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Ashish Kumar Meshram Roll No. mt1402102002 M.Tech. Communication & Signal Processing Discipline of Electrical Engineering IIT – Indore | EE642 | Wireless Communication COOPERATIVE DIVERSITY An Introduction to Cooperative Communication

Cooperative Diversity - An Introduction to Cooperative Comm

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Page 1: Cooperative Diversity - An Introduction to Cooperative Comm

Ashish Kumar MeshramRoll No. mt1402102002M.Tech. Communication & Signal ProcessingDiscipline of Electrical Engineering

IIT – Indore | EE642 | Wireless Communication

COOPERATIVEDIVERSITY

An Introduction to Cooperative Communication

Page 2: Cooperative Diversity - An Introduction to Cooperative Comm

01IIT – Indore | EE642 | Wireless Communication

Contents

Motivation

Introduction

Application Scenario

Relay Channel

Cooperation Protocols

Pros and Cons of cooperation

System Tradeoffs

References

Page 3: Cooperative Diversity - An Introduction to Cooperative Comm

Multiple transmit antennas provide spatial diversity

Unfortunately, this is not easy to implement in the uplink of a cellular system, due to the size of the mobile unit

How to overcome this limitation?

In order to overcome this limitation, yet still emulate transmit antenna diversity, an alternative form of spatial diversity is being considered, where diversity gains are achieved via the cooperation of in-cell users.

02IIT – Indore | EE642 | Wireless Communication

Motivation

Tx Rx

Introduction

Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity–Part I: System description” and “User cooperation diversity–Part II: implementation aspects and performance analysis. IEEE Transactions on

Communications 51(11) 1927–1938 and 1939–1948 (2003)

Page 4: Cooperative Diversity - An Introduction to Cooperative Comm

Andrew Sendonaris, User Cooperation Diversity—Part I - System Description03IIT – Indore | EE642 | Wireless Communication

Motivation

– In each cell, each user may have a ‘partner.’

– Each of the two partners would be responsible for transmitting not only their own information, but also the information of their partner, which they receive and detect.

– Spatial diversity would be achieved through the use of the partner’s antenna.

𝑌0 𝑡 = ℎ10𝑋1 𝑡 + ℎ20𝑋2 𝑡 + 𝑛0(𝑡)

𝑌1 𝑡 = ℎ21𝑋2 𝑡 + 𝑛1(𝑡)

𝑌2 𝑡 = ℎ12𝑋1 𝑡 + 𝑛2(𝑡)

The mathematical formulation of the model is:

System Modeling and Channel Model

Page 5: Cooperative Diversity - An Introduction to Cooperative Comm

Andrew Sendonaris, User Cooperation Diversity—Part I - System Description04IIT – Indore | EE642 | Wireless Communication

Motivation Probability of outage

Page 6: Cooperative Diversity - An Introduction to Cooperative Comm

𝑇𝑥1

𝑇𝑥2

𝑅𝑥𝑐ℎ𝑎𝑛𝑛𝑒𝑙

05IIT – Indore | EE642 | Wireless Communication

Cooperative DiversityIntroduction

Cooperative diversity is a cooperative multiple antenna technique for improving or maximizing total network channel capacities for any given set of bandwidths which exploits user diversity by decoding the combined signal of

the relayed signal and the direct signal in wireless multihop networks.[

[

Page 7: Cooperative Diversity - An Introduction to Cooperative Comm

– A conventional single hop system uses direct transmission where a receiver decodes the information only based on

the direct signal while regarding the relayed signal as interference, whereas the cooperative diversity considers the

other signal as contribution;

– Cooperative diversity makes use of available mobile terminals as relays that cooperate together to form a virtual

antenna array

– The relay channel can be thought of as an auxiliary channel to the direct channel between the source and

destination;

– A key aspect of the cooperative communication process is the processing of the signal received from the source node

done by the relay;

– These different processing schemes result in different cooperative communications protocol

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski 06IIT – Indore | EE642 | Wireless Communication

