Joint Channel Estimation and Co-Channel Interference Mitigation in Wireless Networks Using Belief Propagation
|
|
|
- Regina Melissa White
- 5 years ago
- Views:
Transcription
1 Joint Channel Estimation and Co-Channel Interference Mitigation in Wireless Networks Using Belief Propagation Yan Zhu, Dongning Guo and Michael L. Honig Northwestern University May. 21, 2008 Y. Zhu, D. Guo and M. Honig (EECS) 1 / 17
2 Introduction Key Challenges in Wireless Networks 10 5 Channel Uncertainty (fading) Channel Gain in db Time in Seconds Interference Desired Signal Co Channel Interference Y. Zhu, D. Guo and M. Honig (EECS) 2 / 17
3 System Model System Model Interference: Y i = H i X i + H i X i + N i N i CN (0, σn 2 ), H i CN (0, σ 2 H ), H i CN (0, σ 2 H ), X i, X i {±1}. Fading process Problem i = 1... n H i = αh i α 2 W i H i = αh i α 2 W i (α 1) Given Y 1... Y n and known pilots in X 1... X n, detect the remaining unknown symbols in X 1... X n. Y. Zhu, D. Guo and M. Honig (EECS) 3 / 17
4 System Model System Model Interference: Y i = H i X i + H i X i + N i N i CN (0, σn 2 ), H i CN (0, σ 2 H ), H i CN (0, σ 2 H ), X i, X i {±1}. Fading process Problem i = 1... n H i = αh i α 2 W i H i = αh i α 2 W i (α 1) Given Y 1... Y n and known pilots in X 1... X n, detect the remaining unknown symbols in X 1... X n. Y. Zhu, D. Guo and M. Honig (EECS) 3 / 17
5 Graphical Model and Belief Propagation Algorithm Graphical Model Y i = H i X i + H i X i + N i 1 α 2 W i H i = αh i 1 + H i = αh i α 2 W i i = 1... n Observation H i X i (i = 1... n) is not Gaussian process; treating it as Gaussian leads to poor performance. We propose Using statistical inference on factor graph to solve this problem. Y. Zhu, D. Guo and M. Honig (EECS) 4 / 17
6 Graphical Model and Belief Propagation Algorithm Graphical Model Y i = H i X i + H i X i + N i 1 α 2 W i H i = αh i 1 + H i = αh i α 2 W i i = 1... n Observation H i X i (i = 1... n) is not Gaussian process; treating it as Gaussian leads to poor performance. We propose Using statistical inference on factor graph to solve this problem. Y. Zhu, D. Guo and M. Honig (EECS) 4 / 17
7 Graphical Model and Belief Propagation Algorithm Graphical Model Graphical Model {H i, H i } form a Markov Chain. Conditioned on {H i, H i }, (Y i, X i, X i ) is independent over time. Y. Zhu, D. Guo and M. Honig (EECS) 5 / 17
8 Graphical Model and Belief Propagation Algorithm Graphical Model Graphical Model {H i, H i } form a Markov Chain. Conditioned on {H i, H i }, (Y i, X i, X i ) is independent over time. Hi = αhi α 2 Wi H i = αh i α 2 W i H i 1,H i 1 H i,h i H i+1,h i+1 X i 1,X i 1 X i,x i X i+1,x i+1 Yi = HiXi + H i X i + Ni Y i 1 Y i Y i+1 Y. Zhu, D. Guo and M. Honig (EECS) 5 / 17
9 Graphical Model and Belief Propagation Algorithm Statistical Inference Via Message Passing Message Passing Optimal detection on the unknown X i computation of p(x i y n 1 ). H i 1,H i 1 H i,h i H i+1,h i+1 X i 1,X i 1 X i,x i X i+1,x i+1 Y i 1 Y i Y i+1 The key is to compute p(h i, h i similar to the BCJR algorithm. y i 1 1 ) and p(h i, h i y n i+1 ) recursively. It is Y. Zhu, D. Guo and M. Honig (EECS) 6 / 17
10 Graphical Model and Belief Propagation Algorithm Statistical Inference Via Message Passing Message Passing Optimal detection on the unknown X i computation of p(x i y n 1 ). H i 1,H i 1 H i,h i H i+1,h i+1 p(hi,h i yi 1 1,yi+1 n ) X i 1,X i 1 X i,x i p(x i y n 1) X i+1,x i+1 yi Y i 1 Y i Y i+1 The key is to compute p(h i, h i similar to the BCJR algorithm. y i 1 1 ) and p(h i, h i y n i+1 ) recursively. It is Y. Zhu, D. Guo and M. Honig (EECS) 6 / 17
11 Graphical Model and Belief Propagation Algorithm Statistical Inference Via Message Passing Message Passing Optimal detection on the unknown X i computation of p(x i y n 1 ). p(hi,h i yi 1 1 ) p(hi,h i yn i+1 ) H i 1,H i 1 H i,h i H i+1,h i+1 p(hi,h i yi 1 1,yi+1 n ) X i 1,X i 1 X i,x i p(x i y n 1) X i+1,x i+1 yi Y i 1 Y i Y i+1 The key is to compute p(h i, h i similar to the BCJR algorithm. y i 1 1 ) and p(h i, h i y n i+1 ) recursively. It is Y. Zhu, D. Guo and M. Honig (EECS) 6 / 17
12 Graphical Model and Belief Propagation Algorithm Statistical Inference Via Message Passing Message Passing Optimal detection on the unknown X i computation of p(x i y n 1 ). p(hi 1,h i 1 yi 2 1 ) H i 1,H i 1 p(hi 1,h i 1 yi 1 1 ) p(hi,h i yi 1 1 ) p(hi,h i yn i+1 ) H i,h i p(hi+1,h i+1 yn i+1 ) p(hi+1,h i+1 yn i+2 ) H i+1,h i+1 p(hi 1,h i 1 yi 1,xi,x i ) p(x i y n 1) p(hi,h i yi 1 1,yi+1 n ) p(hi 1,h i 1 yi 1,xi,x i ) X i 1,X i 1 X i,x i X i+1,x i+1 yi Y i 1 Y i Y i+1 The key is to compute p(h i, h i similar to the BCJR algorithm. y i 1 1 ) and p(h i, h i y n i+1 ) recursively. It is Y. Zhu, D. Guo and M. Honig (EECS) 6 / 17
