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Dimensioning of Multicellular Networks
The previously mentioned performance metrics are very important parameters when leading a dimensioning study. As already stated, the two major stages of a dimensioning study are the coverage study and the traffic analysis. These two research axes where deeply investigated in the literature, we will present some of the works done in these areas.
Coverage Study
The outage probability is a crucial metric for both coverage and capacity studies. In terms of coverage, mobile stations should be able to decode common control channels (like pilots or broadcast channels) and thus to attain a certain SINR threshold on these channels 70 2. Radio Propagation Models and Performance Metrics with high probability. In this case, we are interested in the low SINR region of the SINR distribution to evaluate the cell coverage. In terms of capacity and for systems implementing link adaptation on shared downlink channels (such as HSPA or LTE), the whole SINR distribution is needed for performance evaluation. The ergodic capacity at a certain distance from the base station is indeed evaluated as an expectation of the Shannon classical formula over the channel variations. The cell capacity is obtained by integration over the cell area.
Many works were devoted to the coverage study of cellular systems. In [22, 23, 24], coverage studies were performed based on the outage probability. In [22], the authors considered a CDMA system with log-normal attenuation model, they proved that the soft handoff improves the cell coverage by a factor of 2 to 2.5. In [23], the authors considered shadowed-Rician/shadowed-Nakagami fading environments. In [24], only path-loss and shadowing were considered while studying the impact of the transmitting power reduction on coverage. It was proven that it is possible to drastically reduce the transmit power without any major loss in the QoS.
Traffic Study
The traffic analysis is the second stage of a dimensioning study after the coverage study. In the literature, the traffic analysis has been based either on simulations or on the Markov chain theory. Many studies have been led following the second approach. In [14], Bonald and Proutière conducted a dynamic traffic study, first for a single cell then for a multicell system considering only path-loss effect. The authors studied the performance of the two systems, assuming a uniform traffic demand in the cell and a Poisson distribution data flows arrival, considering different admission control criteria and different scheduling strategies. It was observed that multicell interference degrades considerably the capacity of the cell. It was also shown that considering a fair scheduling algorithm (Round Robin, proportional fair) or an opportunistic scheduling does not considerably improve the system performance compared to what can be observed in a static study. The authors considered two admission control schemes: the first one is based on the maximum number of active users and hence independent on users locations contrarily to the second scheme that is based on the minimum data rate. For a fixed blocking rate less than 10%, it was shown that both schemes are equivalent in terms of cell capacity. We based our dynamic study presented in Chapter 9 on this analysis. In [15], Borst studied the performance of the proportional fair scheduling considering a dynamic system with random finite-size service demands. Assuming K classes of users where each class is characterized by an arrival rate λk, if the fluctuation in the feasible rates of the users are statistically identical, it was shown that the user-level performance may be evaluated by means of a multi-class Processor-Sharing (PS) model. This assumption is roughly valid when the users feasible rates are linear functions of the SNR. However in case of an asymmetric scenario where the users statistical rates fluctuations are different, the PS approach is no more valid. The system performance were evaluated in terms of mean transfer delay and mean number of active users. In [31], the authors considers the performance of a multicellular dynamic CDMA system handling two types of services: voice and data. The blocking probability, the dropping probability corresponding to each service and the mean throughput of the cell were calculated by subdividing the cell into concentric rings and characterizing each ring by its arrival rate. Different prioritization strategies between the two services are compared in terms of overall dropping probability and in terms of voice blocking probability. It is shown that prioritizing the service requiring the lower effective bandwidth (a notion introduced in [31] depending on the mobile position and on the SIR required for the service) permits to achieve a low dropping probability at an acceptable blocking rate for voice calls. In [59], the authors proposes a two stages dimensioning methodology for an OFDMA network. In the coverage study, authors presented a semi-analytical approximation of the spatial SINR distribution based on a fitting of the simulated SINR distribution. This distribution
is used to calculate the MCS probabilities. The second stage is traffic analysis taking as inputs the latter probabilities and through Markovian approach, provides dimensioning parameters as the average throughput per user, the average number of active users and the average duration of a transfer. This two stages study is performed considering different scheduling schemes and mixed traffic profiles.