Cooperative DiversityIntroduction

Page 8: Cooperative Diversity - An Introduction to Cooperative Comm

– Cellular Capacity and Coverage Extension

– WLAN Capacity and Coverage Extension

– Vehicle-to-Vehicle Communication

– Wireless Sensor Networks

Cooperative Communications Hardware Channel and PHY, Mischa Dohler Yonghui Li

a b

c d

07IIT – Indore | EE642 | Wireless Communication

Application Scenario

Page 9: Cooperative Diversity - An Introduction to Cooperative Comm

Source Destination

Relay

𝑝(𝑦1, 𝑦2|𝑥, 𝑥12)𝑋

𝑋12 𝑌1𝑌2

08IIT – Indore | EE642 | Wireless Communication

IntroductionRelay Channel

– In information theory, a relay channel is a probability model of the communication between a sender and a receiver aided by one or more intermediate relay nodes;

– The RC is a three-terminal channel composed of a source node, a destination node, and one node called the relay, which is neither a source nor a sink;

– The role of the relaying node is to improve the overall performance of the communication between the source and destination.

Mathematically speaking, the RC consists of four finite sets:𝑋, 𝑋12, 𝑌1,and 𝑌1

and a collection of probability distributions:𝑝(𝑦1, 𝑦2|𝑥, 𝑥12)

Page 10: Cooperative Diversity - An Introduction to Cooperative Comm

ℎ𝑠,𝑑

ℎ𝑠,𝑟 ℎ𝑟,𝑑

𝑆𝑜𝑢𝑟𝑐𝑒 𝐷𝑒𝑠𝑡𝑖𝑛𝑎𝑡𝑖𝑜𝑛

𝑅𝑒𝑙𝑎𝑦

𝑃1

𝑃2

Phase 1Phase 2

09IIT – Indore | EE642 | Wireless Communication

Simplified Cooperation Model - Single Relay System ModelRelay Channel

Phase 1: From SourceTransmitted signal received by relay;

𝑦𝑠,𝑟 = 𝑃ℎ𝑠,𝑟𝑥 + 𝑛𝑠,𝑟Transmitted signal received by destination;

𝑦𝑠,𝑑 = 𝑃ℎ𝑠,𝑑𝑥 + 𝑛𝑠,𝑑Phase 2: From RelayTransmitted signal received by destination;

𝑦𝑟,𝑑 = ℎ𝑟,𝑑𝑞(𝑦𝑠,𝑟) + 𝑛𝑟,𝑑

…(1)

… (2)

… (3)

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

Page 11: Cooperative Diversity - An Introduction to Cooperative Comm

10IIT – Indore | EE642 | Wireless Communication

Simplified Cooperation Model - Single Relay System ModelRelay Channel

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

ℎ𝑠,𝑑; channel coefficients from source to destination

𝑥; transmitted information symbol

𝑃 ; transmitted power

𝑛𝑠,𝑑; additive noise for source to destination

𝑞(∙); function depending on processing implemented at relay

𝛿𝑠,𝑑2 ; variance of source to destination

𝛿𝑠,𝑟2 ; variance of source to relay

𝑛𝑠,𝑟; additive noise for source to relay

ℎ𝑠,𝑟; channel coefficients from source to relay

ℎ𝑟,𝑑; channel coefficients from relay to destination

𝑛𝑟,𝑑; additive noise for relay to destination

𝛿𝑟,𝑑2 ; variance of relay to destination

Page 12: Cooperative Diversity - An Introduction to Cooperative Comm

11IIT – Indore | EE642 | Wireless Communication

Relay Channel

– Fixed Cooperation Strategies

– Adaptive Cooperation Strategies

In fixed relaying, the channel resources are divided between the source and the relay in a fixed (deterministic) manner. The processing at the relay differs according to the employed protocols.