13 Graphical Model and Belief Propagation Algorithm Practical Issues Practical Issues (1/2) Hi 1,H i 1 Hi,H i Hi+1,H i+1 Xi 1,X i 1 Xi,X i Xi+1,X i+1 Yi 1 Yi Yi+1 All r.v. s on graph are either Gaussian or discrete; the messages are of mixture Gaussian form. j ρ jcn (h i, h i ; m j, K j ). Enough to pass amplitudes, means and variances. No integrals. No cycle The BP algorithm is ultimately optimal. Y. Zhu, D. Guo and M. Honig (EECS) 7 / 17
14 Graphical Model and Belief Propagation Algorithm Practical Issues Practical Issues (1/2) Hi 1,H i 1 Hi,H i Hi+1,H i+1 Xi 1,X i 1 Xi,X i Xi+1,X i+1 Yi 1 Yi Yi+1 All r.v. s on graph are either Gaussian or discrete; the messages are of mixture Gaussian form. j ρ jcn (h i, h i ; m j, K j ). Enough to pass amplitudes, means and variances. No integrals. No cycle The BP algorithm is ultimately optimal. Y. Zhu, D. Guo and M. Honig (EECS) 7 / 17
15 Graphical Model and Belief Propagation Algorithm Practical Issues Practical Issues (1/2) Hi 1,H i 1 Hi,H i Hi+1,H i+1 Xi 1,X i 1 Xi,X i Xi+1,X i+1 Yi 1 Yi Yi+1 All r.v. s on graph are either Gaussian or discrete; the messages are of mixture Gaussian form. j ρ jcn (h i, h i ; m j, K j ). Enough to pass amplitudes, means and variances. No integrals. No cycle The BP algorithm is ultimately optimal. Y. Zhu, D. Guo and M. Honig (EECS) 7 / 17
16 Graphical Model and Belief Propagation Algorithm Practical Issues Practical Issues (2/2) Hi 1,H i 1 Hi,H i Hi+1,H i+1 Xi 1,X i 1 Xi,X i Xi+1,X i+1 Yi 1 Yi Yi+1 The number of Gaussian components increases exponentially as belief propagates and can only be approximated from time to time. Here, we limit the maximum number of Gaussian components in each step. Complexity is constant per bit. (The constant is typically larger than linear estimation) Y. Zhu, D. Guo and M. Honig (EECS) 8 / 17
17 Graphical Model and Belief Propagation Algorithm Practical Issues Practical Issues (2/2) Hi 1,H i 1 Hi,H i Hi+1,H i+1 Xi 1,X i 1 Xi,X i Xi+1,X i+1 Yi 1 Yi Yi+1 The number of Gaussian components increases exponentially as belief propagates and can only be approximated from time to time. Here, we limit the maximum number of Gaussian components in each step. Complexity is constant per bit. (The constant is typically larger than linear estimation) Y. Zhu, D. Guo and M. Honig (EECS) 8 / 17
18 Simulation Results Performance Evaluation Simulation Conditions uncoded system. snr = σh 2 /σ2 N and α =.99. block length 200; one pilot every 4 symbols. We compare the following receivers: 1 BP. 2 Linear-MMSE channel estimation: Interference treated as white Gaussian noise. 3 Genie-aided ML: A genie reveals channel to receiver. Y. Zhu, D. Guo and M. Honig (EECS) 9 / 17
19 Simulation Results BER Performance Medium Interference: Interference 3dB weaker Y i = H i X i + H i X i + N i 10 0 Linear MMSE Alg. Bit Error Performance Genie aided ML BP Alg SNR (db) Y. Zhu, D. Guo and M. Honig (EECS) 10 / 17
20 Simulation Results BER Performance Strong Interference: Interference with same strength Y i = H i X i + H i X i + N i 10 0 Linear MMSE Alg. Bit Error Performance Genie aided ML BP Alg SNR (db) Y. Zhu, D. Guo and M. Honig (EECS) 11 / 17
21 Simulation Results BER Performance Weak Interference: Interference 10dB weaker Y i = H i X i + H i X i + N i 10 0 Bit Error Performance Genie aided ML Linear MMSE Alg. BP Alg SNR (db) Y. Zhu, D. Guo and M. Honig (EECS) 12 / 17
22 Simulation Results Channel Estimation Channel estimation under medium interference Y i = H i X i + H i X i + N i Average Mean Squared Error of Channel Estimates (db) BP Alg. Linear MMSE Alg SNR (db) Y. Zhu, D. Guo and M. Honig (EECS) 13 / 17
23 Simulation Results Channel Estimation Channel estimation under medium interference Y i = H i X i + H i X i + N i Average Mean Squared Error of Channel Estimates (db) BP Alg. Linear MMSE Alg SNR (db) Im True Value of H i Complex Plane Belief of H i, i.e., p(h i y 1 n ) Re Y. Zhu, D. Guo and M. Honig (EECS) 13 / 17
24 Simulation Results Effect of Mixture Approximation Effect of Mixture Approximation Hi 1,H i 1 Hi,H i Hi+1,H i+1 Xi 1,X i 1 Xi,X i Xi+1,X i+1 Yi 1 Yi Yi Bit Error Performance Components 4 Components 8 Components 16 Components SNR (db) Y. Zhu, D. Guo and M. Honig (EECS) 14 / 17
