Decomposing the MIMO Wiretap Channel
|
|
- Alexandrina Morgan
- 5 years ago
- Views:
Transcription
1 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, 2014
2 Model Capacity SISO Goal Part I Problem Setting
3 Model Capacity SISO Goal Channel Model: Gaussian MIMO Wiretap Channel H B Alice H E Bob y B = H B x+z B Eve y E = H E x+z E x N A 1 input vector of power P y B, y E N B 1, N E 1 received vectors H B, H E N B N A, N E N A channel matrices z B CN(0,I NB ), z E CN(0,I NE ) noise vectors Closed loop (full channel knowledge everywhere).
4 Capacity Model Capacity SISO Goal Gaussian SISO channel capacity [Leung-Yan-Cheong, Hellman 78] I(X;Y B ) I(X;Y E ) [{ ( }} ){{ ( }} )] { C S (h B,h E ) = log 1+ h B 2 P log 1+ h E 2 P Gaussian MIMO channel capacity [Khisti,Wornell 10][Oggier,Hassibi 11] C S (H B,H E ) = max K: trace{k} P I(X;Y B ) I(X;Y E ) [{}}{{}}{ ] log I+H B KH B log I+H E KH E Maximization over all admissible covariance matrices K Power constraint can be replaced with covariance constraint [Liu, Shamai 09] +
5 Model Capacity SISO Goal Capacity-achieving Codes for Gaussian SISO Wiretap Great effort in constructing practical capacity-achieving codes: LDPC-based [Klinc et al. 11][Andresson, PhD 11] Lattice-based [Oggier et al., submitted 13] Polar-based [Mahdavifar, Vardy 11] Black-box approach [Tyagi, Vardy, ISIT 14] More... What to do for MIMO?
6 Model Capacity SISO Goal Goal: Practical MIMO Scheme Black box approach Signal processing (SVD-based scheme [Telatar 99], V-BLAST [Foschini 96],...) Any good SISO wiretap codes Achieves capacity Gap-to-capacity dictated by gap-to-capacity of the SISO codes
7 Model Capacity SISO Goal Goal: Practical MIMO Scheme Black box approach Signal processing (SVD-based scheme [Telatar 99], V-BLAST [Foschini 96],...) Any good SISO wiretap codes Achieves capacity Gap-to-capacity dictated by gap-to-capacity of the SISO codes High SNR [Khisti, Wornell 10] Generalized SVD (GSVD) + linear zero-forcing Any good SISO wiretap codes Optimal at SNR B,SNR E Suboptimal at SNR B,SNR E <
8 SVD V-BLAST (QR) Part II Background: MIMO Without Secrecy
9 SVD V-BLAST (QR) SVD with water-filling SVD for Given K Practical Schemes for MIMO Without Secrecy (No Eve) Singular-Value Decomposition (SVD) Scheme [Telatar 99] H B = Q B D B V A Q B and V A unitary Alice applies V A and Bob applies Q B d d y 1 = d 1 x 1 +z 1 D B = y 2 = d 2 x 2 +z d N 1 0. y d N = d N x N +z N N Results in parallel scalar sub-channels (each sub-channel has a different SNR) Apply water-filling on {x 1,...,x N }: x = V A Wc
10 SVD V-BLAST (QR) SVD with water-filling SVD for Given K Practical Schemes for MIMO Without Secrecy (No Eve) SVD-based scheme for a given input covariance K H B K 1/2 = Q B D B V A Q B and V A unitary Alice applies K 1/2 V A and Bob applies Q B d d y 1 = d 1 x 1 +z 1 D B = y 2 = d 2 x 2 +z d N 1 0. y d N = d N x N +z N N Results in parallel scalar sub-channels (each sub-channel has a different SNR) Apply water-filling on {x 1,...,x n }: x = V A Wc x = K 1/2 V A c
11 SVD V-BLAST (QR) SVD with water-filling SVD for Given K Practical Schemes for MIMO Without Secrecy (No Eve) SVD scheme with given K achieves : R = log I NA +H B KH B For optimal choice of K attains capacity Can be used to attain capacity for other covariance constraint scenarios (e.g., individual power constraints)
12 SVD V-BLAST (QR) ZF MMSE Precoded Practical Schemes for MIMO Without Secrecy (No Eve) QR decomp. [Foschini 96][Wolniansky et al. 98] zero-forcing VBLAST H B = Q B T B Q B unitary; T B triangular Bob applies Q B (no SP is required by Alice) t 1 0 t 2 T B = t N t N Off-diagonal elements are canceled via successive interference cancellation (SIC) y eff 1 = t 1 x 1 +z 1 y eff 2 = t 2 x 2 +z 2. yn eff = t Nx N +z N
13 SVD V-BLAST (QR) ZF MMSE Precoded Practical Schemes for MIMO Without Secrecy (No Eve) QRD MMSE-VBLAST for a given covariance K [Hassibi 00] [ HB K 1/2 ] = Q B T B I NA Q B unitary; Q B N B N A submatrix of Q B Bob applies Q B (no SP is required by Alice) Q B contains Wiener-filtering ( FFE ) Effective noise has channel noise and ISI components Effective SNRs satisfy: t 2 i = 1+SNR i log(t 2 i ) = log(1+snr i) = I(c i ;y B c N A i+1 ) Off-diagonal elements above diagonal canceled via SIC
