Get Complete Project Material File(s) Now! »

## Rate maximization problem in OFDM systems with peak-power constraints

In this section, we consider the rate maximization problem under total and peakpower constraints in OFDM systems. Then, based on analytic results, we propose a new algorithm that can achieve the global optimum solution with a reduced complexity as compared to other algorithms in the literature. To this end, we exploit the bit vector obtained by rounding the water-lling algorithm solution to the associated continuous-input rate maximization problem as an ecient initial bit vector of the Greedy algorithm. We theoretically prove that this bit vector has two interesting properties. The rst one states that it is an ecient bit vector, i.e., there is no movement of a bit from one subcarrier to another that reduces the total used power. The second one states that the optimized throughput, starting from this initial bit vector, is achieved by adding or removing bits on each subcarrier at most once.

### Hybrid approach between the Z-GBA and M-GBR algorithms

In Section 3.2.1, we have reminded that the complexity of the Z-GBA algorithm and of the M-GBR algorithm are a non-decreasing function and a non-increasing function of the total allowable power, respectively. Thus, in the region of high values of Ptot, the M-GBR algorithm should be used instead of the Z-GBA algorithm and vice versa. In this section, we propose a simple threshold to switch between the two algorithms. In fact, the complexity of both algorithms is dominated by a product of the number of iterations to obtain the optimum bit and power allocation vectors (bop and Pop) and the complexity per iteration. Moreover, the complexity per iteration of both algorithms is almost the same, i.e., we nd the subcarrier that requires minimum power to add one bit or nd the subcarrier for which the power gain when removing one bit is maximal and then adjust the number of bits on this subcarrier. Let us denote by `BA and `BR the number of iterations to obtain bop in the Z-GBA and the M-GBR algorithms and L denotes the number of used subcarriers. They are dominated by `BAL and `BRL. Note that in these algorithms, only one bit is added or removed at each iteration. Then we have `BA = kbopk1, `BR = kbr maxk1 kbopk1, where kk1 denotes the l1 vector norm. Let us dene PBR and PBA by PBR = kPr maxk1 kPopk1.

#### Power consumption minimization in OFDM systems with peak-power constraint

In this section, we x the throughput and the goal is the power consumption reduction. We thus search for the best bit/power allocation that minimizes the total power under a xed throughput and spectral mask constraints. We assume an interferencefree OFDM system. We propose to apply the WFR-GBL algorithm in section 3.2 and we compare it to other algorithms of the state-of-art.

**Table of contents :**

Remerciements

Table of contents

Abbreviations

Notations

List of gures

List of tables

Abstract

Resume

**1. PLC: State-of-art **

1.1. Introduction

1.2. Classication, major players, projects and standard

1.2.1. Classication

1.2.2. Major players

1.2.3. Projects

1.2.4. Standard

1.3. In-home SISO PLC characterization

1.3.1. SISO PLC channel model

1.3.2. SISO PLC noise model

1.3.3. Colored background noise

1.4. Introduction to MIMO-PLC

1.4.1. MIMO-PLC Coupling

1.4.2. MIMO PLC channel model

1.4.3. MIMO PLC noise model

1.5. Contributions to PLC channel and noise characterization

1.5.1. SISO-PLC channel classication

1.5.2. SISO-PLC noise modeling

1.5.3. Discussion

1.6. Conclusion

**2. Inter-symbol and inter-carrier interference analysis in In-home PLC systems **

2.1. Introduction

2.2. Conventional OFDM versus Windowed-OFDM

2.2.1. OFDM

2.2.2. Windowed-OFDM

2.3. Interference Calculation

2.3.1. Interference calculation in SISO-PLC systems

2.3.2. Interference calculation in MIMO-PLC systems

2.3.3. Inuence of interference on the capacity in MIMO-PLC systems

2.4. Conclusion

Appendix A. Calculation of IN

**3. Optimal Bit-Loading Algorithm for PLC systems without interference **

3.1. State-of-the art

3.2. Rate maximization problem in OFDM systems with peak-power constraints

3.2.1. Rate maximization problem and existing algorithms .

3.2.2. Hybrid approach between the Z-GBA and M-GBR algorithms .

3.2.3. A new low-complexity loading algorithm: Theoretical analysis and implementation

3.2.4. Simulation results

3.2.5. Conclusion

3.3. Power consumption minimization in OFDM systems with peak-power constraint

3.3.1. Power consumption minimization problem and existing solutions 65

3.3.2. Application of WFR-GBL algorithm to power minimization problem

3.3.3. Complexity analysis

3.3.4. Simulation results

3.3.5. Conclusion

3.4. Conclusion

**Appendix B. Proofs **

B.1. Proof of Theorem 1

B.2. Proof of Theorem 2

B.3. Proof of Theorem 3

B.4. Proof of Theorem 4

B.5. Proof of Theorem 5

B.6. Proof of Theorem 6

B.7. Proof of Theorem 7

B.8. Proof of Theorem 8

**4. Resource allocation in PLC Systems in the Presence of Interference **

4.1. Introduction

4.2. Bit loading in SISO-PLC systems with interference

4.2.1. System model

4.2.2. Greedy principle and reduced complexity approaches .

4.2.3. Proposed Reduced Complexity Algorithm (RCA)

4.2.4. Simulations results

4.3. Bit loading in MIMO-PLC systems with interference

4.3.1. MIMO-Windowed OFDM PLC system model

4.3.2. Bit loading for MIMO-PLC with the presence of interference

4.3.3. Simulation results

4.3.4. Conclusion

4.4. GI adaptation in PLC systems

4.4.1. Achievable throughput optimization in OFDM-PLC systems taking into account the GI

4.4.2. Guard interval length optimization based on a linear regression .

4.4.3. Simulation results

4.4.4. Conclusion

4.5. General conclusions and perspectives

**Appendix C. Proofs **

C.1. Proof of Theorem 1

C.2. Proof of Theorem 2

C.3. Proof of Theorem 3

C.4. Proof of Theorem 4

C.5. Proof of Theorem 5

**5. MIMO precoding for PLC systems **

5.1. Introduction

5.2. MIMO-PLC model

5.3. MIMO precoded spatial multiplexing technique

5.3.1. SVD-based precoding

5.3.2. Optimized Linear Precoder

5.3.3. Orthogonalized spatial multiplexing (OSM)

5.3.4. Performance degradation due to parameter quantization

5.3.5. Maximum mutual information for SVD and OSM schemes

5.4. Simulation results

5.4.1. Equal power allocation

5.4.2. Optimized power allocation

5.5. Conclusion

Conclusion

**Bibliography**