25 Conclusions and More Recent Results Conclusions and More Recent Results Joint channel estimation and interference mitigation based on BP. Unlike linear receivers, BP exploits the non-gaussian statistics of the interference. Constant complexity per bit. Simulation shows significant gain over linear receiver. Y. Zhu, D. Guo and M. Honig (EECS) 15 / 17
26 Conclusions and More Recent Results More Recent Result: Factor graph with LDPC code Hi 1,H i 1 Hi,H i Hi+1,H i+1... Hj,H j Yi 1,X i 1 Yi,X i Yi+1,X i+1... Yj,X j Xi 1 Xi Xi+1... Xj... LDPC Check Nodes Y. Zhu, D. Guo and M. Honig (EECS) 16 / 17
27 Conclusions and More Recent Results More Recent Result: BER performance with MIMO and LDPC 10 0 Bit Error Performance BP separate Det./Dec. Joint BP Alg. Linear MMSE Alg. ML with full CSI SNR (db) Y. Zhu, D. Guo and M. Honig (EECS) 17 / 17
A Message-Passing Approach for Joint Channel Estimation, Interference Mitigation and Decoding
1 A Message-Passing Approach for Joint Channel Estimation, Interference Mitigation and Decoding Yan Zhu, Student Member, IEEE, Dongning Guo, Member, IEEE, and Michael L. Honig, Fellow, IEEE Abstract Channel
A Message-Passing Approach for Joint Channel Estimation, Interference Mitigation and Decoding
A Message-Passing Approach for Joint Channel Estimation, Interference Mitigation and Decoding 1 Yan Zhu, Dongning Guo and Michael L. Honig Department of Electrical Engineering and Computer Science Northwestern
Expectation propagation for symbol detection in large-scale MIMO communications
Expectation propagation for symbol detection in large-scale MIMO communications Pablo M. Olmos olmos@tsc.uc3m.es Joint work with Javier Céspedes (UC3M) Matilde Sánchez-Fernández (UC3M) and Fernando Pérez-Cruz
Expectation propagation for signal detection in flat-fading channels
Expectation propagation for signal detection in flat-fading channels Yuan Qi MIT Media Lab Cambridge, MA, 02139 USA yuanqi@media.mit.edu Thomas Minka CMU Statistics Department Pittsburgh, PA 15213 USA
Multiple-Input Multiple-Output Systems
Multiple-Input Multiple-Output Systems What is the best way to use antenna arrays? MIMO! This is a totally new approach ( paradigm ) to wireless communications, which has been discovered in 95-96. Performance
Improved Multiple Feedback Successive Interference Cancellation Algorithm for Near-Optimal MIMO Detection
Improved Multiple Feedback Successive Interference Cancellation Algorithm for Near-Optimal MIMO Detection Manish Mandloi, Mohammed Azahar Hussain and Vimal Bhatia Discipline of Electrical Engineering,
9 Forward-backward algorithm, sum-product on factor graphs
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.438 Algorithms For Inference Fall 2014 9 Forward-backward algorithm, sum-product on factor graphs The previous
Single-Gaussian Messages and Noise Thresholds for Low-Density Lattice Codes
Single-Gaussian Messages and Noise Thresholds for Low-Density Lattice Codes Brian M. Kurkoski, Kazuhiko Yamaguchi and Kingo Kobayashi kurkoski@ice.uec.ac.jp Dept. of Information and Communications Engineering
5. Density evolution. Density evolution 5-1
5. Density evolution Density evolution 5-1 Probabilistic analysis of message passing algorithms variable nodes factor nodes x1 a x i x2 a(x i ; x j ; x k ) x3 b x4 consider factor graph model G = (V ;
Information Theoretic Imaging
Information Theoretic Imaging WU Faculty: J. A. O Sullivan WU Doctoral Student: Naveen Singla Boeing Engineer: James Meany First Year Focus: Imaging for Data Storage Image Reconstruction Data Retrieval
A Gaussian Tree Approximation for Integer Least-Squares
A Gaussian Tree Approximation for Integer Least-Squares Jacob Goldberger School of Engineering Bar-Ilan University goldbej@eng.biu.ac.il Amir Leshem School of Engineering Bar-Ilan University leshema@eng.biu.ac.il
Probabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 2950-P, Spring 2013 Prof. Erik Sudderth Lecture 12: Gaussian Belief Propagation, State Space Models and Kalman Filters Guest Kalman Filter Lecture by
Lecture 2. Capacity of the Gaussian channel
Spring, 207 5237S, Wireless Communications II 2. Lecture 2 Capacity of the Gaussian channel Review on basic concepts in inf. theory ( Cover&Thomas: Elements of Inf. Theory, Tse&Viswanath: Appendix B) AWGN
Interleave Division Multiple Access. Li Ping, Department of Electronic Engineering City University of Hong Kong
Interleave Division Multiple Access Li Ping, Department of Electronic Engineering City University of Hong Kong 1 Outline! Introduction! IDMA! Chip-by-chip multiuser detection! Analysis and optimization!