14 SVD V-BLAST (QR) ZF MMSE Precoded Practical Schemes for MIMO Without Secrecy (No Eve) For square invertible H, ZF-VBLAST achieves: R = H B H B ( ) Using K at the transmitter achieves: R = H B KH B MMSE-VBLAST achieves: R = I NB +H B KH B
15 SVD V-BLAST (QR) ZF MMSE Precoded Practical Schemes for MIMO Without Secrecy (No Eve) MMSE-VBLAST with precoding for a given covariance K [ HB K 1/2 ] V A = Q B T B I NA V A can be used to design diagonal values design SNRs
16 SVD V-BLAST (QR) ZF MMSE Precoded Practical Schemes for MIMO Without Secrecy (No Eve) MMSE-VBLAST with precoding for a given covariance K [ HB K 1/2 ] V A = Q B T B I NA V A can be used to design diagonal values design SNRs SVD-scheme as MMSE-VBLAST (QR) Choosing V A of the SVD of H B K 1/2 SVD scheme (no SIC needed)
17 SVD V-BLAST (QR) ZF MMSE Precoded Practical Schemes for MIMO Without Secrecy (No Eve) MMSE-VBLAST with precoding for a given covariance K [ HB K 1/2 ] V A = Q B T B I NA V A can be used to design diagonal values design SNRs SVD-scheme as MMSE-VBLAST (QR) Choosing V A of the SVD of H B K 1/2 SVD scheme (no SIC needed) Geometric-mean decomposition [Jiang et al. 05]/ QRS [Zhang et al. 05] V A is choosing s.t. all diagonal values (all SNRs) are equal The same codebook can be used over all subchannels No need for bit-loading
18 Idea Superposition General scheme Part III Back to Wiretap...
19 Idea Superposition General scheme New Scheme for Finite SNR T B { }} { [ HB K 1/2 ] b 1 V A = Q I B. 0.., bi 2 = 1+SNR B i NA 0 0 b N T E { }} { [ HE K 1/2 ] e 1 V A = Q I E. 0.., ei 2 = 1+SNR E i NA 0 0 e N Use any good SISO wiretap codes for SNR-pairs (b 2 i 1,e 2 i 1)
20 Idea Superposition General scheme New Scheme for Finite SNR T B { }} { [ HB K 1/2 ] b 1 V A = Q I B. 0.., bi 2 = 1+SNR B i NA 0 0 b N T E { }} { [ HE K 1/2 ] e 1 V A = Q I E. 0.., ei 2 = 1+SNR E i NA 0 0 e N Use any good SISO wiretap codes for SNR-pairs (b 2 i 1,e 2 i 1) V A of Eve s SVD Easy secrecy analysis + strong secrecy
21 Idea Superposition General scheme New Scheme for Finite SNR T B { }} { [ HB K 1/2 ] b 1 V A = Q I B. 0.., bi 2 = 1+SNR B i NA 0 0 b N T E { }} { [ HE K 1/2 ] e 1 V A = Q I E. 0.., ei 2 = 1+SNR E i NA 0 0 e N Use any good SISO wiretap codes for SNR-pairs (b 2 i 1,e 2 i 1) V A of Eve s SVD Easy secrecy analysis + strong secrecy V A of Bob s SVD No need for V-BLAST
22 Idea Superposition General scheme New Scheme for Finite SNR T B { }} { [ HB K 1/2 ] b 1 V A = Q I B. 0.., bi 2 = 1+SNR B i NA 0 0 b N T E { }} { [ HE K 1/2 ] e 1 V A = Q I E. 0.., ei 2 = 1+SNR E i NA 0 0 e N Use any good SISO wiretap codes for SNR-pairs (b 2 i 1,e 2 i 1) V A of Eve s SVD Easy secrecy analysis + strong secrecy V A of Bob s SVD No need for V-BLAST diag{t B },diag{t E } are const. Same code over all channels
23 Idea Superposition General scheme Strong/weak secrecy Orthogonalizing Eve s Channel Take optimal covariance matrix K
24 Idea Superposition General scheme Strong/weak secrecy Orthogonalizing Eve s Channel Take optimal covariance matrix K Use optimal SVD-based scheme matched for H E with K: H E K 1/2 = Q E D E V A
25 Idea Superposition General scheme Strong/weak secrecy Orthogonalizing Eve s Channel Take optimal covariance matrix K Use optimal SVD-based scheme matched for H E with K: H E K 1/2 = Q E D E V A Alice: x = K 1/2 V A c
26 Idea Superposition General scheme Strong/weak secrecy Orthogonalizing Eve s Channel Take optimal covariance matrix K Use optimal SVD-based scheme matched for H E with K: H E K 1/2 = Q E D E V A Alice: x = K 1/2 V A c Eve: ỹ E = Q E y E = Q E H EK 1/2 V A cq E +z E = D E c+ z E
27 Idea Superposition General scheme Strong/weak secrecy Orthogonalizing Eve s Channel Take optimal covariance matrix K Use optimal SVD-based scheme matched for H E with K: H E K 1/2 = Q E D E V A Alice: x = K 1/2 V A c Eve: ỹ E = Q E y E = Q E H EK 1/2 V A cq E +z E = D E c+ z E Eve sees parallel subchannels Easy secrecy analysis
28 Idea Superposition General scheme Strong/weak secrecy Orthogonalizing Eve s Channel Take optimal covariance matrix K Use optimal SVD-based scheme matched for H E with K: H E K 1/2 = Q E D E V A Alice: x = K 1/2 V A c Eve: ỹ E = Q E y E = Q E H EK 1/2 V A cq E +z E = D E c+ z E Eve sees parallel subchannels Easy secrecy analysis Bob Uses MMSE-VBLAST: ỹ B = Q B y B = T B c+ z B
