Introduction to Wireless Systems--A Tutorial--Part II

Cellular Concepts
Interference control is the key to allowing reuse of channels within a given geographic area. We therefore begin our discussion of cellular concepts by developing a simple model to predict the interference levels caused by geographically separated transmitters operating on a common channel.

Consider two cells whose base stations (BS₁ and BS₂ respectively) are separated by a distance D. Each base station has a circular coverage area of radius R as shown in Figure 4.1. Assume that the propagation environment is uniform within and completely surrounding the two cells and that the path-loss exponent is ½. Let the two base stations receive on the same channel, with center frequency f₁. Also shown in Figure 4.1 are two mobile units, MU₁ and MU₂, served by base stations BS₁ and BS₂ respectively. The mobile units are located at the boundaries of their respective cells, each at distance R from its base station. To keep the discussion simple, we consider transmission on the reverse channel, from mobile unit to base station, only.

From our work in Chapter 3, the level of the signal received at base station BS₁ from mobile unit MU₁ can be expressed as:

where K₁ is a constant that incorporates the transmitter power, the antenna gains, the antenna heights, and so on. The received signal level at base station BS₁ from mobile unit MU₂ can be written:

Now from the perspective of base station BS₁, P₁ represents "signal" and P₂ is cochannel interference. The signal-to-noise-and-interference ratio at base station BS₁ is:

Where P_n is thermal noise referred to the base station input. When the receiver noise is significantly greater than the interference--that is, when P_n > > P₂--we describe the system as "noise limited," as explained earlier. For this case:

When the received noise is significantly less than the interference--that is, when P_n < < P₂--the system is "interference limited." Then we can write:

For identical mobile units transmitting at the same power level, the previous Equation becomes:

The locations of the mobile units in Figure 4.1 have been chosen to illustrate the worst case of signal-to-interference ratio (SIR). Mobile unit MU₁ is at the perimeter of its cell, as far as possible from the base station serving it. Mobile unit MU₂ is also at the perimeter of its cell, as close to base station BS₁ as it can get while remaining in the cell served by BS₂. It should be evident that for this geometry the signal-to-interference ratio would be the same if we calculated it at base station BS₂ or at either mobile unit.

In a realistic cellular system there are likely to be more than two cells, and cochannel interference may come from more than one source. If there are J cells surrounding base station BS₁, each containing a mobile unit, and all of these mobile units are transmitting on the same channel, then the signal-to-interference ratio at BS₁ can be written

where P_j, j = 2,...,J = 1 represent cochannel interference from mobile units in the surrounding cells. In the discussion that follows, we will see that in the most important case all of the interference sources are identical, and all are located at distances approximately D from the base station BS receiver. In this case Equation (4.9) becomes