MIMO Systems
A pioneering work of Foschini [60] and Telatar [51] highlighted the performance gains promised by MIMO systems in reliability improvement as well as in capacity enhancement. In what follows we will distinguish two MIMO systems: point-to-point MIMO communication and multiuser MIMO communication and discuss the performance gains in each system. Before explaining the promised MIMO gains in these two systems we will first present a primordial notion conditioning the achievement of these gains which is the Channel State Information (CSI). Indeed, MIMO gains are obtained under the condition of the availability of CSI at the receiver (CSIR) and/or CSI at the transmitter (CSIT).
• CSIR
Typically, obtaining the CSIR may be straightforward since it can be measured through the channel estimation via the transmission of pilots. The CSIR is an indispensable condition to achieve almost all MIMO gains.
• CSIT
Unlike the CSIR, the CSIT is somewhat tricky to obtain especially in frequency division duplex (FDD) systems. In this case, the CSI is sent to the receiver via feedback signaling which can be constrained by a limited capacity and a high delay. However, in time division duplex (TDD) systems, CSIT is much easier to obtain since it relies on the uplink-downlink channel reciprocity assumption which is an idealist hypothesis. In reality, in cellular systems the reciprocity may be imperfect, which alters the quality of the CSIT.
Table of contents :
1 Introduction
1.1 Cellular Networks Evolution
1.2 Cellular Network Dimensioning
1.2.1 Coverage Analysis
1.2.2 Traffic Analysis
1.3 Contributions and Thesis Summary
2 Radio Propagation Models and Performance Metrics
2.1 Introduction
2.2 Fading Models
2.2.1 Small Scale Fading
2.2.1.1 Flat Fading
2.2.1.2 Frequency Selective Fading
2.2.2 Large Scale Fading
2.2.2.1 Path-loss
2.2.2.2 Shadowing
2.3 MIMO Channel Models
2.3.1 Narrowband MIMO Channel
2.3.2 Frequency Selective MIMO Channel
2.3.3 3GPP MIMO Channel Model
2.4 Static Study Performance Metrics
2.4.1 Average SINR
2.4.1.1 Interference Limited Systems
2.4.1.2 Noise Limited Systems
2.4.2 Outage Probability
2.4.3 Average Error Probability
2.4.4 Data Rate
2.5 Dynamic Study Performance Metrics
2.6 Dimensioning of Multicellular Networks
2.6.1 Coverage Study
2.6.2 Traffic Study
2.7 Conclusion
3 Overview of MIMO and CoMP Schemes
3.1 Introduction
3.2 MIMO Systems
3.2.1 Single User MIMO Communication Systems
3.2.1.1 Point-to-Point Communication
3.2.1.2 Spatial Diversity Gain
3.2.1.3 Spatial Multiplexing Gain
3.2.1.4 Diversity Multiplexing Gain Tradeoff
3.2.1.5 Space-Time Block Coding (STBC)
3.2.2 Multiuser MIMO Communication Systems
3.2.2.1 Single Cell Multiuser MIMO System Model
3.2.2.2 Multiuser Diversity
3.2.2.3 User Scheduling
3.2.2.4 Transmission Schemes
3.2.3 Multi Cell MIMO Communication Systems
3.2.3.1 Multicellular Single User MIMO System Model
3.2.3.2 Multicell Multiuser MIMO System Model
3.2.4 MIMO Systems in the Standards
3.3 CoMP Transmission
3.3.1 CoMP Strategies
3.3.1.1 Coordinated Beamforming/Scheduling
3.3.1.2 Joint Processing
3.3.2 Selection Algorithms