29 Idea Superposition General scheme Orthogonalizing Eve s Channel Take optimal covariance matrix K Strong/weak secrecy Use optimal SVD-based scheme matched for H E with K: Alice: x = K 1/2 V A c H E K 1/2 = Q E D E V A Eve: ỹ E = Q E y E = Q E H EK 1/2 V A cq E +z E = D E c+ z E Eve sees parallel subchannels Easy secrecy analysis Bob Uses MMSE-VBLAST: ỹ B = Q B y B = T B c+ z B Use SISO wiretap codes over parallel wiretap subchannels: (SNR B i,snr E i ) ( t B i,d E i )
30 Idea Superposition General scheme Orthogonalizing Eve s Channel Take optimal covariance matrix K Strong/weak secrecy Use optimal SVD-based scheme matched for H E with K: Alice: x = K 1/2 V A c H E K 1/2 = Q E D E V A Eve: ỹ E = Q E y E = Q E H EK 1/2 V A cq E +z E = D E c+ z E Eve sees parallel subchannels Easy secrecy analysis Bob Uses MMSE-VBLAST: ỹ B = Q B y B = T B c+ z B Use SISO wiretap codes over parallel wiretap subchannels: (SNR B i,snr E i ) ( t B i,d E i ) Achieves capacity for optimal K: R = I NA +H B KH B I NA +H E KH E C S }{{}}{{} Bob Eve
31 Idea Superposition General scheme Orthogonalizing Eve s Channel Strong/weak secrecy SVD of Eve s channel allows easy secrecy-constraints proof Strong/weak secrecy of the SISO codes Strong/weak secrecy of the MIMO scheme Can we use SVD for Bob s channel? Can the same SISO codebook be used over all subchannels?
32 Idea Superposition General scheme Superposition Coding for the Memoryless Wiretap Channel Theorem p(y B x) and p(y E x) transition distributions for Bob and Eve x = ϕ(c 1,...,c NA ) c i drawn i.i.d. p ci ( ) Weak-secrecy rates of ( ) ( ) c N R i = I c i ;y A c N B i+1 I c i ;y A E i+1, i = 1,...,N A are achievable Genie-aided secrecy-proof Eve tries to recover sub-messages sequentially (from last to first) For the recovery of sub-message i all previous sub-messages (i = i +1,...,N A ) are revealed
33 Idea Superposition General scheme and 2-GMD General Multi-Stream Scheme for the Gaussian MIMO Wiretap Apply QR decompositions for both Bob and Eve: [ HB K 1/2 ] [ V A HE K = Q B T B, 1/2 ] V A = Q E T E I NA The resulting SNRs satisfy: I NA log(1+snr B;i ) = log(b 2 i ) = I(c i;y B c N A i+1 ) log(1+snr E;i ) = log(e 2 i ) = I(c i;y E c N A i+1 ) Superpoisition theorem Capacity is achieved with SISO codebooks of SNR-pairs (b 2 i 1,e 2 i 1) = Alice can apply any V A!
34 Idea Superposition General scheme and 2-GMD General Multi-Stream Scheme for the Gaussian MIMO Wiretap Bob Choose V A such that H B K 1/2 = Q B D B V A Bob: ỹ B = D B c+ z B Same codebook over all subchannels Choose V A s.t. T B and T E have constant diagonals: SNR B 1 = SNRB 2 = = SNRB N SNR E 1 = SNR E 2 = = SNR E N Possible using a space time structure [Khina et al. 11]
35 High SNR scheme Part IV Supplementary
36 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A
37 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A A invertible matrix; Q B, Q E unitary
38 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A A invertible matrix; Q B, Q E unitary D B, D E diagonal, s.t. D 2 B +D2 E = I
39 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A A invertible matrix; Q B, Q E unitary D B, D E diagonal, s.t. D 2 B +D2 E = I Alice uses linear zero-forcing inverts Tx: x = A 1 c
40 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A A invertible matrix; Q B, Q E unitary D B, D E diagonal, s.t. D 2 B +D2 E = I Alice uses linear zero-forcing inverts Tx: x = A 1 c Bob and Eve apply Q B and Q E
41 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A A invertible matrix; Q B, Q E unitary D B, D E diagonal, s.t. D 2 B +D2 E = I Alice uses linear zero-forcing inverts Tx: x = A 1 c Bob and Eve apply Q B and Q E Results in parallel subchannels: D B, D E
42 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, Wornell 10] Apply Generalized SVD (GSVD) to H B and H E : H B = Q B D B A H E = Q E D E A A invertible matrix; Q B, Q E unitary D B, D E diagonal, s.t. D 2 B +D2 E = I Alice uses linear zero-forcing inverts Tx: x = A 1 c Bob and Eve apply Q B and Q E Results in parallel subchannels: D B, D E Transmit only over subchannels with d B;i > d E;i using good SISO wiretap codes
43 High SNR scheme MIMO Wiretap Scheme for High SNR [Khisti, High-SNR (P ) Approaches capacity: N A i=1 log 1+Pd2 B;i 1+Pd 2 E;i N A i=1 log Pd2 B;i Pd 2 E;i Linear zero-forcing attains capacity at high SNR (In contrast to communication without secrecy!) Strong/weak secrecy of the SISO codes Strong/weak secrecy of the MIMO scheme Wasteful at finite SNR!