– AF (Amplify-and-Forward) Protocol– DF (Decode-and-Forward) Protocol– CF (Compress-and-forward) Protocol

– Selective DF– Incremental

Fixed relaying suffers from deterministic loss in the transmission rate. Moreover, fixed DF relaying suffers from the fact that the performance is limited by the weakest source–relay and relay–destination channels which reduces the diversity gains to one. To overcome this problem, adaptive relaying protocols can be developed to improve the inefficiency.

Cooperation Protocols

Page 13: Cooperative Diversity - An Introduction to Cooperative Comm

𝛽𝑟 =𝑃

𝑃 ℎ𝑠,𝑟2+ 𝑁0

𝑆𝑁𝑅𝑠,𝑑 = Γ ℎ𝑠,𝑑2

The relay does that by simply scaling the received signal by a factor that is inversely proportional to the received power, which is denoted by

…(6)

The SNR from the source link is given by

where Γ = 𝑃 𝑁0

…(7)

12IIT – Indore | EE642 | Wireless Communication

Amplify-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

Transmitted signal received by relay;

𝑦𝑠,𝑟 = 𝑃ℎ𝑠,𝑟𝑥 + 𝑛𝑠,𝑟Transmitted signal received by destination;

𝑦𝑠,𝑑 = 𝑃ℎ𝑠,𝑑𝑥 + 𝑛𝑠,𝑑

…(4)

… (5)

In a fixed AF relaying protocol, which is often simply called an AF protocol, the relay scales the received version and transmits an amplified version of it to the destination.[

[

In Phase 1:

Page 14: Cooperative Diversity - An Introduction to Cooperative Comm

𝑦𝑟,𝑑 =𝑃

𝑃 ℎ𝑠,𝑟2+ 𝑁0

ℎ𝑟,𝑑𝑦𝑠,𝑟 + 𝑛𝑟,𝑑

𝑦𝑟,𝑑 =𝑃

𝑃 ℎ𝑠,𝑟2+ 𝑁0

𝑃ℎ𝑟,𝑑ℎ𝑠,𝑟𝑥 + 𝑛𝑟,𝑑′

𝑁0′ =

𝑃 ℎ𝑟,𝑑2

𝑃 ℎ𝑠,𝑟2+ 𝑁0

+ 1 𝑁0

The received signal at the destination in phase 2 according to eq. (6) is given by

…(8)

… (9)

where 𝑛𝑟,𝑑′ =

𝑃

𝑃 ℎ𝑠,𝑟2+𝑁0

ℎ𝑟,𝑑𝑛𝑠,𝑟 + 𝑛𝑟,𝑑

13IIT – Indore | EE642 | Wireless Communication

Amplify-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

In Phase 2:

From eq. (4);

Assuming that the noise terms 𝑛𝑟,𝑑and 𝑛𝑠,𝑟 are independent

…(10)

Page 15: Cooperative Diversity - An Introduction to Cooperative Comm

𝑦 = 𝑎1𝑦𝑠,𝑑 + 𝑎2𝑦𝑟,𝑑

𝑎1 =𝑃ℎ𝑠,𝑑

𝑁0

𝑎2 =

𝑃

𝑃 ℎ𝑠,𝑟2+ 𝑁0

𝑃ℎ𝑠,𝑟∗ ℎ𝑟,𝑑

𝑃 ℎ𝑟,𝑑2

𝑃 ℎ𝑠,𝑟2+ 𝑁0

+ 1 𝑁0

𝛾 = 𝛾1 + 𝛾2

14IIT – Indore | EE642 | Wireless Communication

Amplify-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

The destination receives two copies from the signal x through the source link and relay link. With knowledge of the

channel coefficients the output of the MRC detector at the destination can be written as

The combining factors 𝑎1 and 𝑎2 should be designed to maximize the combined SNR. Therefore, 𝑎1 and 𝑎2 are given by

…(11)

… (12)

By assuming that the transmitted symbol x in eq. (3) has average energy 1, the instantaneous SNR of the MRC output is

…(13)