Approximate Inference Part 1 of 2
Approximate Inference Part 1 of 2 Tom Minka Microsoft Research, Cambridge, UK Machine Learning Summer School 2009 http://mlg.eng.cam.ac.uk/mlss09/ Bayesian paradigm Consistent use of probability theory
Approximate Inference Part 1 of 2
Approximate Inference Part 1 of 2 Tom Minka Microsoft Research, Cambridge, UK Machine Learning Summer School 2009 http://mlg.eng.cam.ac.uk/mlss09/ 1 Bayesian paradigm Consistent use of probability theory
One-Bit LDPC Message Passing Decoding Based on Maximization of Mutual Information
One-Bit LDPC Message Passing Decoding Based on Maximization of Mutual Information ZOU Sheng and Brian M. Kurkoski kurkoski@ice.uec.ac.jp University of Electro-Communications Tokyo, Japan University of
NAME... Soc. Sec. #... Remote Location... (if on campus write campus) FINAL EXAM EE568 KUMAR. Sp ' 00
NAME... Soc. Sec. #... Remote Location... (if on campus write campus) FINAL EXAM EE568 KUMAR Sp ' 00 May 3 OPEN BOOK exam (students are permitted to bring in textbooks, handwritten notes, lecture notes
Graph-based Codes for Quantize-Map-and-Forward Relaying
20 IEEE Information Theory Workshop Graph-based Codes for Quantize-Map-and-Forward Relaying Ayan Sengupta, Siddhartha Brahma, Ayfer Özgür, Christina Fragouli and Suhas Diggavi EPFL, Switzerland, UCLA,
Improved MU-MIMO Performance for Future Systems Using Differential Feedback
Improved MU-MIMO Performance for Future 80. Systems Using Differential Feedback Ron Porat, Eric Ojard, Nihar Jindal, Matthew Fischer, Vinko Erceg Broadcom Corp. {rporat, eo, njindal, mfischer, verceg}@broadcom.com
Machine Learning for Data Science (CS4786) Lecture 24
Machine Learning for Data Science (CS4786) Lecture 24 Graphical Models: Approximate Inference Course Webpage : http://www.cs.cornell.edu/courses/cs4786/2016sp/ BELIEF PROPAGATION OR MESSAGE PASSING Each
Lecture 9: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1
: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1 Rayleigh Friday, May 25, 2018 09:00-11:30, Kansliet 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless
Lecture 8: MIMO Architectures (II) Theoretical Foundations of Wireless Communications 1. Overview. Ragnar Thobaben CommTh/EES/KTH
MIMO : MIMO Theoretical Foundations of Wireless Communications 1 Wednesday, May 25, 2016 09:15-12:00, SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication 1 / 20 Overview MIMO
Lecture 5: Antenna Diversity and MIMO Capacity Theoretical Foundations of Wireless Communications 1. Overview. CommTh/EES/KTH
: Antenna Diversity and Theoretical Foundations of Wireless Communications Wednesday, May 4, 206 9:00-2:00, Conference Room SIP Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication
SIGNAL detection in flat Rayleigh fading channels can be. Window-Based Expectation Propagation for Adaptive Signal Detection in Flat-Fading Channels
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 1 Window-Based Expectation Propagation for Adaptive Signal Detection in Flat-Fading Channels Yuan Qi and Thomas P. Minka Abstract
Adaptive Linear Filtering Using Interior Point. Optimization Techniques. Lecturer: Tom Luo
Adaptive Linear Filtering Using Interior Point Optimization Techniques Lecturer: Tom Luo Overview A. Interior Point Least Squares (IPLS) Filtering Introduction to IPLS Recursive update of IPLS Convergence/transient
ON DECREASING THE COMPLEXITY OF LATTICE-REDUCTION-AIDED K-BEST MIMO DETECTORS.