Anatoly Khina. Joint work with: Uri Erez, Ayal Hitron, Idan Livni TAU Yuval Kochman HUJI Gregory W. Wornell MIT
Network Modulation: Transmission Technique for MIMO Networks Anatoly Khina Joint work with: Uri Erez, Ayal Hitron, Idan Livni TAU Yuval Kochman HUJI Gregory W. Wornell MIT ACC Workshop, Feder Family Award
More informationIncremental Coding over MIMO Channels
Model Rateless SISO MIMO Applications Summary Incremental Coding over MIMO Channels Anatoly Khina, Tel Aviv University Joint work with: Yuval Kochman, MIT Uri Erez, Tel Aviv University Gregory W. Wornell,
More informationPhysical-Layer MIMO Relaying
Model Gaussian SISO MIMO Gauss.-BC General. Physical-Layer MIMO Relaying Anatoly Khina, Tel Aviv University Joint work with: Yuval Kochman, MIT Uri Erez, Tel Aviv University August 5, 2011 Model Gaussian
More informationThe Dirty MIMO Multiple-Access Channel
The Dirty MIMO Multiple-Access Channel Anatoly Khina, Caltech Joint work with: Yuval Kochman, Hebrew University Uri Erez, Tel-Aviv University ISIT 2016 Barcelona, Catalonia, Spain July 12, 2016 Motivation:
More informationSimultaneous SDR Optimality via a Joint Matrix Decomp.
Simultaneous SDR Optimality via a Joint Matrix Decomposition Joint work with: Yuval Kochman, MIT Uri Erez, Tel Aviv Uni. May 26, 2011 Model: Source Multicasting over MIMO Channels z 1 H 1 y 1 Rx1 ŝ 1 s
More informationJoint Unitary Triangularization for MIMO Networks
1 Joint Unitary Triangularization for MIMO Networks Anatoly Khina, Student Member, IEEE, Yuval Kochman, Member, IEEE, and Uri Erez, Member, IEEE Abstract This work considers communication networks where
More informationELEC E7210: Communication Theory. Lecture 10: MIMO systems
ELEC E7210: Communication Theory Lecture 10: MIMO systems Matrix Definitions, Operations, and Properties (1) NxM matrix a rectangular array of elements a A. an 11 1....... a a 1M. NM B D C E ermitian transpose
More informationImproved Rates and Coding for the MIMO Two-Way Relay Channel
Improved Rates and Coding for the MIMO Two-Way Relay Channel Anatoly Khina Dept. of EE Systems, TAU Tel Aviv, Israel Email: anatolyk@eng.tau.ac.il Yuval Kochman School of CSE, HUJI Jerusalem, Israel Email:
More informationIncremental Coding over MIMO Channels
Incremental Coding over MIMO Channels Anatoly Khina EE-Systems Dept, TAU Tel Aviv, Israel Email: anatolyk@engtauacil Yuval Kochman EECS Dept, MIT Cambridge, MA 02139, USA Email: yuvalko@mitedu Uri Erez
More informationThe Dirty MIMO Multiple-Access Channel
The Dirty MIMO Multiple-Access Channel Anatoly Khina, Yuval Kochman, and Uri Erez Abstract In the scalar dirty multiple-access channel, in addition to Gaussian noise, two additive interference signals
More informationImproved Rates and Coding for the MIMO Two-Way Relay Channel
Improved Rates and Coding for the MIMO Two-Way Relay Channel Anatoly Khina Dept. of EE Systems, TAU Tel Aviv, Israel Email: anatolyk@eng.tau.ac.il Yuval Kochman School of CSE, HUJI Jerusalem, Israel Email:
More informationAugmented 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
More informationACOMMUNICATION situation where a single transmitter
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 50, NO. 9, SEPTEMBER 2004 1875 Sum Capacity of Gaussian Vector Broadcast Channels Wei Yu, Member, IEEE, and John M. Cioffi, Fellow, IEEE Abstract This paper
More informationPrecoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap
Precoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap Or Ordentlich Dept EE-Systems, TAU Tel Aviv, Israel Email: ordent@engtauacil Uri Erez Dept EE-Systems, TAU Tel Aviv,
More informationSecure Degrees of Freedom of the MIMO Multiple Access Wiretap Channel
Secure Degrees of Freedom of the MIMO Multiple Access Wiretap Channel Pritam Mukherjee Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland, College Park, MD 074 pritamm@umd.edu
More informationSingle-User MIMO systems: Introduction, capacity results, and MIMO beamforming
Single-User MIMO systems: Introduction, capacity results, and MIMO beamforming Master Universitario en Ingeniería de Telecomunicación I. Santamaría Universidad de Cantabria Contents Introduction Multiplexing,
More informationDegrees of Freedom Region of the Gaussian MIMO Broadcast Channel with Common and Private Messages
Degrees of Freedom Region of the Gaussian MIMO Broadcast hannel with ommon and Private Messages Ersen Ekrem Sennur Ulukus Department of Electrical and omputer Engineering University of Maryland, ollege
More informationLecture 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
More informationDecode-and-Forward Relaying via Standard AWGN Coding and Decoding
1 Decode-and-Forward Relaying via tandard AWGN Coding and Decoding Anatoly Khina, tudent Member, IEEE, Yuval Kochman, Member, IEEE, Uri Erez, Member, IEEE, and Gregory W. Wornell, Fellow, IEEE Abstract
More informationSOLUTIONS TO ECE 6603 ASSIGNMENT NO. 6
SOLUTIONS TO ECE 6603 ASSIGNMENT NO. 6 PROBLEM 6.. Consider a real-valued channel of the form r = a h + a h + n, which is a special case of the MIMO channel considered in class but with only two inputs.