Page 16: Cooperative Diversity - An Introduction to Cooperative Comm

𝛾2 =

𝑎1𝑃

𝑃 ℎ𝑠,𝑟2+ 𝑁0

𝑃ℎ𝑟,𝑑ℎ𝑠,𝑟

2

𝑁0′ 𝑎2

2 =

𝑃2

𝑃 ℎ𝑠,𝑟2+ 𝑁0

ℎ𝑠,𝑟2ℎ𝑟,𝑑

2

𝑃 ℎ𝑟,𝑑2

𝑃 ℎ𝑠,𝑟2+𝑁0

+ 1 𝑁0

=1

𝑁0

𝑃2 ℎ𝑠,𝑟2ℎ𝑟,𝑑

2

𝑃 ℎ𝑠,𝑟2+ 𝑃 ℎ𝑟,𝑑

2+ 𝑁0

From the above, the instantaneous mutual information as a function of the fading coefficients for amplify-and-forward is given by

𝐼𝐴𝐹 =1

2log 1 + 𝛾1 + 𝛾2 =

1

2log(1 + Γ ℎ𝑠,𝑑

2+ 𝑓(Γ ℎ𝑠,𝑟

2, Γ ℎ𝑟,𝑑

2))

where 𝑓 𝑥, 𝑦 ≜𝑥𝑦

𝑥+𝑦+1

𝛾1 =𝑎1 𝑃ℎ𝑠,𝑑

2

𝑎12𝑁0

=𝑃 ℎ𝑠,𝑑

2

𝑁0

15IIT – Indore | EE642 | Wireless Communication

Amplify-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

where

…(14)

…(15)

…(16)

…(17)

Page 17: Cooperative Diversity - An Introduction to Cooperative Comm

The outage probability can be obtained by averaging over the exponential channel gain distribution, as follows:

Pr 𝐼𝐴𝐹 < 𝑅 = Εℎ𝑠,𝑑,ℎ𝑠,𝑟,ℎ𝑟,𝑑1

2log(1 + Γ ℎ𝑠,𝑑

2+ 𝑓(Γ ℎ𝑠,𝑟

2, Γ ℎ𝑟,𝑑

2)) < 𝑅

Calculating the above integration, the outage probability at high SNR is given by

Pr 𝐼𝐴𝐹 < 𝑅 ≃𝜎𝑠,𝑟2 +𝜎𝑟,𝑑

2

2𝜎𝑠,𝑟2 (𝜎𝑠,𝑟

2 𝜎𝑠,𝑟2 )

22𝑅 − 1

Γ

2

where the multiplicative factor of 2 in 2R is because half of the bandwidth is lost in cooperation by allocating them to the relay. The outage expression decays as −2, which means that the AF protocol achieves diversity 2.

16IIT – Indore | EE642 | Wireless Communication

Amplify-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

…(18)

… (19)

Page 18: Cooperative Diversity - An Introduction to Cooperative Comm

17IIT – Indore | EE642 | Wireless Communication

Decode-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

In a fixed DF relaying protocol, the relay decodes the received signal, re-encode it and then transmit to the destination.[

[

𝐼𝐷𝐹 =1

2min log 1 + Γ ℎ𝑠,𝑟

2, log(1 + Γ ℎ𝑠,𝑑

2+ Γ ℎ𝑟,𝑑

2)

where the min operator in the above equation takes into account the fact that the relay only transmits if decoded correctly, and hence the performance is limited by the weakest link between the source–destination and source–relay.

