The Fundamentals of Cellular Radio

Co-Channel Interference Calculations

Introduction

 In a cellular system, a large geographic area is divided up into cells. In each of the cells there is located a base station (BS), which is often, but not always, near the centre of the cell. The base station, via microwave links, etc., is connected to a central control centre for mobile validation, etc., and then to the public switched network. When a mobile station (MS), is within a cell, and is making or receiving a call, it communicates with the base station of that cell. When the mobile moves into another cell, it communicates with the base station of the new cell.

The number of users a network can support is fundamentally dependent on the common air interface (CAI) over which users communicate. User capacity is dependent on many factors, but the main ones are: the amount of spectrum the regulators allocate, the size of the radio coverage area from a BS, and the amount of interference a particular radio link can tolerate.

Each BS transceives with a number of mobiles that reside within its radio coverage area. This area is known as a cell. For the purposes of design, the cell is hexagonally shaped, and is a separate entity from its surrounding cells. In practice, BSs are deployed so that each cell partially overlaps with other cells in the vicinities of their boundaries. It is this overlapping of cells that permits the mobile station to maintain near continuous communications with the called party whilst moving between cells.

Cells are arranged in clusters, and usually each cluster uses the entire allocated spectrum. In the simple case, the clusters are designed in a mosaic fashion so that the limited spectrum is repeatedly used over large geographic areas, with each cluster supporting the same numbers of users. In the more complicated cases, the cell sizes are different and the cluster sizes, that is the number of cells per cluster, are different. However, this discussion and this applet will consider only the simple case where the cell sizes are the same area and the cluster sizes contain the same number of cells. If, for example, the number of cells in a cluster is four, then the entire allocated bandwidth will be used for this cluster. This means that each of the four cells can be allocated a quarter of the available bandwidth. If each cell is labelled 1, 2, 3, 4, 5, 6 and 7, then the cells in adjacent clusters will also have their cells labelled 1, 2, 3, 4, 5, 6, and 7, where each numbered cell contains the same band of frequencies as its equivalent cell number in an adjacent cluster. Should cluster A, say have its cell 1, next to cell 1 in cluster B, then the problem of co-channel interference arises. This co-channel interference is contained to acceptable limits by keeping the distance at a maximum between cells containing the same bands. One of the objects in the planning of cellular systems is to maximize the distance between cells in different clusters, which operate on the same band of frequencies. Perhaps, now it can be seen why as a mobile travels from one cell to another, which may be in a different cluster and is certainly communicating with a different base station, it is assigned automatically, a different channel. That is, a different frequency - as each channel of the mobile operates on a different frequency.

This applet, permits the cluster size to be changed mentally. However, the number inside of each cell is allocated for a seven cell cluster with the centre cell left blank, for ease in identification. The size of the cells, that is the size of each cell's radius, is fixed, so that 385 cells can be displayed on the screen. The number of channels allocated to the cluster is the same as the allocated bandwidth for the system, for example, if each MS channel is 30 kHz wide, then for a cluster bandwidth of 25MHz, there will be 833 channels available (actually in practice, 832).

Microcell design

The minimum separation (Ds) required between two nearby co-channel cells is based on specifying a tolerable co-channel interference, which is measured by a required carrier-to-interference ratio (C/I)s. The (C/I)s ratio also is a function of the minimum acceptable voice quality of the system. In an AMPS system, (C/I)s is equal to about 18 dB (the point at which 75% of the users call the system "good" or "excellent") and the minimum required separation, based on (C/I)s = 18dB, is about 4.6R, where R is the radius of the cell (to the point where two faces of the hexagon join). In a cellular system, the number of cells K in a cell re-use pattern is a function of the co-channel separation Ds. For Ds = 4.6R, then K = 7. This means that a cluster of seven cells can share the entire allocated spectrum. In each of the two bands allocated for cellular in the USA (824-849 MHz mobile/869-894 MHz base) with the mobile channel spacing of 30 kHz, there are 832 voice channels, which gives about 119 channels, on average, per cell. In 1991, the conventional cellular systems in use since 1984 began to reach their capacity in the larger markets. In order to increase system capacity, approaches based on the co-channel interference reduction factor (CIRF) qs, were taken. The CIRF is defined for an AMPS system of cluster size K = 3 or 7, as,