More informationThe RF-Chain Limited MIMO System: Part II Case Study of V-BLAST and GMD
The RF-Chain Limited MIMO System: Part II Case Study of V-BLAST and GMD Yi Jiang Mahesh K. Varanasi Abstract In Part I of this paper, we have established the fundamental D-M tradeoff of a RF-chain limited
More informationLecture 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
More informationApplications 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
More informationShannon meets Wiener II: On MMSE estimation in successive decoding schemes
Shannon meets Wiener II: On MMSE estimation in successive decoding schemes G. David Forney, Jr. MIT Cambridge, MA 0239 USA forneyd@comcast.net Abstract We continue to discuss why MMSE estimation arises
More informationRematch and Forward: Joint Source-Channel Coding for Communications
Background ρ = 1 Colored Problem Extensions Rematch and Forward: Joint Source-Channel Coding for Communications Anatoly Khina Joint work with: Yuval Kochman, Uri Erez, Ram Zamir Dept. EE - Systems, Tel
More informationInteger-Forcing Linear Receivers
IEEE TRANS INFO THEORY, TO APPEAR Integer-Forcing Linear Receivers Jiening Zhan, Bobak Nazer, Member, IEEE, Uri Erez, Member, IEEE, and Michael Gastpar, Member, IEEE arxiv:0035966v4 [csit] 5 Aug 04 Abstract
More informationSum Capacity of Gaussian Vector Broadcast Channels
Sum Capacity of Gaussian Vector Broadcast Channels Wei Yu, Member IEEE and John M. Cioffi, Fellow IEEE Abstract This paper characterizes the sum capacity of a class of potentially non-degraded Gaussian
More informationJoint Optimization of Transceivers with Decision Feedback and Bit Loading
Joint Optimization of Transceivers with Decision Feedback and Bit Loading Ching-Chih Weng, Chun-Yang Chen and P. P. Vaidyanathan Dept. of Electrical Engineering, C 136-93 California Institute of Technology,
More informationarxiv: v1 [cs.it] 11 Apr 2017
Noname manuscript No. (will be inserted by the editor) Enhancement of Physical Layer Security Using Destination Artificial Noise Based on Outage Probability Ali Rahmanpour Vahid T. Vakili S. Mohammad Razavizadeh
More informationThe Robustness of Dirty Paper Coding and The Binary Dirty Multiple Access Channel with Common Interference
The and The Binary Dirty Multiple Access Channel with Common Interference Dept. EE - Systems, Tel Aviv University, Tel Aviv, Israel April 25th, 2010 M.Sc. Presentation The B/G Model Compound CSI Smart
More informationMulti-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
More informationAppendix 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
More informationParallel Additive Gaussian Channels
Parallel Additive Gaussian Channels Let us assume that we have N parallel one-dimensional channels disturbed by noise sources with variances σ 2,,σ 2 N. N 0,σ 2 x x N N 0,σ 2 N y y N Energy Constraint:
More informationMulti-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
More informationSamah A. M. Ghanem, Member, IEEE, Abstract
Multiple Access Gaussian Channels with Arbitrary Inputs: Optimal Precoding and Power Allocation Samah A. M. Ghanem, Member, IEEE, arxiv:4.0446v2 cs.it] 6 Nov 204 Abstract In this paper, we derive new closed-form
More informationInformation Theory for Wireless Communications, Part II:
Information Theory for Wireless Communications, Part II: Lecture 5: Multiuser Gaussian MIMO Multiple-Access Channel Instructor: Dr Saif K Mohammed Scribe: Johannes Lindblom In this lecture, we give the
More informationThe Capacity Region of the Gaussian Cognitive Radio Channels at High SNR
The Capacity Region of the Gaussian Cognitive Radio Channels at High SNR 1 Stefano Rini, Daniela Tuninetti and Natasha Devroye srini2, danielat, devroye @ece.uic.edu University of Illinois at Chicago Abstract
More informationMIMO Wiretap Channel with ISI Heterogeneity Achieving Secure DoF with no CSI
MIMO Wiretap Channel with ISI Heterogeneity Achieving Secure DoF with no CSI Jean de Dieu Mutangana Deepak Kumar Ravi Tandon Department of Electrical and Computer Engineering University of Arizona, Tucson,
More information12.4 Known Channel (Water-Filling Solution)
ECEn 665: Antennas and Propagation for Wireless Communications 54 2.4 Known Channel (Water-Filling Solution) The channel scenarios we have looed at above represent special cases for which the capacity
More informationCHANNEL FEEDBACK QUANTIZATION METHODS FOR MISO AND MIMO SYSTEMS
CHANNEL FEEDBACK QUANTIZATION METHODS FOR MISO AND MIMO SYSTEMS June Chul Roh and Bhaskar D Rao Department of Electrical and Computer Engineering University of California, San Diego La Jolla, CA 9293 47,
More informationLattice 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
More informationLecture 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
More informationLecture 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
More informationProbability Bounds for Two-Dimensional Algebraic Lattice Codes
