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MIMO PLC noise model
In the literature, MIMO-PLC noise modeling is little addressed. In this section, we rst introduce the MIMO background noise model in frequency domain proposed by Hashmat et al. in [49]. Second, we describe a more complicated time-domain model of the MIMO-PLC background noise proposed by Hashmat et al. in [50].
Statistical Frequency Domain Models for MIMO PL Noise:
This MIMO PL noise model takes into account the statistical properties of model parameters for the three receive ports L-N, N-PE and PE-L. It is based on the Esmailian model, and provides the statistics of the parameters a, b and c for L-N, N-PE and PEL sequences. The statistics of the parameters are given in Table 1.5. Fig. 1.10 shows the PSD of the measured MIMO-PLC noises at three receive ports. Fig. 1.11 shows the PSD of the measured and modeled noise at N-PE receive port. Both gures are extracted from [49].
This background noise model provides a very simple and brief picture of the noise present in the power line channel. A complete and detailed noise model can be achieved only through time domain modeling techniques that will be presented in the following.
Contributions to PLC channel and noise characterization
At the end of the 2nd year of my thesis, we obtained some data of channel and noise measurements from Orange Labs, Lannion, France. I cooperated with an internship student to study channel and noise characteristic in PLC systems. Based on available data, we aim to propose a simpler models for PLC channel and noise as compared to the existing one. Since the time budget for this task as well as the available data were limited, it was not possible to get general conclusions. Thus, in the following, only some main contributions are presented. We also give some conclusions and perspectives of this work.
SISO-PLC channel classication
A channel classication has been proposed in OMEGA project [14] relying on channel capacity. In this project, PLC channels were classied into nine classes with ascending order of channel capacity. Capacity is calculated by the Shannon’s capacity formula with a same referenced noise and PSD at the transmitter side. As shown in Table 1.1, these 9 classes are dened by equally dividing the capacity interval from where Ps, Pn denote the PSD of the transmitted signal and of the noise, respectively; Hi is the channel frequency response at subcarrier i and f is the subcarrier bandwidth. In the following, we focus on classication methods for PLC channels. Instead of applying a criterion based on equal capacity division, we propose an unsupervised classication technique which uses a Gaussian mixture model (GMM). The probability density function of a GMM is dened as follows.
In uence of interference on the capacity in MIMO-PLC systems
In this section, we gure out the in uence of interference on the capacity in MIMOPLC systems. Indeed, the interference causes a decrease of the signal-to-interferenceplus- noise ratio (SINR) as well as a degradation of the capacity. Since the number of used subcarriers employed in practical PLC systems is quite large, we assume that the interference on a given subcarrier is normally distributed (following the central limit theorem). Dierent normality tests for the interference have been introduced in [89]. According to this analysis, our assumption is valid in practical PLC systems. Under a Gaussian continuous input distribution, taking into account the interference and assuming that a perfect channel state information is available at the receiver, the theoretical capacity is given by [90] CMIMO(m0) = log2 det I2x2 + 1 IN(m0)A(m0)Q(m0)AH(m0) .
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
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
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 takinginto 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
