives: 1) basic channel models 2) factors that determines throughput/bit error rate in wireless communication Readings: 1. Rappaport, Wireless Communications: Principles and Practice, Pearson (chap

### Course Curriculum for Master Degree in Electrical Engineering/Wireless Communications

Course Curriculum for Master Degree in Electrical Engineering/Wireless Communications The Master Degree in Electrical Engineering/Wireless Communications, is awarded by the Faculty of Graduate Studies

### Notes for STA 437/1005 Methods for Multivariate Data

Notes for STA 437/1005 Methods for Multivariate Data Radford M. Neal, 26 November 2010 Random Vectors Notation: Let X be a random vector with p elements, so that X = [X 1,..., X p ], where denotes transpose.

### THE NEXT-generation wireless systems are required to

IEEE JOURNAL ON SELECT AREAS IN COMMUNICATIONS, VOL. 16, NO. 8, OCTOBER 1998 1451 A Simple Transmit Diversity Technique for Wireless Communications Siavash M. Alamouti Abstract This paper presents a simple

### Implementation of Digital Signal Processing: Some Background on GFSK Modulation

Implementation of Digital Signal Processing: Some Background on GFSK Modulation Sabih H. Gerez University of Twente, Department of Electrical Engineering s.h.gerez@utwente.nl Version 4 (February 7, 2013)

### Wireless Communication Technologies

1 Wireless Communication Technologies Lin DAI Requirement 2 Prerequisite: Principles of Communications A certain math background Probability, Linear Algebra, Matrix Be interactive in class! Think independently!

### Lecture 18 October 30

EECS 290S: Network Information Flow Fall 2008 Lecture 18 October 30 Lecturer: Anant Sahai and David Tse Scribe: Changho Suh In this lecture, we studied two types of one-to-many channels: (1) compound channels

### CNR Requirements for DVB-T2 Fixed Reception Based on Field Trial Results

CNR Requirements for DVB-T2 Fixed Reception Based on Field Trial Results Iñaki Eizmendi, Gorka Berjon-Eriz, Manuel Vélez, Gorka Prieto, Amaia Arrinda This letter presents the C/N requirements for DVB-T2

### Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur

Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture - 3 Rayleigh Fading and BER of Wired Communication

### Optimum Frequency-Domain Partial Response Encoding in OFDM System

1064 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL 51, NO 7, JULY 2003 Optimum Frequency-Domain Partial Response Encoding in OFDM System Hua Zhang and Ye (Geoffrey) Li, Senior Member, IEEE Abstract Time variance

### ADAPTIVE EQUALIZATION. Prepared by Deepa.T, Asst.Prof. /TCE

ADAPTIVE EQUALIZATION Prepared by Deepa.T, Asst.Prof. /TCE INTRODUCTION TO EQUALIZATION Equalization is a technique used to combat inter symbol interference(isi). An Equalizer within a receiver compensates

### Comparative Study of OFDM and CDMA Technique

IOSR Journal of Electronics and Communication Engineering (IOSR-JECE) e-issn: 2278-2834,p- ISSN: 2278-8735. Volume 5, Issue 3 (Mar. - Apr. 2013), PP 26-30 Comparative Study of OFDM and CDMA Technique Lalit

### Estimation and Equalization of Fiber-Wireless Uplink for Multiuser CDMA 4g Networks

Estimation and Equalization of Fiber-Wireless Uplink for Multiuser CDMA 4g Networks Vangala susmitha *1, Nagandla Bhavana* 2, Lankisetti Divya Sai Ratna *3, Bhuma Naresh *4 1,2,3,4 Dept. of Electronics

### BER Performance Analysis of SSB-QPSK over AWGN and Rayleigh Channel

Performance Analysis of SSB-QPSK over AWGN and Rayleigh Channel Rahul Taware ME Student EXTC Department, DJSCOE Vile-Parle (W) Mumbai 056 T. D Biradar Associate Professor EXTC Department, DJSCOE Vile-Parle

### Kristine L. Bell and Harry L. Van Trees. Center of Excellence in C 3 I George Mason University Fairfax, VA 22030-4444, USA kbell@gmu.edu, hlv@gmu.