Probability Bounds for Two-Dimensional Algebraic Lattice Codes David Karpuk Aalto University April 16, 2013 (Joint work with C. Hollanti and E. Viterbo) David Karpuk (Aalto University) Probability Bounds
More informationApproximately achieving the feedback interference channel capacity with point-to-point codes
Approximately achieving the feedback interference channel capacity with point-to-point codes Joyson Sebastian*, Can Karakus*, Suhas Diggavi* Abstract Superposition codes with rate-splitting have been used
More informationFinite-State Markov Chain Approximation for Geometric Mean of MIMO Eigenmodes
Finite-State Markov Chain Approximation for Geometric Mean of MIMO Eigenmodes Ping-Heng Kuo Information and Communication Laboratory Industrial Technology Research Institute (ITRI) Hsinchu, Taiwan pinghengkuo@itri.org.tw
More informationMulti-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
More informationSpace-Time Coding for Multi-Antenna Systems
Space-Time Coding for Multi-Antenna Systems ECE 559VV Class Project Sreekanth Annapureddy vannapu2@uiuc.edu Dec 3rd 2007 MIMO: Diversity vs Multiplexing Multiplexing Diversity Pictures taken from lectures
More informationEE 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 IV: MIMO Systems March 21,
More informationOn the diversity of the Naive Lattice Decoder
On the diversity of the Naive Lattice Decoder Asma Mejri, Laura Luzzi, Ghaya Rekaya-Ben Othman To cite this version: Asma Mejri, Laura Luzzi, Ghaya Rekaya-Ben Othman. On the diversity of the Naive Lattice
More informationOn the Impact of Quantized Channel Feedback in Guaranteeing Secrecy with Artificial Noise
On the Impact of Quantized Channel Feedback in Guaranteeing Secrecy with Artificial Noise Ya-Lan Liang, Yung-Shun Wang, Tsung-Hui Chang, Y.-W. Peter Hong, and Chong-Yung Chi Institute of Communications
More informationLecture 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
More informationMultiple Antennas in Wireless Communications
Multiple Antennas in Wireless Communications Luca Sanguinetti Department of Information Engineering Pisa University luca.sanguinetti@iet.unipi.it April, 2009 Luca Sanguinetti (IET) MIMO April, 2009 1 /
More informationSecret Key Agreement Using Asymmetry in Channel State Knowledge
Secret Key Agreement Using Asymmetry in Channel State Knowledge Ashish Khisti Deutsche Telekom Inc. R&D Lab USA Los Altos, CA, 94040 Email: ashish.khisti@telekom.com Suhas Diggavi LICOS, EFL Lausanne,
More informationStructured Codes in Information Theory: MIMO and Network Applications. Jiening Zhan
Structured Codes in Information Theory: MIMO and Network Applications by Jiening Zhan A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering-Electrical
More informationThe Effect of Ordered Detection and Antenna Selection on Diversity Gain of Decision Feedback Detector
The Effect of Ordered Detection and Antenna Selection on Diversity Gain of Decision Feedback Detector Yi Jiang Mahesh K. Varanasi Dept. Electrical & Computer Engineering, University of Colorado Boulder,
More informationJoint Channel Estimation and Co-Channel Interference Mitigation in Wireless Networks Using Belief Propagation
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.
More informationMorning Session Capacity-based Power Control. Department of Electrical and Computer Engineering University of Maryland
Morning Session Capacity-based Power Control Şennur Ulukuş Department of Electrical and Computer Engineering University of Maryland So Far, We Learned... Power control with SIR-based QoS guarantees Suitable
More informationCooperative Interference Alignment for the Multiple Access Channel
1 Cooperative Interference Alignment for the Multiple Access Channel Theodoros Tsiligkaridis, Member, IEEE Abstract Interference alignment (IA) has emerged as a promising technique for the interference
More informationIEEE C80216m-09/0079r1
Project IEEE 802.16 Broadband Wireless Access Working Group Title Efficient Demodulators for the DSTTD Scheme Date 2009-01-05 Submitted M. A. Khojastepour Ron Porat Source(s) NEC
More informationSecure Multiuser MISO Communication Systems with Quantized Feedback
Secure Multiuser MISO Communication Systems with Quantized Feedback Berna Özbek*, Özgecan Özdoğan*, Güneş Karabulut Kurt** *Department of Electrical and Electronics Engineering Izmir Institute of Technology,Turkey
More informationExplicit Capacity-Achieving Coding Scheme for the Gaussian Wiretap Channel. Himanshu Tyagi and Alexander Vardy
Explicit Capacity-Achieving Coding Scheme for the Gaussian Wiretap Channel Himanshu Tyagi and Alexander Vardy The Gaussian wiretap channel M Encoder X n N(0,σ 2 TI) Y n Decoder ˆM N(0,σ 2 WI) Z n Eavesdropper
More informationOn the Rate Duality of MIMO Interference Channel and its Application to Sum Rate Maximization
On the Rate Duality of MIMO Interference Channel and its Application to Sum Rate Maximization An Liu 1, Youjian Liu 2, Haige Xiang 1 and Wu Luo 1 1 State Key Laboratory of Advanced Optical Communication