The outage probability for the fixed DF relaying scheme is given by Pr 𝐼𝐷𝐹 < 𝑅 ; Since log is a monotonic function, the outage event is equivalent to

min ℎ𝑠,𝑟2, ℎ𝑠,𝑑

2+ ℎ𝑟,𝑑

2<22𝑅 − 1

Γ

… (20)

… (21)

The mutual information for decode-and-forward transmission in terms of the channel fades can be given by

Page 19: Cooperative Diversity - An Introduction to Cooperative Comm

18IIT – Indore | EE642 | Wireless Communication

Decode-and-ForwardCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

The outage probability can be written as

Pr 𝐼𝐷𝐹 < 𝑅 = Pr ℎ𝑠,𝑟2<22𝑅 − 1

Γ+ Pr ℎ𝑠,𝑟

2>22𝑅 − 1

ΓPr ℎ𝑠,𝑑

2+ ℎ𝑟,𝑑

2<22𝑅 − 1

Γ

Since the channel is Rayleigh fading, the above random variables are all exponential random variables with parameter one. Averaging over the channel conditions, the outage probability for decode-and-forward at high SNR is given by

Pr 𝐼𝐷𝐹 < 𝑅 ≃1

𝜎𝑠,𝑟2

22𝑅 − 1

Γ

… (22)

… (23)

Page 20: Cooperative Diversity - An Introduction to Cooperative Comm

19IIT – Indore | EE642 | Wireless Communication

Compress-and-forward cooperationCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

The main difference between compress-and-forward and decode/amplify-and-forward is that while in the later the relay transmits a copy of the received message, in compress-and-forward the relay transmits a quantized and compressed version of the received message. Therefore, the destination node will perform the reception functions by combining the received message from the source node and its quantized and compressed version from the relay node

Page 21: Cooperative Diversity - An Introduction to Cooperative Comm

20IIT – Indore | EE642 | Wireless Communication

Selective DFCooperation Protocols

Cooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

In a selective DF relaying scheme, if the signal-to-noise ratio of a signal received at the relay exceeds a certain threshold, the relay decodes the received signal and forwards the decoded information to the destination. On the other hand, if the channel between the source and the relay suffers a severe fading such that the signal-to-noise

ratio falls below the threshold, the relay idles.[

[

𝐼𝑆𝐷𝐹 =

1

2log 1 + 2Γ ℎ𝑠,𝑑

2,

1

2log 1 + Γ ℎ𝑠,𝑑

2+ Γ ℎ𝑟,𝑑

2,

1

2log 1 + 2Γ ℎ𝑠,𝑑

2,

1

2log 1 + Γ ℎ𝑠,𝑑

2+ Γ ℎ𝑟,𝑑

2,

ℎ𝑠,𝑟2< 𝑔(Γ)

ℎ𝑠,𝑟2≥ 𝑔(Γ)

where 𝑔 Γ =22𝑅−1

Γ

…(24)

… (25)

The mutual information for selective DF relaying is given by

Page 22: Cooperative Diversity - An Introduction to Cooperative Comm

21IIT – Indore | EE642 | Wireless CommunicationCooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

The outage probability for selective relaying can be derived as follows. Using the law of total probability, conditioning on whether the relay forwards the source signal or not, we have

𝑃𝑟 𝐼𝑆𝐷𝐹 < 𝑅 = 𝑃𝑟 𝐼𝑆𝐷𝐹 < 𝑅| ℎ𝑠,𝑟2< 𝑔(Γ) Pr ℎ𝑠,𝑟

2< 𝑔(Γ)

+𝑃𝑟 𝐼𝑆𝐷𝐹 < 𝑅| ℎ𝑠,𝑟2> 𝑔(Γ) Pr ℎ𝑠,𝑟

2> 𝑔(Γ)

From eq.(24), the outage probability for selective DF relaying is given by

𝑃𝑟 𝐼𝑆𝐷𝐹 < 𝑅 = 𝑃𝑟1

2log 1 + 2Γ ℎ𝑠,𝑑

2< 𝑅| ℎ𝑠,𝑟

2< 𝑔(Γ) Pr ℎ𝑠,𝑟

2< 𝑔(Γ)

+𝑃𝑟1

2log 1 + Γ ℎ𝑠,𝑑

2+ Γ ℎ𝑟,𝑑

2< 𝑅| ℎ𝑠,𝑟

2> 𝑔(Γ) Pr ℎ𝑠,𝑟

2> 𝑔(Γ)

… (26)