17th European Signal Processing Conference (EUSIPCO 009) Glasgow, Scotland, August 4-8, 009 ON DECREASING THE COMPLEXITY OF LATTICE-REDUCTION-AIDED K-BEST MIMO DETECTORS. Sandra Roger, Alberto Gonzalez,
Multi-Branch MMSE Decision Feedback Detection Algorithms. with Error Propagation Mitigation for MIMO Systems
Multi-Branch MMSE Decision Feedback Detection Algorithms with Error Propagation Mitigation for MIMO Systems Rodrigo C. de Lamare Communications Research Group, University of York, UK in collaboration with
Linear Dynamical Systems
Linear Dynamical Systems Sargur N. srihari@cedar.buffalo.edu Machine Learning Course: http://www.cedar.buffalo.edu/~srihari/cse574/index.html Two Models Described by Same Graph Latent variables Observations
LECTURE 3. Last time:
LECTURE 3 Last time: Mutual Information. Convexity and concavity Jensen s inequality Information Inequality Data processing theorem Fano s Inequality Lecture outline Stochastic processes, Entropy rate
On the Shamai-Laroia Approximation for the Information Rate of the ISI Channel
On the Shamai-Laroia Approximation for the Information Rate of the ISI Channel Yair Carmon and Shlomo Shamai (Shitz) Department of Electrical Engineering, Technion - Israel Institute of Technology 2014
Lecture 9: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1. Overview. Ragnar Thobaben CommTh/EES/KTH
: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1 Rayleigh Wednesday, June 1, 2016 09:15-12:00, SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication
Trust Degree Based Beamforming for Multi-Antenna Cooperative Communication Systems
Introduction Main Results Simulation Conclusions Trust Degree Based Beamforming for Multi-Antenna Cooperative Communication Systems Mojtaba Vaezi joint work with H. Inaltekin, W. Shin, H. V. Poor, and
Interactions of Information Theory and Estimation in Single- and Multi-user Communications
Interactions of Information Theory and Estimation in Single- and Multi-user Communications Dongning Guo Department of Electrical Engineering Princeton University March 8, 2004 p 1 Dongning Guo Communications
arxiv:cs/ v2 [cs.it] 1 Oct 2006
![arxiv:cs/ v2 [cs.it] 1 Oct 2006](/thumbs/89/97933712.jpg "arxiv:cs/ v2 [cs.it] 1 Oct 2006")
A General Computation Rule for Lossy Summaries/Messages with Examples from Equalization Junli Hu, Hans-Andrea Loeliger, Justin Dauwels, and Frank Kschischang arxiv:cs/060707v [cs.it] 1 Oct 006 Abstract
Constrained Detection for Multiple-Input Multiple-Output Channels
Constrained Detection for Multiple-Input Multiple-Output Channels Tao Cui, Chintha Tellambura and Yue Wu Department of Electrical and Computer Engineering University of Alberta Edmonton, AB, Canada T6G
Codes on Graphs. Telecommunications Laboratory. Alex Balatsoukas-Stimming. Technical University of Crete. November 27th, 2008
Codes on Graphs Telecommunications Laboratory Alex Balatsoukas-Stimming Technical University of Crete November 27th, 2008 Telecommunications Laboratory (TUC) Codes on Graphs November 27th, 2008 1 / 31
Wideband Fading Channel Capacity with Training and Partial Feedback
Wideband Fading Channel Capacity with Training and Partial Feedback Manish Agarwal, Michael L. Honig ECE Department, Northwestern University 145 Sheridan Road, Evanston, IL 6008 USA {m-agarwal,mh}@northwestern.edu
LDPC Codes. Intracom Telecom, Peania
LDPC Codes Alexios Balatsoukas-Stimming and Athanasios P. Liavas Technical University of Crete Dept. of Electronic and Computer Engineering Telecommunications Laboratory December 16, 2011 Intracom Telecom,
A SEMI-BLIND TECHNIQUE FOR MIMO CHANNEL MATRIX ESTIMATION. AdityaKiran Jagannatham and Bhaskar D. Rao
A SEMI-BLIND TECHNIQUE FOR MIMO CHANNEL MATRIX ESTIMATION AdityaKiran Jagannatham and Bhaskar D. Rao Department of Electrical and Computer Engineering University of California, San Diego La Jolla, CA 9093-0407
Estimation of the Capacity of Multipath Infrared Channels
Estimation of the Capacity of Multipath Infrared Channels Jeffrey B. Carruthers Department of Electrical and Computer Engineering Boston University jbc@bu.edu Sachin Padma Department of Electrical and
Sub-Gaussian Model Based LDPC Decoder for SαS Noise Channels
Sub-Gaussian Model Based LDPC Decoder for SαS Noise Channels Iulian Topor Acoustic Research Laboratory, Tropical Marine Science Institute, National University of Singapore, Singapore 119227. iulian@arl.nus.edu.sg
Adaptive Bit-Interleaved Coded OFDM over Time-Varying Channels
Adaptive Bit-Interleaved Coded OFDM over Time-Varying Channels Jin Soo Choi, Chang Kyung Sung, Sung Hyun Moon, and Inkyu Lee School of Electrical Engineering Korea University Seoul, Korea Email:jinsoo@wireless.korea.ac.kr,
Problem 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
Iterative Timing Recovery