More informationV-BLAST in Lattice Reduction and Integer Forcing
V-BLAST in Lattice Reduction and Integer Forcing Sebastian Stern and Robert F.H. Fischer Institute of Communications Engineering, Ulm University, Ulm, Germany Email: {sebastian.stern,robert.fischer}@uni-ulm.de
More informationPOWER ALLOCATION AND OPTIMAL TX/RX STRUCTURES FOR MIMO SYSTEMS
POWER ALLOCATION AND OPTIMAL TX/RX STRUCTURES FOR MIMO SYSTEMS R. Cendrillon, O. Rousseaux and M. Moonen SCD/ESAT, Katholiee Universiteit Leuven, Belgium {raphael.cendrillon, olivier.rousseaux, marc.moonen}@esat.uleuven.ac.be
More informationBlind MIMO communication based on Subspace Estimation
Blind MIMO communication based on Subspace Estimation T. Dahl, S. Silva, N. Christophersen, D. Gesbert T. Dahl, S. Silva, and N. Christophersen are at the Department of Informatics, University of Oslo,
More informationMIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper
MIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper Xiang He, Ashish Khisti, Aylin Yener Dept. of Electrical and Computer Engineering, University of Toronto, Toronto, ON, M5S 3G4, Canada
More informationTransmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters 1
2005 Conference on Information Sciences and Systems, The Johns Hopkins University, March 6 8, 2005 Transmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters Alkan
More information3F1: Signals and Systems INFORMATION THEORY Examples Paper Solutions
Engineering Tripos Part IIA THIRD YEAR 3F: Signals and Systems INFORMATION THEORY Examples Paper Solutions. Let the joint probability mass function of two binary random variables X and Y be given in the
More informationEstimation of Performance Loss Due to Delay in Channel Feedback in MIMO Systems
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com Estimation of Performance Loss Due to Delay in Channel Feedback in MIMO Systems Jianxuan Du Ye Li Daqing Gu Andreas F. Molisch Jinyun Zhang
More informationLimited Feedback in Wireless Communication Systems
Limited Feedback in Wireless Communication Systems - Summary of An Overview of Limited Feedback in Wireless Communication Systems Gwanmo Ku May 14, 17, and 21, 2013 Outline Transmitter Ant. 1 Channel N
More informationEfficient Inverse Cholesky Factorization for Alamouti Matrices in G-STBC and Alamouti-like Matrices in OMP
Efficient Inverse Cholesky Factorization for Alamouti Matrices in G-STBC and Alamouti-like Matrices in OMP Hufei Zhu, Ganghua Yang Communications Technology Laboratory Huawei Technologies Co Ltd, P R China
More informationOn the Capacity and Degrees of Freedom Regions of MIMO Interference Channels with Limited Receiver Cooperation
On the Capacity and Degrees of Freedom Regions of MIMO Interference Channels with Limited Receiver Cooperation Mehdi Ashraphijuo, Vaneet Aggarwal and Xiaodong Wang 1 arxiv:1308.3310v1 [cs.it] 15 Aug 2013
More information6726 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 16, NO. 10, OCTOBER 2017
676 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 0, OCTOBER 07 Optimal Beamforming for Gaussian MIMO Wiretap Channels With Two Transmit Antennas Mojtaba Vaezi, Member, IEEE, Wonjae Shin, Student
More informationROBUST SECRET KEY CAPACITY FOR THE MIMO INDUCED SOURCE MODEL. Javier Vía
ROBUST SECRET KEY CAPACITY FOR THE MIMO INDUCED SOURCE MODEL Javier Vía University of Cantabria, Spain e-mail: jvia@gtas.dicom.unican.es web: gtas.unican.es ABSTRACT This paper considers the problem of
More informationIEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY Uplink Downlink Duality Via Minimax Duality. Wei Yu, Member, IEEE (1) (2)
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY 2006 361 Uplink Downlink Duality Via Minimax Duality Wei Yu, Member, IEEE Abstract The sum capacity of a Gaussian vector broadcast channel
More informationCapacity Pre-log of Noncoherent SIMO Channels via Hironaka s Theorem
Capacity Pre-log of Noncoherent SIMO Channels via Hironaka s Theorem Veniamin I. Morgenshtern 22. May 2012 Joint work with E. Riegler, W. Yang, G. Durisi, S. Lin, B. Sturmfels, and H. Bőlcskei SISO Fading
More informationAdvanced Topics in Digital Communications Spezielle Methoden der digitalen Datenübertragung
Advanced Topics in Digital Communications Spezielle Methoden der digitalen Datenübertragung Dr.-Ing. Carsten Bockelmann Institute for Telecommunications and High-Frequency Techniques Department of Communications
More informationGeneralized Triangular Transform Coding
Generalized Triangular Transform Coding Ching-Chih Weng, Chun-Yang Chen, and P. P. Vaidyanathan Dept. of Electrical Engineering, MC 136-93 California Institute of Technology, Pasadena, CA 91125, USA E-mail:
More informationDegrees-of-Freedom Robust Transmission for the K-user Distributed Broadcast Channel
/33 Degrees-of-Freedom Robust Transmission for the K-user Distributed Broadcast Channel Presented by Paul de Kerret Joint work with Antonio Bazco, Nicolas Gresset, and David Gesbert ESIT 2017 in Madrid,