POSERIOR CRAMÉR-RAO BOUND FOR RACKING ARGE BEARING Kristine L. Bell and Harry L. Van rees Center of Excellence in C 3 I George Mason University Fairfax, VA 22030-4444, USA bell@gmu.edu, hlv@gmu.edu ABSRAC

### Adaptive Equalization of binary encoded signals Using LMS Algorithm

SSRG International Journal of Electronics and Communication Engineering (SSRG-IJECE) volume issue7 Sep Adaptive Equalization of binary encoded signals Using LMS Algorithm Dr.K.Nagi Reddy Professor of ECE,NBKR

### ADAPTIVE modulation is a promising technique that is

716 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 5, MAY 2004 Impact of Channel Estimation Error on Adaptive Modulation Performance in Flat Fading José F. Paris, M. Carmen Aguayo-Torres, and José T.

### An Overview of Limited Feedback in Wireless Communication Systems

An Overview of Limited Feedback in Wireless Communication Systems David J. Love, Member, IEEE, Robert W. Heath Jr, Senior Member, IEEE, Vincent K. N. Lau, Senior Member, IEEE, David Gesbert, Senior Member,

### Lezione 6 Communications Blockset

Corso di Tecniche CAD per le Telecomunicazioni A.A. 2007-2008 Lezione 6 Communications Blockset Ing. Marco GALEAZZI 1 What Is Communications Blockset? Communications Blockset extends Simulink with a comprehensive

### Privacy and Security in the Internet of Things: Theory and Practice. Bob Baxley; bob@bastille.io HitB; 28 May 2015

Privacy and Security in the Internet of Things: Theory and Practice Bob Baxley; bob@bastille.io HitB; 28 May 2015 Internet of Things (IoT) THE PROBLEM By 2020 50 BILLION DEVICES NO SECURITY! OSI Stack

Fading multipath radio channels Narrowband channel modelling Wideband channel modelling Wideband WSSUS channel (functions, variables & distributions) Low-pass equivalent (LPE) signal ( ) = Re ( ) s t RF

### CDMA Performance under Fading Channel

CDMA Performance under Fading Channel Ashwini Dyahadray 05307901 Under the guidance of: Prof Girish P Saraph Department of Electrical Engineering Overview Wireless channel fading characteristics Large

### Chapter 2 Mobile Communication

Page 77 Chapter 2 Mobile Communication 2.1 Characteristics of Mobile Computing 2.2 Wireless Communication Basics 2.3 Wireless Communication Technologies PANs (Bluetooth, ZigBee) Wireless LAN (IEEE 802.11)

### Bi-directional Signalling Strategies for Dynamic TDD Networks

12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 1 Bi-directional Signalling Strategies for Dynamic TDD Networks Antti Tölli Praneeth Jayasinghe, Jarkko Kaleva University

### A SIMULATION STUDY ON SPACE-TIME EQUALIZATION FOR MOBILE BROADBAND COMMUNICATION IN AN INDUSTRIAL INDOOR ENVIRONMENT

A SIMULATION STUDY ON SPACE-TIME EQUALIZATION FOR MOBILE BROADBAND COMMUNICATION IN AN INDUSTRIAL INDOOR ENVIRONMENT U. Trautwein, G. Sommerkorn, R. S. Thomä FG EMT, Ilmenau University of Technology P.O.B.

1 Adaptive Training for Correlated Fading Channels with Feedback Manish Agarwal, Michael Honig, and Baris Ata Northwestern University arxiv:98.164v1 [cs.it] 1 Aug 9 {m-agarwal,mh,b-ata}@northwestern.edu