III The signal-to-interference-to-noise ratio (SINR) coverage model: in between Voronoi and Boolean. Reception is possible if the signal-to-interference (and noise) ratio is N. SINR) on the receiver large enough;. FDMA: Frequency Division Multiple Access; different channels get different sub-frequencies of a given bandwidth (first generation technology, analog wireless communication).
Time division multiple access; different channels get different time slots of a given time unit (current GSM technology). CDMA: Code division multiple access; different channels become different. pseudo)-orthogonal codes to modulate their signals with (technology of the upcoming UMTS). The signature process ci is used by the receiver to modulate the total received signal.
This returns the original signal of user i and some (Gaussian) noise due to the lack of perfect orthogonality between signatures ci. Users form an ad-hoc network that is responsible for transmitting information over a distance over multiple hops. The optimal receiver among them is responsible for forwarding this packet in (one of) its next emission time slots.
Capacity: How much own traffic each node can send, as it must forward traffic from other nodes.
II BASIC GEOMETRIC MODELS
The number of points Φ(B ) of Φ in a subset B of the plane is a Poisson random variable with parameter λ | B |, where | · | is the Lebesgue measure on the plane; i.e. This modeling consists of treating a given network architecture as a snapshot of a (homogeneous) random model and its statistical analysis. Instead, the method allows capturing essential spatial characteristics of network performance essentially through the density of these point processes (i.e., the density of network devices).
Given a collection of points Φ = { Xi} in the plane and a given point x, we define the Voronoi cell of this point Cx = Cx(Φ) as the subset of the plane of all locations closer to x than any point of Φ; that is The points indicate the location of various structural elements (devices) of the network (base station antennas and/or network controllers in mobile networks, concentrators in fixed telephony, access nodes in ad hoc networks, etc.). Cells indicate mutually exclusive regions of the aircraft served in some sense by these devices.
Given the actual response function L( · ) of the distance on the plane, we define the Shot-Noise field.
III SINR COVERAGE MODEL
Tessellations in wireless communication networks: Voronoi and beyond F. coverage probability of the point is some distance from the antenna, simultaneous coverage of several points, mean area of the cell). overlap of cells, coverage probability of a typical point, distance to different handover modes). Tessellations in wireless communication networks: Voronoi and beyond F. coverage probability of the point is some distance from the antenna, simultaneous coverage of several points, mean area of the cell). overlap of cells, coverage probability of a typical point, distance to different handover modes).
CDMA handoff cells
Almost exact simulation of the shot noise For a given size of the observation window (radius R) one selects a larger influence window (radius R0) to get a good estimate of the shot noise term Iφ in the . One constructs a Markov process (˜Zt) of point patterns that has the conditional distribution as a stationary distribution. Points are generated in exponential periods and are located in the window, but only if their presence does not violate the conditions for maximum coverage of the points.
Points placed in the window remain there for exponential times and are removed, but only if their absence does not violate the conditions for maximum coverage of the points zi0. The exact stationary distribution of the Markov process (˜ Zt ) is obtained using backward simulation (coupling from the past) similar to that proposed by Kendall.
IV POWER CONTROL IN CDMA
Global power allocation is feasible if there exist antenna powers 0 ≤ Sj < ∞ (total . transmitted powers in traffic channels) such that. Decentralized Power Distribution Principle (DPAP) Each BS j verifies for the NMj pattern of mobiles checking whether. Tessellations in Wireless Communication Networks: Voronoi and Beyond it F. P-V and Hex model peak load estimations.
Given the density of BS's λBS, for any λM > 0 in both P-V and Hex model, the spectral radius of A is equal to ∞ with probability 1, and therefore power allocation is not possible. It says how often an unbounded Poisson configuration of users in a given cell cannot be fully accepted by the access scheme DPAP. Define blocking rate associated with a given location in the cell as the fraction of users that arrive according to the SBD process at that location and are rejected.
The stationary (time limit) distribution of the (unlimited) SBD process of received calls is the distribution of the (spatial) Poisson process Π with density λ(. Approximations of the blocking probability as a function of the distance to the BS for an average number of M ¯ = 27 users per cell Baccelli & Blaszczyszyn & Tournois ( 2003) Downstream Access/Congestion Control and Peak Load in CDMA Networks, IEEE INFOCOM.
Baccelli & Blaszczyszyn & Karray (2005) Blocking rates in large CDMA networks via the spatial Erlang formula, IEEE INFOCOM.
SUMMARY
Going deeper into the engineering details of the performance of the CDMA cellular network (power control aspect), we evaluated the capacity of a large such network under a simplified (Voronoi) model of its architecture. Many interesting problems related to geometry arise when analyzing so-called ad-hoc networks (without a fixed cellular structure), but I do not have time to address this topic.
