The Bubble Oscillation Algorithm

The bubble oscillation algorithm proposed by Lin [164] is an efficient algorithm in terms of computing optimised coverage pattern/shapes quickly. The algorithm finds shapes by encouraging BSs to cover less efficient users in order to achieve better network-wide performance.

3.5.3.1. The Quantisation Cell Model

The BOA computes the cell boundaries defined by a curvilinear grid-based cell model. and is shown in Fig. 3-8. A cell is divided into many grids called Quantisation Cells (QC) by Lin and each ( and specifies angular and radial steps respectively)

is a container for those mobiles whose directions of arrival of signals to the BS is within the angular range and the distance range . The

67

traffic demand of each QC is the aggregate demands of mobiles within it. The BOA is tasked to determine which QC should be covered according to their importance.

Fig. 3-8 Cell model with Quantisation Cells (QC)

An important reason for working on this model is to avoid producing unrealisable cell shapes for a physical semi-smart antenna and also decrease the amount of computation for the BOA by reducing the number of items from mobiles to ‘heavier’ QCs. The granularity used in our studies is then 5˚ wide for each QC and 20 steps on the radial direction from the centre of cells to their frontier (which corresponds to the minimum CIR level required for listening to control channels by mobiles).

3.5.3.2. Description of the BOA

In the following, the BOA and its application in a WCDMA cellular network is briefly described. There are some important properties of the algorithm [164]:

1. In BOA each cell’s downlink capacity is used to define the size of individual resource pools. The capacity of a cell depends on the type of wireless network the BOA optimises for. Each cell could have 3 or 6 sectors.

2. The demand of a QC is the total demands of mobiles within it. Demands are measured in the same unit as capacity of cells (Number of users supported). 3. BS’s maximum transmitting power constraint is not applied in the BOA.

4. A QC can be covered by any number of sectors (not necessarily to have its mobiles A A B A A B

68

served by all of them simultaneously though).

5. Each base station has a maximum communication distance depending on minimum acceptable CIR levels defined as (refer to Table. 3-1 and for cell radius and other parameters):

To decide each QC’s priority, Lin has intoduced a notion called repulsion force, which is defined as the vector (magnitude and direction)

[164](3.5)

where and are the distance and angle from the i-th base station to the j-th QC,

and is the distance to the frontier of the i-th base station. The magnitude of the

repulsion force is given by and represents the QC’s initial priority. BSs

then assign QCs according to their priority. The BOA is an iterative approach. After the initial assignment, uncovered QCs (if there is not enough resource) create an impact on all the QCs in a network, modifying their priority. This is done by introducing a second kind of vector named ‘attraction force’. Uncovered QCs are imagined to be vacuums generating attraction forces which are applied on all rest QCs within the same cell, changing its priority incrementally by each iteration. The attraction force from the k-th un-served QC to the j-th QC in the i-th cell are given by the following vetors

If ,

If , [164] (3.6) where and are the angles from the i-th base station BSi to QC k and j

respectively and are used to calculate vector directions, is the demand of the k-th QC and because the attraction is from the k-th QC itself. After applying the attraction force from uncovered QCs in each cell, the assignment procedure is carried out again, and followed by another round of calculation of attraction forces and further assignment afterwards. The iterative procedure goes on until the performance

69

of network measured by total number of users served can no longer be improved.

Procedural steps of the BOA are given below.

1. In the first iteration, calculate the repulsion forces for each QC of each base station using (3.5). The magnitude of forces is regarded as the priority value of QCs. 2. Sort the QCs of each BS by their priority value in descending order.

3. For each BS, assign its QCs as long as the capacity allows. Unassigned QCs become ‘vacuums’.

In the following iterations:

1. For each cell, calculate the attraction forces generated by un-covered QCs for each QC using (3.6).

2. Calculate the updated priority of each QC by using the summation of attraction vectors applied to it from each uncovered QC and the QC’s own repulsion vector. The value is given by the final magnitude of sum of all vectors:

[164](3.7)

3. Sort by descending order in each cell.

4. For each BS, assign its QCs as long as the capacity allows.

5. Evaluate the capacity of the network. If it does improve from previous iteration then go back to step.1 and start a new iteration. Otherwise exit the procedure.

The BOA stops [158, 164] until reaching a maximum iteration number (100 iterations) or when the number of un-served traffic remains constant for as long as 10 iterations. At the point of convergence or algorithm termination, the covered QCs of each cell can be used to map coverage patterns. The BOA is essentially a greedy algorithm that sort users by their efficiencies and each cell assigns as much users as it can independently. The assignment of each cell is done in parallel, followed by an update of assignment status of users for all cells. QCs in a cell are mapped to other QCs in neighbouring

70

cells [164]. If a QC is covered, its mappings in other cells are also counted as covered.