… (27)

Cooperation Protocols Selective DF

Page 23: Cooperative Diversity - An Introduction to Cooperative Comm

22IIT – Indore | EE642 | Wireless CommunicationCooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

Cooperation Protocols Selective DF

Calculating the above integration, the outage probability at high SNR is given by

Pr 𝐼𝑆𝐷𝐹 < 𝑅 ≃𝜎𝑠,𝑟2 +𝜎𝑟,𝑑

2

2𝜎𝑠,𝑟2 (𝜎𝑠,𝑟

2 𝜎𝑠,𝑟2 )

22𝑅 − 1

Γ

2

…(28)

which has the same diversity gain as the AF case. This means that at high SNR, both selective DF relaying and AF relaying have the same diversity gain.

Page 24: Cooperative Diversity - An Introduction to Cooperative Comm

23IIT – Indore | EE642 | Wireless CommunicationCooperative Communications and Networking, K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski

Cooperation Protocols Incremental Relaying

For incremental relaying, it is assumed that there is a feedback channel from the destination to the relay. The destination sends an acknowledgement to the relay if it was able to receive the source’s message

correctly in the first transmission phase, so the relay does not need to transmit.[

[

Page 25: Cooperative Diversity - An Introduction to Cooperative Comm

Laneman, J.N., Tse, D.N.C., Wornell, G.W.: Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory 50(12), 3062–3080 (2004)

References

24IIT – Indore | EE642 | Wireless Communication

Outage Probabilities versus 𝑺𝑵𝑹𝒏𝒐𝒓𝒎

Page 26: Cooperative Diversity - An Introduction to Cooperative Comm

– Performance Gains– Balanced Quality of Service– Infrastructure-Less Deployment– Reduced Costs

– Complex Schedulers– Increased Overhead– Partner Choice– Increased Interference– Extra Relay Traffic– Increased End-to-End Latency– Tight Synchronization– More Channel Estimates

25IIT – Indore | EE642 | Wireless Communication

Pros & Cons

Page 27: Cooperative Diversity - An Introduction to Cooperative Comm

– Coverage versus Capacity

– Algorithmic versus Hardware Complexity

– Interference versus Performance

– Ease-of-Deployment versus Performance

– Cost versus Performance

Ease-of-Deployment

Interference Performance Cost

Coverage ↔ Capacity Algorithmic ↔ Hardware

Cooperative Communications Hardware Channel and PHY, Mischa Dohler Yonghui Li26IIT – Indore | EE642 | Wireless Communication

System Tradeoffs

At a given performance level, coverage can be traded capacity and algorithmic with hardware complexity. Performance can also be traded against amount of interference, ease-of-deployment and cost[

[

Page 28: Cooperative Diversity - An Introduction to Cooperative Comm

27IIT – Indore | EE642 | Wireless Communication

References

Bibliography:

Literatures:

1. Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity–Part I: System description” and “User cooperation diversity–Part II: implementation aspects and performance analysis. IEEE Transactions on Communications 51(11) 1927–1938 and 1939–1948 (2003)

2. Laneman, J.N., Wornell, G.W.: Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks. IEEE Transactions on Information Theory 49(10), 2415–2425 (2003)

3. Scaglione, A., Hong, Y.-W.: Opportunistic large arrays: Cooperative transmission in wireless multihop ad hoc networks to reach far distances. IEEE Transactions on Signal Processing 51(8), 2082–2092 (2003)

4. Laneman, J.N., Tse, D.N.C., Wornell, G.W.: Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory 50(12), 3062–3080 (2004)

1. K. J. Ray Liu, Ahmed K. Sadek, Weifeng Su, Andres Kwasinski: Cooperative Communications and Networking2. Mischa Dohler Yonghui Li: Cooperative Communications Hardware Channel and PHY3. Savo G Glisic: Advanced Wireless Communications, 2e

Page 29: Cooperative Diversity - An Introduction to Cooperative Comm

THANKSAshish Meshram