where Ds is the minimum required distance between any two co-channel cells in a cellular system corresponding to the required carrier-to-interference ratio (C/I) received at both the cell site and the mobile unit in a cell. R is the cell radius, and K is the number of cells in a cell re-use pattern, or the number of cells in a cluster. K is also called the cell re-use factor. The above equation is derived from an idealized hexagonal cell layout and is commonly used. The applet permits verification of the above equation for K = 7, by increasing the length of a radial from a central cell, to reach into other clusters. The length of this radial in units of R when extended to reach a cell in another cluster with the same blank centre cell (same cell band as the central cell) gives a measure of the minimum required distance between any two co-channel cells. It is easily seen that for a cluster size of seven cells, where there are say seven clusters, a distance of 4.6R must be traversed before another cell of the same number is reached. The applet permits a circle to be drawn on selecting a cell. This circle can be used to identify other clusters by looking around the circumference of the circle for another blank hexagon. This blank hexagon will be the centre hexagon of another seven-hexagon cluster. Note that the most recently selected cell turns blue. This permits you to easily recognize the cell you have just selected from the others that are red. The red cells are those which were selected before the most recent blue.

Calculation of Carrier-to-Interference ratio

The in an AMPS system is based on two requirements. The first is, that all co-channel cells are at a distance of 4.6R away from the serving cell, and second is that, the value of qs = 4.6 . This second requirement is based on a C/I of 18dB, where the interference is received from six co-channel cells in the first tier. To calculate the C/I the following equation is used;

for i = 1,2,…n, j = 1,2,.. k
 where R1, is the radius of the serving cell, Di is the distance to the next cell at tier (ring) j, with the same number (frequency band) expressed in terms of R1. At a different distance from the serving cell, another tier (tier 2) will contain cells with the same channels, and again at another tier, etc., until tier k is reached.

For example, if a seven cell cluster is taken on the applet, then, there are six cells (n = 6), surrounding the serving cell at a distance Di = 4.583R1 at tier j=1 and another further four cells (n = 4), at a distance Di = 7.937 at tier j=2, and another two (n = 2), at Di = 9.165 at tier j = 3. If there are no further tiers (clusters outside of these seven surrounding the central cluster), then,

This 18.27 dB is confirmed by the applet's calculations which is more accurate than the above calculation because more decimal places are taken for the distances Di in the above calculation

If further tiers exist, it is expected that this would reduce the 18.27 dB even more. If the first tier contained six interferers, the second also six interferers and the third tier again six, the C/I would be 62.646 or 17.969 dB. The applet gives 17.967 dB. These interfering rings (which are close to being a worst case scenario) show why 18 dB is used in the AMPS system as a design criterion for C/I.
 
 

The Applet

Using Netscape 4.05, open the browser first full screen. Make sure the three personal toolbars on the browser screen are minimized by clicking on the triangle of each. This will ensure that you have enough room on your screen for the applet display. Select from the "file", "open page", the directory in which you stored the applet and then open the file "mobile.html". Do not click on any hexagon until you have aligned the display with the right hand scroll-bar. With the mouse, select a hexagon that has no number inside it. This hexagon is the centre of a surrounding cluster. The selected hexagon will turn blue and a C/I will be displayed on the top left- hand side of the screen in blue writing. On the right hand side will appear the x, y coordinate normalized to the cell radius R1, and the normalized radius of the circle will also be given. From the circle drawn through the selected hexagon, it is easy to find other hexagons that are blank. Each blank hexagon represents the centre cell of a seven-hexagon cluster. Choosing the next blank hexagon outside of this circle will cause another circle to be drawn in which other blank hexagons can be found.

Note that each time you select a different hexagon, it turns blue and the previous chosen hexagon turns red. The blue hexagon allows you to see the hexagon you have just chosen from the others, and read its coordinates as the bottom-most listing on the top right hand side of the screen. The C/I for the latest chosen hexagon, together with all of the others is displayed on the top left-hand side of the screen. Each time you select a hexagon, this number changes, reflecting the updated value of C/I as more interferers are added to the system.

You will notice that tier 1 has a maximum of six interferers, tier 2: six, tier 3:6, tier 4: 12, tier 5: 6, tier 6: 6, and tier 7: 12. In a real system, due to the geography of the land (you may be out at sea), you may not find that the maximum number of interferers per tier can be used.

The applet is sensitive to movement of the scroll-bar once a hexagon has been selected and will give erroneous selections if moved. Once set up, do not move the scroll bar or minimize the screen. If you make a mistake, then close down Netscape and reopen. Reloading Netscape will not help. The applet may not work with Explorer 4.

The source code (version 98/07/17) is available according to the GNU Public License.


Tony Townsend, tonyart@ieee.org