Iterative Timing Recovery John R. Barry School of Electrical and Computer Engineering, Georgia Tech Atlanta, Georgia U.S.A. barry@ece.gatech.edu 0 Outline Timing Recovery Tutorial Problem statement TED:
Probabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 295-P, Spring 213 Prof. Erik Sudderth Lecture 11: Inference & Learning Overview, Gaussian Graphical Models Some figures courtesy Michael Jordan s draft
EE 5407 Part II: Spatial Based Wireless Communications
EE 5407 Part II: Spatial Based Wireless Communications Instructor: Prof. Rui Zhang E-mail: rzhang@i2r.a-star.edu.sg Website: http://www.ece.nus.edu.sg/stfpage/elezhang/ Lecture II: Receive Beamforming
Optimal Transmit Strategies in MIMO Ricean Channels with MMSE Receiver
Optimal Transmit Strategies in MIMO Ricean Channels with MMSE Receiver E. A. Jorswieck 1, A. Sezgin 1, H. Boche 1 and E. Costa 2 1 Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut 2
STA 414/2104: Machine Learning
STA 414/2104: Machine Learning Russ Salakhutdinov Department of Computer Science! Department of Statistics! rsalakhu@cs.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 9 Sequential Data So far
Physical Layer Binary Consensus. Study
Protocols: A Study Venugopalakrishna Y. R. and Chandra R. Murthy ECE Dept., IISc, Bangalore 23 rd Nov. 2013 Outline Introduction to Consensus Problem Setup Protocols LMMSE-based scheme Co-phased combining
Distributed Source Coding Using LDPC Codes
Distributed Source Coding Using LDPC Codes Telecommunications Laboratory Alex Balatsoukas-Stimming Technical University of Crete May 29, 2010 Telecommunications Laboratory (TUC) Distributed Source Coding
Lower Bounds on the Graphical Complexity of Finite-Length LDPC Codes
Lower Bounds on the Graphical Complexity of Finite-Length LDPC Codes Igal Sason Department of Electrical Engineering Technion - Israel Institute of Technology Haifa 32000, Israel 2009 IEEE International
Complex Gaussian Ratio Distribution with Applications for Error Rate Calculation in Fading Channels with Imperfect CSI
Complex Gaussian Ratio Distribution with Applications for Error Rate Calculation in Fading Channels with Imperfect CSI Robert J. Baxley, Brett T. Walkenhorst, Guillermo Acosta-Marum Georgia Tech Research
Decoupling of CDMA Multiuser Detection via the Replica Method
Decoupling of CDMA Multiuser Detection via the Replica Method Dongning Guo and Sergio Verdú Dept. of Electrical Engineering Princeton University Princeton, NJ 08544, USA email: {dguo,verdu}@princeton.edu
Chapter 4: Continuous channel and its capacity
meghdadi@ensil.unilim.fr Reference : Elements of Information Theory by Cover and Thomas Continuous random variable Gaussian multivariate random variable AWGN Band limited channel Parallel channels Flat
Lecture 4 : Introduction to Low-density Parity-check Codes
Lecture 4 : Introduction to Low-density Parity-check Codes LDPC codes are a class of linear block codes with implementable decoders, which provide near-capacity performance. History: 1. LDPC codes were
Multiuser Capacity in Block Fading Channel
Multiuser Capacity in Block Fading Channel April 2003 1 Introduction and Model We use a block-fading model, with coherence interval T where M independent users simultaneously transmit to a single receiver
STA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.utstat.utoronto.ca/~rsalakhu/ Sidney Smith Hall, Room 6002 Lecture 11 Project
Low-density parity-check (LDPC) codes
Low-density parity-check (LDPC) codes Performance similar to turbo codes Do not require long interleaver to achieve good performance Better block error performance Error floor occurs at lower BER Decoding
Joint Equalization and Decoding for Nonlinear Two-Dimensional Intersymbol Interference Channels with Application to Optical Storage
Joint Equalization and Decoding for Nonlinear Two-Dimensional Intersymbol Interference Channels with Application to Optical Storage 1 arxiv:cs/0509008v1 [cs.it] 4 Sep 2005 Naveen Singla and Joseph A. O
Augmented Lattice Reduction for MIMO decoding
Augmented Lattice Reduction for MIMO decoding LAURA LUZZI joint work with G. Rekaya-Ben Othman and J.-C. Belfiore at Télécom-ParisTech NANYANG TECHNOLOGICAL UNIVERSITY SEPTEMBER 15, 2010 Laura Luzzi Augmented
EE229B - Final Project. Capacity-Approaching Low-Density Parity-Check Codes
EE229B - Final Project Capacity-Approaching Low-Density Parity-Check Codes Pierre Garrigues EECS department, UC Berkeley garrigue@eecs.berkeley.edu May 13, 2005 Abstract The class of low-density parity-check
Utilizing Correct Prior Probability Calculation to Improve Performance of Low-Density Parity- Check Codes in the Presence of Burst Noise
Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2012 Utilizing Correct Prior Probability Calculation to Improve Performance of Low-Density Parity- Check
