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## Evaluation tools for multi-antenna systems

In this section, we present some information theory tools that have been developed to evaluate the performance of MIMO systems. Since a cooperative network can be modeled as a MIMO system, the same tools will be used in this thesis to analyze cooperative protocols.

### MIMO channel model

We consider a multiple-antenna system with nt transmit antennas and nr receive antennas.

Between each transmitting and receiving antennas, the transmission suffers from a independent fading. Multiple-antenna strategies such as space-time block codes are designed to exploit this particular property.

The transmission scheme is represented in Figure 1.5. The binary sequence is first modulated: each modulated symbol corresponds to a given number of bits depending on the chosen constellation. In this work, we will consider only M-QAM constellations (see Figure 1.6), whose modulated symbols carry log2M bits. The mapping is done according to a Gray coding so as to minimize the Hamming distance between neighbor symbols. In a second step, these modulated symbols are coded with the chosen STBC. Finally the resulting codeword is sent through the channel. At the destination side, the received signal is first decoded and the resulting symbols are demodulated to generate the estimated binary sequence.

#### A tradeoff between performance and complexity: Sequential decoders

Sub-optimal decoding algorithms such as ZF or MMSE have a low complexity but poor performance. On the contrary, ML decoding algorithms such as SD or SE allow to reach the optimal performance of a MIMO system, but have a high complexity.

Sequential decoders like Fano and stack allows to obtain a range of performance from ML to ZF-DFE, with proportional complexity. A bias is added to the cost function (Euclidean distance) to accelerate the search by favoring the long paths on the search tree. If the bias is equal to 0, the ML performance is obtained, and if the bias is high, ZF-DFE performance is obtained. Depending on the application constraints, the bias is chosen so as to provide the desired performance level.

**Relay channel model**

We consider a wireless network composed of one source, N relays and one destination.

The channel links are assumed to be Rayleigh distributed and slow fading, so their coefficients can be considered constant during the transmission of at least one frame. Besides, we suppose a symmetric scenario, i.e. all the channel links are subject to the same average SNR.

In each time slot, the total power of transmitted signals is set to Ptot = 1. When several nodes are transmitting simultaneously, this power has to be shared. The terminals we consider are half-duplex; they cannot receive and transmit at the same time. They are equipped with only one antenna; the MIMO case is not considered in this thesis.

**Table of contents :**

Acknowledgements

English abstract

French abstract

French summary

List of figures

List of notation

Introduction

**1 Cooperative diversity and distributed space-time coding **

1.1 Cooperative communications

1.1.1 Cooperative diversity

1.1.2 Relaying nodes

1.1.3 Relaying strategies

1.1.4 Cooperative protocols

1.2 A virtual MIMO system

1.2.1 Modeling of the cooperative network as a MIMO system

1.2.2 Distributed space-time block codes

1.3 Evaluation tools for multi-antenna systems

1.3.1 MIMO channel model

1.3.2 Information theory tools

1.4 Space-Time Block Codes

1.4.1 Design criteria

1.4.2 State of the art of space-time block codes

Charlotte Hucher, TELECOM ParisTech

1.5 Lattice decoding

1.5.1 Lattice representation

1.5.2 Maximum Likelihood decoding

1.5.3 A tradeoff between performance and complexity: Sequential decoders

1.6 Conclusion of the chapter

**2 Relay channel I: performance of cooperative protocols **

2.1 Relay channel model

2.2 Existing protocols: state-of-the-art

2.2.1 Amplify-and-forward (AF) protocols

2.2.2 Decode-and-forward (DF) protocols

2.3 Implementation constraints

2.3.1 Influence of relay location

2.3.2 Impact of power allocation

2.3.3 Effect of a desynchronization

2.4 Adaptive protocols

2.4.1 Adaptive AF strategy

2.4.2 Example of the Adaptive NAF

2.4.3 Adaptive DF strategy

2.5 Conclusion of the chapter

**3 Relay channel II: toward a practical decode-and-forward protocol **

3.1 Alamouti Decode-and-Forward

3.1.1 Transmission scheme of the Alamouti DF

3.1.2 Theoretical performance of the Alamouti DF

3.2 Asymmetric Decode-and-Forward (ADF)

3.2.1 Transmission scheme of the Asymmetric DF

3.2.2 Implementation: example of the one-relay case

Charlotte Hucher, TELECOM ParisTech

3.2.3 Theoretical performance of the Asymmetric DF protocol

3.3 Incomplete Decode-and-Forward (IDF)

3.3.1 Transmission scheme of the Incomplete DF

3.3.2 Theoretical and simulation performance of the Incomplete DF

3.3.3 Reducing the decoding complexity at relays for a higher number of relays .

3.3.4 Reducing the decoding complexity at relays for a larger constellation

3.4 Conclusion of the chapter

**4 Generalization of the relay channel **

4.1 Cooperative Multiple Access (CMA) networks

4.1.1 CMA channel model

4.1.2 Original CMA-NAF protocol and proposed implementation

4.1.3 Improvements of the CMA-NAF

4.1.4 Decode-and-forward strategy: CMA-IDF

4.1.5 Performance of the proposed protocols

4.2 Multi-hop networks

4.2.1 KPP channel model

4.2.2 Existing works

4.2.3 Proposed protocol using an amplify-and-forward strategy

4.2.4 Generalization to the decode-and-forward strategy

4.2.5 Generalization to different path lengths

4.2.6 Implementation issues

4.3 Conclusion of the chapter

Conclusion and future works

**A Appendix **

A.1 Preliminaries

Charlotte Hucher, TELECOM ParisTech

A.2 Proof of Theorem 1

A.3 Proof of Theorem 2

A.4 Proof of Theorem 4

A.5 Proof of Theorem 5

**Bibliography**