# MIT 6 454 - Cooperative Diversity for Wireless Networks (34 pages)

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## Cooperative Diversity for Wireless Networks

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- Pages:
- 34
- School:
- Massachusetts Institute of Technology
- Course:
- 6 454 - Graduate Seminar in Area I

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Cooperative Diversity for Wireless Networks Vijay Divi Signals Information and Algorithms Laboratory November 17th 2004 Introduction Fading is a major limitation in wireless systems Different forms of diversity used to overcome fading Spatial Diversity Temporal Diversity Frequency Diversity Focus on specific form of spatial diversity named cooperative diversity Other terminals in network act as relays between source and dest Relays experience independent fading and act as a virtual antenna array V Divi Nov 17th 2004 Background Scalar Fading Channel Slow Fast Fading Transmitter CSI MIMO Communication System Diversity Gain Multiplexing Gain Connection to Cooperative Diversity V Divi Nov 17th 2004 Scalar Fading Channel Input signal experiences Rayleigh fading h and additive Gaussian noise w y hx w where x CN 0 2x w CN 0 2w SNR SNR 2x 2w Two major questions How often does the realization of h change Does the transmitter have knowledge of h V Divi Nov 17th 2004 Transmission Cases Fading Slow Fading Channel does not change within time period of interest Fast Fading Channel changes on the order of symbols codewords Channel State Information CSI Tx CSI Transmitter has knowledge of h No Tx CSI Transmitter does not know h only its distribution Tx CSI Slow Fading Fast Fading Deterministic Capacity Time Water filling C log 1 h 2 No Tx CSI Outage Capacity R pout V Divi Nov 17th 2004 Ergodic Capacity C E log 1 h 2 Slow Fading No Tx CSI Most difficult case Any non zero rate chosen by the transmitter may be above the supported rate of the channel Channel is not changing with time non ergodic the transmission may always fail with some non zero probability Shannon capacity is zero i e system cannot guarantee that any amount of information can be transmitted reliably Outage capacity given R and SNR there is a non zero probability that the channel does not support this rate this probability is known as the outage probability pout Can use relays to improve transmission act like a virtual MIMO system V Divi Nov 17th 2004 Multiple Antenna Systems The discrete time MIMO channel model for system with m transmit and n receive antennas is y Hx w H is an n m matrix of channel gains whose entries are i i d CN 0 1 H drawn from such a distribution causes Outages in the system Increases degrees of freedom for communications V Divi Nov 17th 2004 Diversity Gain High SNR regime the diversity gain d measures the rate at which the error probability decays with SNR 1 d log Pe log d lim For a system with m transmit and n receive antennas in the best case the error can be made to decay with SNR as 1 mn Diversity is a result of the mn independent paths between the transmit and receive antennas V Divi Nov 17th 2004 Multiplexing Gain Because the path gains are independent the channel matrix is well conditioned with high probability Can view the MIMO system as min m n independent spatial channels between the transmitter and receiver Fast fading ergodic capacity C min m n log O 1 For slow fading spatial multiplexing gain r measures the rate at which R increases with respect log and is formally defined as R log r lim R r log Multiplexing gain can be thought of as the number of independent spatial channels being used optimally which is upper bounded by min m n V Divi Nov 17th 2004 Diversity Multiplexing Tradeoff Natural to talk about a tradeoff between the r and d V Divi Nov 17th 2004 Connection to Cooperative Diversity Scalar fading channel provides a lower bound for the performance of any valid cooperative diversity scheme Can always ignore use of the relay non cooperative protocol and achieve scalar channel performance 2 1 MIMO system provides an upper bound In MIMO system the transmitter has full control over both antennas and can code across both of them allowing more flexibility Often referred to as genie aided protocol V Divi Nov 17th 2004 System Model R S D xs n and xr n are the transmitted signals from the source and relay yr n and yd n are the received signals of the relay and destination Direct source to destination transmission modeled as yd n as d xs n zd n Fading ai j CN 0 2i j and independent Noise z j n CN 0 N0 mutually independent V Divi Nov 17th 2004 Model Assumptions Half duplex antennas cannot transmit and receive simultaneously Channels experience independent flat Rayleigh fading and white complex Gaussian noise Slow fading environment Transmitters have no CSI Receivers have full CSI Each terminal has one antenna with power constraint P V Divi Nov 17th 2004 Case Analysis 1 Single Relay Systems Amplify and Forward Decode and Forward 2 Multiple Terminal System AF Revisited DF Revisited Cooperative Broadcast Channel Cooperative Multiple Access Channel V Divi Nov 17th 2004 Single Relay Systems Three terminals source relay destination Relay can either amplify or decode re encode and transmit Work by Laneman Wornell Tse Additional constraint that only one terminal is transmitting at a time Work by Azarian El Gamal Schniter Allow multiple terminals to transmit simultaneously Protocols optimal in certain regimes V Divi Nov 17th 2004 Basic Amplify and Forward Relay can only transmit amplified version of received signal R S R D D R n N 2 1 N S Relay power constraint n 1 N 2 as r xs n zr n as d xs n zd n R D D r ar d yr n N 2 zd n P as r 2 P No V Divi Nov 17th 2004 Basic AF Performance Mutual information between the input and 2 outputs as 1 IAF log 1 as d 2 f as r 2 ar d 2 2 where f x y xy x y 1 For an outage event small fading coefficients f x y can be approximated as min x y V Divi Nov 17th 2004 Basic AF Performance cont Thus our outage event becomes I R 1 log as d 2 R 2 log log as d 2 2r log log as d 2 2r 1 log as d 2 2r 1 Since and as d 2 are both exponential the probability of outage becomes 2r 1 2 Diversity multiplexing tradeoff of d r 2 1 2r V Divi Nov 17th 2004 Non Orthogonal Amplify and Forward AF general form y as d A1 0 as r ar d B as d A2 x 0 ar d B zr zd N N N N N N N N N N where y x zr zd C A1 C B C A2 C Initial protocol N N 2 A1 B IN 2 and A2 0 NAF protocol N N 2 and A1 A2 B IN 2 A1 A2 IN 2 maximizes mutual information between x and y B diagonal to prevent ISI size N 2 for max symbol repetition V Divi Nov 17th 2004 NAF cont R S D n N 2 1 N R S R D n 1 N 2 as r xs n zr n as d xs n …

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