Before starting the discussion of the proposed formats, we develop a small scenario called Tiny. We will use this scenario to agree on terminology, to explain parameters of a cellular phone network, and to give examples. The scenario is depicted in Figure 1.
There are three sites , named A,
B, and C. Site A has three sectors with sector numbers 1, 2, and 3. Sites B and C have only two sectors, numbered
1 and 2. The tuples written next to the site name are the coordinates of
the site locations . The locations
of site A, B, and C are (3, 5), (1, 10), and (9, 10), respectively.
A cell is served by one sector of one site.
The numbers of elementary transceivers (TRXs) installed
per cell are given in Table 1.
Let us say that Tiny is a GSM900 network with radio frequency band 891.0 - 893.4 MHz available for the downlinks and band 936.0 - 938.4 MHz available for the uplinks. This corresponds to 13 downlink and 13 uplink frequency slots of 200 kHz each. We call such a frequency slot a channels . The Absolute Radio Frequency Channel Numbers (ARFCNs) of those channels are 5-17 for the downlinks and 230-242 for the uplinks. In GSM900 networks, the radio frequency bands for downlink and uplink always differ by 45 MHz. Therefore, it suffices to specify the downlink band. We call the ARFCNs of the downlink channels the spectrum .
Due to technical and regulatory restrictions, some channels in the spectrum may not be available in every cell. Such channels are called locally blocked . Local blockings can be specified for every cell. We assume that channels 5 and 6 are blocked in cell B 2, and that channel 13 is blocked in cell C 1. (This implies that the uplink channels 230 and 231 are blocked in cell B 2 as well as that the uplink channel 238 is blocked in cell C 1.)
For the time being, we are considering fixed frequency assignment problems without radio frequency hopping. In this case, the number of TRXs per cell equals the number of channels that have to be assigned to the cell in a frequency plan. However, some forms of radio frequency hopping allow to use more channels in a cell than TRXs are installed. Therefore, we introduce the notion of a carrier to express the demand of one channel. A channel is then assigned to a carrier. And the number of carriers in a cell is the number of channels that have to be assigned to that cell in a frequency plan. In each cell, we number the carriers starting at zero. Let us say that the carrier numbered zero operates the broadcast control channel (BCCH). (No frequency hopping is used for the BCCH.) The carriers numbered 1 and higher operate traffic channels (TCHs). In case no radio frequency hopping is used, carriers and TRXs correspond one-to-one. As we have no radio frequency hopping in this scenario, we will use the familiar term TRX for the rest of this section. In the more general setting of the other sections, the term carrier will be used exclusively.
The difference of the ARFCNs of two channels is a measure for their proximity. We call this difference their separation . For a pair of TRXs, there is sometimes a restriction as to how close their channels may be. We call this a separation requirement . Separation requirements arise in several ways. Their purpose is to ensure that the TRXs can operate properly and to avoid strong interference. Interference can occur if two TRXs use channels with no or little separation. Significant interference between the signals of TRXs installed at the same site is ruled out by appropriate separation requirements. We will discuss those requirements below. Between TRXs installed at different sites, only co-channel and adjacent-channel interference is relevant. Co-channel interference may occur if the TRXs use the same channel. Adjacent-channel interference may occur if the ARFCNs of the used channels differ by one.
There are several ways to rate interference. Area-based and
traffic-based ratings are examples.
We specify area-based interference in our scenario.
The interference is specified for pairs of cells. The underlying assumption
is that all TRXs in a cell use the same technology, the same transmission
power, and emit their signals via the same antenna. The interference relation
does not have to be symmetric, i.e., if cell B 1 is an interferer in cell A 1,
then cell A 1 is not necessarily an interferer in cell B 1. In case A 1 is
an interferer in cell B 1, the ratings of the interference can be different.
The rating is normalized so that all interference values lie between 0.0
If interference is very strong, it may not be possible to process calls. In this case, interference should be ruled out by means of separation requirements with minimum separation of one or two. A prescribed minimum separation of one rules out co-channel interference, since the involved pairs of TRXs may not use the same channel. A prescribed minimum separation of two rules out co- and adjacent-channel interference.
As stated above, there are other sources of separation requirements. If two or more TRXs are installed at the same site, co-site separation requirements have to be met. For our network, the co-site separation is the same for all sites and is equal to two. Furthermore, if two TRXs serve the same cell, a co-cell separation requirement has to be met. The minimum co-cell separation is equal to three for all the cells in our scenario. In practice, this value may vary from cell to cell, due to different technologies in use.
As a cellular phone is moved, it may be necessary to have TRXs in
different cells serve an on-going call at different times.
The process of passing an on-going call from one cell to another is
called handover .
Technically speaking, the cellular phone switches from using a channel
operated in the passing-on cell to a channel used by some TRX in the
The handover-relation is defined between all ordered pairs of cells and tells from which cell
to which other cell a handover is possible. Let us say that the handover
relation for our network is as given in Table 3.
The interference caused (or induced) by a frequency assignment will serve as a quality measure for assignments. There are, of course, other reasonable ways to measure the quality of an assignment.
Finally, we assume that the frequency assignment given in Table 5 is in use in the network Tiny. If a new frequency assignment for Tiny is to be computed, we may want to keep some of the existing assignments fixed. We call a TRX whose channel shall not be changed unchangeable . Otherwise, the TRX is called changeable .