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Analytical Modeling of Heterogeneous Cellular Networks

Book Description

This self-contained introduction shows how stochastic geometry techniques can be used for studying the behaviour of heterogeneous cellular networks (HCNs). The unified treatment of analytic results and approaches, collected for the first time in a single volume, includes the mathematical tools and techniques used to derive them. A single canonical problem formulation encompassing the analytic derivation of Signal to Interference plus Noise Ratio (SINR) distribution in the most widely-used deployment scenarios is presented, together with applications to systems based on the 3GPP-LTE standard, and with implications of these analyses on the design of HCNs. An outline of the different releases of the LTE standard and the features relevant to HCNs is also provided. A valuable reference for industry practitioners looking to improve the speed and efficiency of their network design and optimization workflow, and for graduate students and researchers seeking tractable analytical results for performance metrics in wireless HCNs.

Table of Contents

  1. Cover
  2. Half Title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. Acknowledgements
  8. List of notation
  9. List of acronyms and abbreviations
  10. 1 Introduction
    1. 1.1 Wireless-channel model
      1. 1.1.1 Path-loss model
      2. 1.1.2 Fading model
    2. 1.2 Distribution of the SINR at an arbitrary user
    3. 1.3 Why SINR distributions are usually found via simulation
    4. 1.4 The role of analytic modeling
  11. 2 Structure of the SINR calculation problem
    1. 2.1 Statement of the SINR calculation problem
      1. 2.1.1 Candidate serving BSs and the serving BS
      2. 2.1.2 Basic definitions
    2. 2.2 SINR distributions
      1. 2.2.1 Joint CCDF of SINRs from candidate serving BSs
      2. 2.2.2 Joint CCDF of SINRs from BSs ordered by serving BS selection criterion
      3. 2.2.3 Conventions and notation
    3. 2.3 The canonical SINR probability
      1. 2.3.1 Form of joint CCDF of SINRs from candidate serving BSs
      2. 2.3.2 Form of joint CCDF of SINRs from BSs ordered by serving BS selection criterion
      3. 2.3.3 Joint CCDF of SINR in canonical probability form
    4. 2.4 Calculation of the canonical probability
      1. 2.4.1 Z-matrices and M-matrices
      2. 2.4.2 Expressions for P{AX > b}
      3. 2.4.3 Expressions for the canonical probability P{AX > Wb}
      4. 2.4.4 Approximating arbitrary PDFs by mixtures of Erlang PDFs
    5. 2.5 Full solution to the canonical probability problem
      1. 2.5.1 Determining when a Z-matrix is an M-matrix
      2. 2.5.2 Analytic form of Laplace transform of W
  12. 3 Poisson point processes
    1. 3.1 Stochastic models for BS locations
    2. 3.2 Complete spatial randomness
    3. 3.3 The Poisson point process
    4. 3.4 Theorems about PPPs
      1. 3.4.1 Mapping theorem
      2. 3.4.2 Superposition theorem
      3. 3.4.3 Coloring theorem
      4. 3.4.4 Marking theorem
    5. 3.5 Applicability of PPP to real-world deployments
    6. 3.6 Other models for BS locations
  13. 4 SINR analysis for a single tier with fixed power
    1. 4.1 Introduction
    2. 4.2 Distribution of total interference power in a single-tier BS deployment
      1. 4.2.1 PPP of received powers at user from BSs in a tier
      2. 4.2.2 Distribution of total received power from all BSs in a tier
    3. 4.3 Distribution of SINR in a single-tier BS deployment
      1. 4.3.1 Serving BS known and fixed
      2. 4.3.2 A note on serving BS selection criteria
      3. 4.3.3 Serving BS is the one nearest to the user
      4. 4.3.4 Serving BS is the one received most strongly at the user
  14. 5 SINR analysis for multiple tiers with fixed powers
    1. 5.1 Introduction
    2. 5.2 Joint CCDF of SINR from candidate serving BSs
      1. 5.2.1 Candidate serving BS in each tier is the one nearest to the user
      2. 5.2.2 Application: camping probability in a macro-femto network
      3. 5.2.3 Candidate serving BS in each tier is the one received most strongly at the user
      4. 5.2.4 Application: coverage probability in an HCN
    3. 5.3 Distributions of serving tier and SINR from serving BS
      1. 5.3.1 Serving BS is the “nearest” (after selection bias) candidate serving BS
      2. 5.3.2 Serving BS is the “strongest” (after selection bias) candidate serving BS
      3. 5.3.3 Serving BS is the max-SINR (after selection bias) candidate serving BS
    4. 5.4 Selection bias and the need for interference control
  15. 6 SINR analysis with power control
    1. 6.1 Introduction
    2. 6.2 Power control from the transmitter perspective
    3. 6.3 Types of power control
    4. 6.4 Distribution of SINR under power control
      1. 6.4.1 Distribution of received power with i.i.d. BS transmit powers
      2. 6.4.2 SINR distribution with non-adaptive power control
      3. 6.4.3 Application: eICIC and feICIC in LTE
      4. 6.4.4 Interference power at the receiver of a given link under OLPC
      5. 6.4.5 Distribution of distance from BS to served user
      6. 6.4.6 CCDF of SINR when all BSs use OLPC
      7. 6.4.7 SINR distribution under CLPC
  16. 7 Spectral and energy efficiency analysis
    1. 7.1 Introduction
    2. 7.2 Spectral efficiency
      1. 7.2.1 Spectral efficiency on the link to an arbitrarily located user
      2. 7.2.2 Spectral efficiency of an HCN
      3. 7.2.3 Application: spectral efficiency of a macro-pico LTE HCN with eICIC
    3. 7.3 Energy efficiency
  17. 8 Closing thoughts: future heterogeneous networks
    1. 8.1 Introduction
    2. 8.2 Analysis of a network with D2D links
    3. 8.3 The role of WiFi in future HCNs
    4. 8.4 Evolution of the network infrastructure
    5. 8.5 New directions in analysis
  18. Appendix A Some common probability distributions
    1. A.1 Discrete distributions
      1. A.1.1 Uniform distribution
      2. A.1.2 Bernoulli distribution
      3. A.1.3 Binomial distribution
      4. A.1.4 Poisson distribution
      5. A.1.5 Negative binomial distribution
      6. A.1.6 Generalized negative binomial distribution
    2. A.2 Continuous distributions
      1. A.2.1 Uniform distribution
      2. A.2.2 Normal or Gaussian distribution
      3. A.2.3 Circularly symmetric complex Gaussian distribution
      4. A.2.4 Rayleigh distribution
      5. A.2.5 Exponential distribution
      6. A.2.6 Erlang distribution
      7. A.2.7 Gamma distribution
      8. A.2.8 Nakagami distribution
      9. A.2.9 Lognormal distribution
  19. Appendix B HCNs in LTE
    1. B.1 3GPP and LTE
    2. B.2 Support for HCNs in LTE
  20. References
  21. Author index
  22. Subject index