Decomposing the MIMO Wiretap Channel
Decomposing the MIMO Wiretap Channel Anatoly Khina, Tel Aviv University Joint work with: Yuval Kochman, Hebrew University Ashish Khisti, University of Toronto ISIT 2014 Honolulu, Hawai i, USA June 30,
Expectation Propagation Algorithm
Expectation Propagation Algorithm 1 Shuang Wang School of Electrical and Computer Engineering University of Oklahoma, Tulsa, OK, 74135 Email: {shuangwang}@ou.edu This note contains three parts. First,
Minimum Feedback Rates for Multi-Carrier Transmission With Correlated Frequency Selective Fading
Minimum Feedback Rates for Multi-Carrier Transmission With Correlated Frequency Selective Fading Yakun Sun and Michael L. Honig Department of ECE orthwestern University Evanston, IL 60208 Abstract We consider
Multiuser Detection of Sparsely Spread CDMA
SUBMITTED TO IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS Multiuser Detection of Sparsely Spread CDMA Dongning Guo, Member, IEEE, and Chih-Chun Wang, Member, IEEE Abstract Code-division multiple access
Message-Passing Decoding for Low-Density Parity-Check Codes Harish Jethanandani and R. Aravind, IIT Madras
Message-Passing Decoding for Low-Density Parity-Check Codes Harish Jethanandani and R. Aravind, IIT Madras e-mail: hari_jethanandani@yahoo.com Abstract Low-density parity-check (LDPC) codes are discussed
An Introduction to Low-Density Parity-Check Codes
An Introduction to Low-Density Parity-Check Codes Paul H. Siegel Electrical and Computer Engineering University of California, San Diego 5/ 3/ 7 Copyright 27 by Paul H. Siegel Outline Shannon s Channel
Lattice Reduction Aided Precoding for Multiuser MIMO using Seysen s Algorithm
Lattice Reduction Aided Precoding for Multiuser MIMO using Seysen s Algorithm HongSun An Student Member IEEE he Graduate School of I & Incheon Korea ahs3179@gmail.com Manar Mohaisen Student Member IEEE
Chapter 8: Differential entropy. University of Illinois at Chicago ECE 534, Natasha Devroye
Chapter 8: Differential entropy Chapter 8 outline Motivation Definitions Relation to discrete entropy Joint and conditional differential entropy Relative entropy and mutual information Properties AEP for
Introduction to Low-Density Parity Check Codes. Brian Kurkoski
Introduction to Low-Density Parity Check Codes Brian Kurkoski kurkoski@ice.uec.ac.jp Outline: Low Density Parity Check Codes Review block codes History Low Density Parity Check Codes Gallager s LDPC code
Information Theory. Coding and Information Theory. Information Theory Textbooks. Entropy
Coding and Information Theory Chris Williams, School of Informatics, University of Edinburgh Overview What is information theory? Entropy Coding Information Theory Shannon (1948): Information theory is
WIRELESS COMMUNICATIONS AND COGNITIVE RADIO TRANSMISSIONS UNDER QUALITY OF SERVICE CONSTRAINTS AND CHANNEL UNCERTAINTY
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Theses, Dissertations, and Student Research from Electrical & Computer Engineering Electrical & Computer Engineering, Department
Applications of Lattices in Telecommunications
Applications of Lattices in Telecommunications Dept of Electrical and Computer Systems Engineering Monash University amin.sakzad@monash.edu Oct. 2013 1 Sphere Decoder Algorithm Rotated Signal Constellations
Appendix B Information theory from first principles
Appendix B Information theory from first principles This appendix discusses the information theory behind the capacity expressions used in the book. Section 8.3.4 is the only part of the book that supposes
Lecture Notes 4 Vector Detection and Estimation. Vector Detection Reconstruction Problem Detection for Vector AGN Channel
Lecture Notes 4 Vector Detection and Estimation Vector Detection Reconstruction Problem Detection for Vector AGN Channel Vector Linear Estimation Linear Innovation Sequence Kalman Filter EE 278B: Random
Coding over Interference Channels: An Information-Estimation View
Coding over Interference Channels: An Information-Estimation View Shlomo Shamai Department of Electrical Engineering Technion - Israel Institute of Technology Information Systems Laboratory Colloquium
Stat 521A Lecture 18 1
Stat 521A Lecture 18 1 Outline Cts and discrete variables (14.1) Gaussian networks (14.2) Conditional Gaussian networks (14.3) Non-linear Gaussian networks (14.4) Sampling (14.5) 2 Hybrid networks A hybrid
Factor Analysis and Kalman Filtering (11/2/04)
CS281A/Stat241A: Statistical Learning Theory Factor Analysis and Kalman Filtering (11/2/04) Lecturer: Michael I. Jordan Scribes: Byung-Gon Chun and Sunghoon Kim 1 Factor Analysis Factor analysis is used
Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User MIMO Systems
Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User MIMO Systems Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User
A Thesis for the Degree of Master. An Improved LLR Computation Algorithm for QRM-MLD in Coded MIMO Systems
A Thesis for the Degree of Master An Improved LLR Computation Algorithm for QRM-MLD in Coded MIMO Systems Wonjae Shin School of Engineering Information and Communications University 2007 An Improved LLR
Message passing and approximate message passing
Message passing and approximate message passing Arian Maleki Columbia University 1 / 47 What is the problem? Given pdf µ(x 1, x 2,..., x n ) we are interested in arg maxx1,x 2,...,x n µ(x 1, x 2,..., x
Information Dimension
Information Dimension Mina Karzand Massachusetts Institute of Technology November 16, 2011 1 / 26 2 / 26 Let X would be a real-valued random variable. For m N, the m point uniform quantized version of
Turbo-AMP: A Graphical-Models Approach to Compressive Inference
Turbo-AMP: A Graphical-Models Approach to Compressive Inference Phil Schniter (With support from NSF CCF-1018368 and DARPA/ONR N66001-10-1-4090.) June 27, 2012 1 Outline: 1. Motivation. (a) the need for
Lecture 7 MIMO Communica2ons
Wireless Communications Lecture 7 MIMO Communica2ons Prof. Chun-Hung Liu Dept. of Electrical and Computer Engineering National Chiao Tung University Fall 2014 1 Outline MIMO Communications (Chapter 10
Performance Analysis of Physical Layer Network Coding
Performance Analysis of Physical Layer Network Coding by Jinho Kim A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Electrical Engineering: Systems)
Secret-Key Generation over Reciprocal Fading Channels
Secret-ey Generation over Reciprocal Fading Channels shish histi Department of Electrical and Computer Engineering University of oronto Nov. 14, 2012 Motivation Secret-ey Generation in Wireless Fading
Graphical Models and Kernel Methods
Graphical Models and Kernel Methods Jerry Zhu Department of Computer Sciences University of Wisconsin Madison, USA MLSS June 17, 2014 1 / 123 Outline Graphical Models Probabilistic Inference Directed vs.
SEQUENTIAL MAP EQUALIZATION OF MIMO CHANNELS WITH UNKNOWN ORDER
SEQUENTIAL MAP EQUALIZATION OF MIMO CHANNELS WITH UNKNOWN ORDER Manuel A. Vázquez Departamento de Electrónica e Sistemas Universidade da Coruña Campus de Elviña s/n, 15071 A Coruña (Spain. mvazquez@udc.es
Inference and Representation
Inference and Representation David Sontag New York University Lecture 5, Sept. 30, 2014 David Sontag (NYU) Inference and Representation Lecture 5, Sept. 30, 2014 1 / 16 Today s lecture 1 Running-time of
An Introduction to Low Density Parity Check (LDPC) Codes
An Introduction to Low Density Parity Check (LDPC) Codes Jian Sun jian@csee.wvu.edu Wireless Communication Research Laboratory Lane Dept. of Comp. Sci. and Elec. Engr. West Virginia University June 3,
DEVICE-TO-DEVICE COMMUNICATIONS: THE PHYSICAL LAYER SECURITY ADVANTAGE
DEVICE-TO-DEVICE COMMUNICATIONS: THE PHYSICAL LAYER SECURITY ADVANTAGE Daohua Zhu, A. Lee Swindlehurst, S. Ali A. Fakoorian, Wei Xu, Chunming Zhao National Mobile Communications Research Lab, Southeast
Superposition Encoding and Partial Decoding Is Optimal for a Class of Z-interference Channels
Superposition Encoding and Partial Decoding Is Optimal for a Class of Z-interference Channels Nan Liu and Andrea Goldsmith Department of Electrical Engineering Stanford University, Stanford CA 94305 Email:
Digital 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,
Expectation Propagation in Factor Graphs: A Tutorial
DRAFT: Version 0.1, 28 October 2005. Do not distribute. Expectation Propagation in Factor Graphs: A Tutorial Charles Sutton October 28, 2005 Abstract Expectation propagation is an important variational
Single-letter Characterization of Signal Estimation from Linear Measurements
Single-letter Characterization of Signal Estimation from Linear Measurements Dongning Guo Dror Baron Shlomo Shamai The work has been supported by the European Commission in the framework of the FP7 Network
Joint Iterative Decoding of LDPC Codes and Channels with Memory
Joint Iterative Decoding of LDPC Codes and Channels with Memory Henry D. Pfister and Paul H. Siegel University of California, San Diego 3 rd Int l Symposium on Turbo Codes September 1, 2003 Outline Channels
x log x, which is strictly convex, and use Jensen s Inequality:
2. Information measures: mutual information 2.1 Divergence: main inequality Theorem 2.1 (Information Inequality). D(P Q) 0 ; D(P Q) = 0 iff P = Q Proof. Let ϕ(x) x log x, which is strictly convex, and
Lecture 4. Capacity of Fading Channels
1 Lecture 4. Capacity of Fading Channels Capacity of AWGN Channels Capacity of Fading Channels Ergodic Capacity Outage Capacity Shannon and Information Theory Claude Elwood Shannon (April 3, 1916 February