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## Packet oriented communications systems

Nowadays, wireless communications system are often based on layer models such as the Open Systems Interconnection (OSI) model which works as follows. The incoming packet at a given layer (coming from its adjacent upper layer) is called a Service Data Unit (SDU). The layer transforms this SDU into a Protocol Data Unit (PDU), typically by adding it a header and/or a footer. Then, the PDU is passed to the adjacent lower layer, where it becomes the SDU of this layer, and so on.

In this layer model, the streamof bits is partitioned into information packets (shortened as packets in the rest of this thesis), which is the smallest piece of information that has to be transmitted. A special case of the above discussion is the Medium Access Control (MAC) which transmits packets of information bits to the Physical (PHY) layer, whose task is to transform those bits into a signal, and to send it through the propagation medium, i.e., the channel. In wireless communications, the transmission takes place in time-varying channel yielding degradations on the signal, which have to be mitigated. To this end, in almost all practical systems, FEC codes are used. Hence, the packets can be retrieved if and only if the receiver is able to decode the codeword.

As a consequence, it appears that the PER is more adequate than Bit Error Rate (BER) to measure wireless systems’ performance due to the underlying packet oriented model. Both ARQ and HARQ are mechanisms allowing to decrease the PER.

### Estimation of K without LoS shadowing

Hereafter, we address the estimation of K without LoS shadowing. In this case, ˆH reduces to a N1 vector, whose elements are i.i.d. complex gaussian random variables with mean aej0 and variance 22h + 22 n. Hence, for the simplicity in this Section the ith element of ˆH is denoted by ˆH[i] instead of ˆH[i; 1]. First, we provide the mathematical expressions of some existing estimators from the literature. Second, we design our four proposed estimators (two deterministic and two Bayesian ones). Third, we derive the deterministic CRLB and finally, we propose numerical results to compare the proposed estimators’ performance with existing ones.

#### Multi user context, perfect CSI at the transmitter

Second, we focus on the works dealing with the RA with EE related criteria in a multiuser contextwhenconsidering perfect CSI at the transmitter side. In this category, a lot of works consider the use of capacity achieving codes [25, 32, 36, 70, 85, 109, 116, 117, 119] while practical MCS are considered in [13]. Among those works, [13, 32, 36, 70, 85, 109, 117, 119] do not consider HARQ whereas this mechanism is taken into account in [25, 116]. In details, when capacity achieving codes are considered with no HARQ, the MSEE problem is solved in [119] while the MMEE problem is solved in [70]. In [117], several heuristics are derived for the MSEE and MMEE problems. The multi-cell context is addressed in [36, 109]. In [109], the MSEE, MPEE, and MGEE problems are solved, while in [85], the MMEE problem is addressed. In [32], centralized and decentralized algorithms are proposed for the MGEE problem. In [36], a distributed algorithm is proposed to solve the MMEE problem. When capacity achieving codes are considered with HARQ and perfect CSI [25, 116], the GEE is optimized in [116] whereas several RA schemes are investigated in [25]. When practical MCS along with perfect CSI are considered without HARQ, the MGEE problem for the LTE downlink is addressed in [13]. All these works address power and/or subcarriers allocation.

**Table of contents :**

List of Acronyms v

General Introduction

**1 General Context **

1.1 Introduction

1.2 Multiuser Context

1.3 Transmitter, Channel and Receiver Model

1.4 HARQ Basics

1.5 Energy Eciency

1.6 EE-based RA as Constrained Optimization Problems

1.7 Thesis Objectives

1.8 Conclusion

**2 Estimation of the Rician K Factor **

2.1 Introduction

2.2 Channel estimation and properties

2.3 Estimation of K without LoS shadowing

2.4 Estimation of K with Nakagami-m LoS shadowing

2.5 Conclusion

**3 Background on Energy Eciency Based Resource Allocation Problems **

3.1 Introduction

3.2 Literature Review on EE based RA

3.3 Convexity, Geometric Programming and Pseudo Convexity

3.4 Fractional Programming

3.5 Other Non-Convex Optimization Procedures

3.6 Conclusion

**4 Resource Allocation for Type-II HARQ Under the Rayleigh Channel **

4.1 Introduction

4.2 Error Probability Approximation

4.3 Problems Formulation

4.4 Solution Methodology

4.5 MSEE Solution

4.6 MPEE Solution

4.7 MMEE Solution

4.8 MGEE Solution

4.9 Adding a maximum PER constraint

4.10 Complexity Analysis

4.11 Numerical Results

4.12 Conclusion

**5 Resource Allocation for Type-I HARQ Under the Rician Channel **

5.1 Introduction

5.2 Error Probability Approximation

5.3 Problem Formulation

5.4 Solution Methodology

5.5 MSEE Solution

5.6 MPEE Solution

5.7 MMEE Solution

5.8 MGEE Solution

5.9 Extension to Type-II HARQ

5.10 Numerical results

5.11 Conclusion

Conclusions and Perspectives

Appendices

**A Appendix related to Chapter 2 **

A.1 Derivations leading to (2.9)

A.2 Derivations leading to (2.10)

A.3 Proof of Result 2.2

A.4 Derivations leading to (2.35)

A.5 Derivations leading to (2.56) and (2.57)

**B Appendix related to Chapter 4 **

B.1 Proof of Theorem 4.2

B.2 Optimal solution of the maximum goodput problem

**C Appendix related to Chapter 5 **

C.1 Proof of Lemma 5.4

C.2 Proof of Lemma 5.6

C.3 Proof of Lemma 5.7

C.4 Proof of Lemma 5.8

C.5 proof of Lemma 5.9

**Bibliography**