Position location strategies, applications (Part 3)
Keywords:wireless network mobility CDMA
In VargasRosales et al. [79], it was shown that this viewpoint has a solution for the blocking probability of new calls and handoff calls with channel reservation. The fundamental idea in this model is that the traffic offered to a cell is given by the new call traffic plus handoffs that have already been accepted in an adjacent cell; that is, if we denote as v_{ij} the handoff traffic offered from cell i to cell j, B_{i} as the new call blocking in cell i, and B_{hi} as the handoff blocking in cell i, we can obtain the handoff rate out of cell j offered to cell i as
Equation (5.2)

where A_{j} is the set of neighbouring cells to cell j, and p_{ij} is the routing probability from cell i to cell j. The first term in Equation (5.2) is due to those new calls offered to cell j that are accepted and after a residence time, handed off to cell i with probability p_{ji}. The second term is due to all handoff calls that are offered and accepted into cell j from its adjacent cells and then handoff to cell i.
One can see that this model helps us to comprehend the effects that mobility has on performance by varying the routing probabilities to increase the proportion of handoff calls being offered. To solve for the blocking probabilities, one needs to consider a fixed point because Equation (5.1) is in terms of traffic offered, and this depends on new call arrivals plus handoffs as given by Equation (5.2). Equation (5.1) now also has traffic from both arrivals of new calls and handoff calls. This immediately tells us that traffic increases, and thus blocking also increases; that is, capacity in terms of number of possible simultaneous users active is reduced.
This model has been evaluated for FDMA and TDMA in VargasRosales et al. [79], and for CDMA in MirandaGuardiola and VargasRosales [53]. In addition, the use of reservation degrades performance for the type of traffic with higher bandwidth requests. Even though these networks have limitations in terms of interference levels, it has been shown that relevant limitations are due to blocking [37].
It is well known that CDMA capacity depends on the processing gain and the bit energytonoise ratio, but from another viewpoint, we can consider a scenario where a central cell is influenced by interference from an infinite number of rings (tiers), each of which contains cells transmitting at the same frequency with users working with perfect power control. The scenario was considered with homogeneous circular cells of radius R in Munoz et al. [56]. The advantages of using such a model are that we get bounds on the interference levels even for an infinite number of cells due to the infinite number of rings surrounding the centre cell.
In the model, the same number of users for each cell is considered, and in order to obtain the major influence of the users, in each cell all users are located at the closest point towards the centre. The model used a simple propagation model with a pathloss exponent between 2. 5 and 4, and cell radius was varied to consider cases with a radius of 3, 5, and 10 km. In the worstcase scenario, a cell capacity of 20 users was obtained when the number of interferents was infinity. Voice activity and sectoring were considered as well. The important aspect of this result is that regardless of the number of interferents, the capacity of CDMA cells with perfect power control will be lowerbounded by 20. We must be cautious when referring to this number since in these conditions FDMA and TDMA would be useless due to interference. The final result of the analysis in [56] is provided by the following lower bound:
Equation (5.3)

where N is the number of users in each cell, y is the pathloss exponent, R is the cell radius, C/I is the carriertointerference level usually set to 15 db, and is the RiemannHurwitz function that converges for x > 1 and y > 0.
In general, network capacity also depends on limitations encountered by the underlying channels. These limitations determine the data rates at which one can transmit with small bit error rates (BERs). Once the physical layer provides a reliable link to transmit, then the network functions take place, consuming some of the available bandwidth in order to achieve network control. So in order to consider capacity in wireless networks, we have to see that channel capacity or singleuser system capacity and multiuser capacity need to be integrated.
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