3.3.3 CSI Feedback and Backhaul Load
3.3.4 Joint Precoding Techniques
3.3.4.1 Full CSIT
3.3.4.2 Partial CSIT
3.3.4.3 Imperfect CSIT
3.4 Conclusion
4 Outage Probability of Multicellular SISO Systems
4.1 Introduction
4.2 Interference Model
4.2.0.4 Propagation Model
4.2.0.5 SIR Calculation
4.2.0.6 Outage Probability
4.3 Fenton-Wilkinson Based Method
4.3.1 Path-Loss and Shadowing Impact
4.3.2 Path-Loss, Shadowing and Fast Fading Impact
4.4 Central Limit Theorem for Causal Functions Method
4.4.1 Path-Loss and Fast Fading Impact
4.4.2 Path-Loss, Shadowing and Fast Fading Impact
4.5 Analytical Fluid Model
4.6 Performance Evaluation
4.6.1 Monte Carlo Simulator
4.6.2 Results
4.7 Conclusion
5 Outage Probability of Time Reversal in Multicellular Systems
5.1 Introduction
5.2 Time Reversal Technique
5.2.1 Time Reversal Formulation
5.2.2 Time Reversal in the Literature
5.2.2.1 TR for SISO systems
5.2.2.2 Time Reversal for MIMO Systems
5.2.2.3 Combination of Time Reversal with Other Techniques
5.3 System Model
5.4 Outage Probability
5.4.1 Useful Power PDF
5.4.2 Interference Power PDF
5.4.3 Outage Probability Calculation
5.5 Simulation Results and Discussions
5.5.1 Mean ISI Power and Mean ICI Power
5.5.2 Simulation Results
5.6 Conclusion
6 Outage Probability of the Alamouti Scheme in a Multicellular Network
6.1 Introduction
6.2 Alamouti Code
6.3 MISO (2 × 1) Alamouti Scheme
6.4 Outage Probability of (2 × 1) MISO Alamouti Scheme
6.4.1 Constant Shadowing
6.4.1.1 Equal Interference Power Assumption
6.4.1.2 Unequal Interference Power Assumption
6.4.2 Log-Normal Shadowing
6.5 MIMO (2 × N) Alamouti Scheme with MRC Receiver
6.6 Outage Probability for the 2×N MIMO Alamouti System with MRC Receiver
6.6.1 Constant Shadowing
6.6.1.1 Equal Interference Power Assumption
6.6.1.2 Unequal Interference Power Assumption
6.6.2 Log-Normal Shadowing
6.7 Fluid Model Approach
6.8 Simulation Results
6.9 Conclusion
7 Outage probability of a Zero Forcing Precoded System
7.1 Introduction
7.2 Zero Forcing MISO System Model
7.3 Outage Probability
7.3.1 Constant Shadowing
7.3.2 Log-Normal Shadowing
7.4 Simulation Results
7.5 Conclusion
8 Outage Probability of an MRT CoMP Transmission
8.1 Introduction
8.2 MRT Scheme
8.3 JP-CoMP MRT System Model
8.4 Outage Probability
8.4.1 Useful Power PDF
8.4.2 Interference Power PDF
8.4.3 Outage Probability
8.5 Simulation results
8.6 Conclusion
9 Dynamic System Performance of SISO, MISO and MIMO Systems
9.1 Introduction
9.2 System Models
9.2.1 SISO System
9.2.2 MISO Alamouti System
9.2.3 MIMO Alamouti System with MRC Receiver
9.2.4 Fluid Model Approximation
9.3 Dynamic Traffic Study
9.3.1 Traffic Model
9.3.2 SISO System Mean Rate
9.3.3 MISO Alamouti Mean Rate
9.3.4 MIMO Alamouti with MRC Receiver Mean Rate
9.4 Systems performance
9.4.1 Assumptions
9.4.2 No Admission Control
9.4.3 With Admission Control
9.5 Conclusion
A Some Intermediate Results
A.1 Sum of Lognormal Random Variables
A.2 Causal Form of the Central Limit Theorem
A.2.1 Central limit Theorem
A.2.2 Causal form of the central limit theorem
A.3 Fluid Model
A.4 Independance of Random Variables
Bibliography