More informationCoding 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
More informationELEC546 MIMO Channel Capacity
ELEC546 MIMO Channel Capacity Vincent Lau Simplified Version.0 //2004 MIMO System Model Transmitter with t antennas & receiver with r antennas. X Transmitted Symbol, received symbol Channel Matrix (Flat
More informationSecure Transmission with Multiple Antennas: The MIMOME Channel
1 Secure Transmission with Multiple Antennas: The MIMOME Channel Ashish Khisti and Gregory Wornell. Abstract The Gaussian wiretap channel model is studied when there are multiple antennas at the sender,
More informationReduced Complexity Sphere Decoding for Square QAM via a New Lattice Representation
Reduced Complexity Sphere Decoding for Square QAM via a New Lattice Representation Luay Azzam and Ender Ayanoglu Department of Electrical Engineering and Computer Science University of California, Irvine
More informationMathematical methods in communication June 16th, Lecture 12
2- Mathematical methods in communication June 6th, 20 Lecture 2 Lecturer: Haim Permuter Scribe: Eynan Maydan and Asaf Aharon I. MIMO - MULTIPLE INPUT MULTIPLE OUTPUT MIMO is the use of multiple antennas
More informationMultiuser 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
More informationCapacity and Power Allocation for Fading MIMO Channels with Channel Estimation Error
Capacity and Power Allocation for Fading MIMO Channels with Channel Estimation Error Taesang Yoo, Student Member, IEEE, and Andrea Goldsmith, Fellow, IEEE Abstract We investigate the effect of channel
More informationMMSE Equalizer Design
MMSE Equalizer Design Phil Schniter March 6, 2008 [k] a[m] P a [k] g[k] m[k] h[k] + ṽ[k] q[k] y [k] P y[m] For a trivial channel (i.e., h[k] = δ[k]), e kno that the use of square-root raisedcosine (SRRC)
More informationCapacity Analysis of MIMO Systems with Unknown Channel State Information
Capacity Analysis of MIMO Systems with Unknown Channel State Information Jun Zheng an Bhaskar D. Rao Dept. of Electrical an Computer Engineering University of California at San Diego e-mail: juzheng@ucs.eu,
More informationInterference Alignment at Finite SNR for TI channels
Interference Alignment at Finite SNR for Time-Invariant channels Or Ordentlich Joint work with Uri Erez EE-Systems, Tel Aviv University ITW 20, Paraty Background and previous work The 2-user Gaussian interference
More informationMinimum BER Linear Transceivers for Block. Communication Systems. Lecturer: Tom Luo
Minimum BER Linear Transceivers for Block Communication Systems Lecturer: Tom Luo Outline Block-by-block communication Abstract model Applications Current design techniques Minimum BER precoders for zero-forcing
More informationThe geometric mean decomposition
Linear Algebra and its Applications 396 (25) 373 384 www.elsevier.com/locate/laa The geometric mean decomposition Yi Jiang a, William W. Hager b,, Jian Li c a Department of Electrical and Computer Engineering,
More informationELG7177: MIMO Comunications. Lecture 8
ELG7177: MIMO Comunications Lecture 8 Dr. Sergey Loyka EECS, University of Ottawa S. Loyka Lecture 8, ELG7177: MIMO Comunications 1 / 32 Multi-User Systems Can multiple antennas offer advantages for multi-user
More informationOn the Secrecy Capacity of the Z-Interference Channel
On the Secrecy Capacity of the Z-Interference Channel Ronit Bustin Tel Aviv University Email: ronitbustin@post.tau.ac.il Mojtaba Vaezi Princeton University Email: mvaezi@princeton.edu Rafael F. Schaefer
More informationGeneralized Writing on Dirty Paper
Generalized Writing on Dirty Paper Aaron S. Cohen acohen@mit.edu MIT, 36-689 77 Massachusetts Ave. Cambridge, MA 02139-4307 Amos Lapidoth lapidoth@isi.ee.ethz.ch ETF E107 ETH-Zentrum CH-8092 Zürich, Switzerland
More informationLarge System Analysis of Projection Based Algorithms for the MIMO Broadcast Channel
Large System Analysis of Projection Based Algorithms for the MIMO Broadcast Channel Christian Guthy and Wolfgang Utschick Associate Institute for Signal Processing, Technische Universität München Joint
More informationA 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
More informationOn the Secrecy Capacity of Fading Channels
On the Secrecy Capacity of Fading Channels arxiv:cs/63v [cs.it] 7 Oct 26 Praveen Kumar Gopala, Lifeng Lai and Hesham El Gamal Department of Electrical and Computer Engineering The Ohio State University
More informationOn the Optimality of Treating Interference as Noise in Competitive Scenarios
On the Optimality of Treating Interference as Noise in Competitive Scenarios A. DYTSO, D. TUNINETTI, N. DEVROYE WORK PARTIALLY FUNDED BY NSF UNDER AWARD 1017436 OUTLINE CHANNEL MODEL AND PAST WORK ADVANTAGES
More informationDuality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels
2658 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 49, NO 10, OCTOBER 2003 Duality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels Sriram Vishwanath, Student Member, IEEE, Nihar
More information