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FIGURE 9.31. Co-channel interference between a desired and an interfering cell.
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Co-channel interference will occur when the ratio of the received (e.g., wanted) signal envelope, S, to the interfering signal envelope, I, is less than some protection ratio pr (a threshold), that is [168], S I pr 9:48
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Now we consider only one co-channel cell as an i part of a cellular network, as shown in Figure 9.31. Assume that only propagation-loss effects are proportional to distances dMS and dI between the desired mobile subscriber and each of the desired and interfering BS, respectively. Then, S dg gI I dMS pr 9:49
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where g is the loss exponent. So, for a given protection we get [168 169] dI dMS pr 1=g 9:50
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In the case when the desired user lies along a straight line between two base stations (the worst case for a user), the co-channel reuse ratio is Q D=Rcell 1 dI =dMS 1 p1=g r 9:51
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For a given protection ratio and modulation scheme, this expression de nes the minimum spacing between co-channel cells in order to avoid interference. For six co-channel cells interferers (Fig. 9.32), which lie only in the rst tier of co-channel cells, we have instead of (9.49), the following expression [103]: S d g MS g I 6dI pr 9:52
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FIGURE 9.32. Scheme of how to eliminate the co-channel interference between neighboring cells operating at the same frequency band.
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The co-channel reuse factor can be expressed as [167] Q D=Rcell 6 S=I 1=g 9:53
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To see how these parameters in uence the co-channel interference occurrence, let us de ne some other parameters of the network. First, we assume that all users are uniformly distributed per cell with a blocking probability of service Pbl constant for all cells. Blocking probability is measured, by the number of users/calls that cannot be served during the period of service. The parameter A (in Erlangs) de nes the traf c intensity offered, where Erlang is a measure of traf c intensity de ning the quantity of traf c on a channel or group of channels (users) per unit time. Then the actual traf c carried is equal to A(1 Pbl ) Erlangs, and the so-called outgoing channel usage ef ciency or loading factor becomes [169] Z A 1 Pbl =nc 9:54
where nc is the total number of channels allocated per cell. We now assume that instead of an omnidirectional base-station antenna we have an adaptive one, which generates M ideal beams with a bandwidth of 2p=M, and a gain equal to that of omniantenna. Each adaptive beam will only carry the channels that are assigned to the mobiles within its coverage area. So, any mobile or group of mobiles can be tracked by using adaptive base-station antennas, as sketched in Figure 9.26.
As the occurrence of co-channel interference between subscribers is a statistical problem, instead of the probability of co-channel interference, Z, we use the outage probability, P S I pr . This probability determines the frequency of failing to obtain satisfactory reception at the mobile in the presence of interference. For identical cells, having equal probability of call blocking, there will be in average nc Z active channels in each cell. Then, for the omnidirectional base-station antenna, assuming the desired mobile is already allocated a channel, the probability of that channel being active in an interfering cell is the required outage probability, given by P S I pr number of active channels Znc Z nc total number of channels 9:55
Hence, when the desired mobile is in the region of co-channel interference for the omniterminal antennas, the outage probability is identical to the probability of cochannel interference. For adaptive antennas with M beams per base-station, we have nc Z=M channels per beam with a uniform distribution of subscribers. Here, a desired mobile is always covered by at least one beam from the co-channel cell. Then, the outage probability is equal to the probability that one of the channels in the aligned beam is the corresponding active co-channel (i.e., the channel that has been allocated to the desired mobile). Thus, this probability equals P S I pr number of channels per beam Znc =M Z  total number of channels nc M 9:56
Thus, the co-channel interference decreases with an increase in the number of antenna elements in the adaptive array or the number of beams in the multibeam antenna. Now using a simple geometry presented in Figure 9.31, it can be shown, that for the six co-channel cells in the rst tier, the outage probability at the regions of interference equals P S I pr  Z 6 M 9:57
that is, it decreases M 6 times with an increase of M. This means that there are six beams aligned onto the desired mobile at any time, and the outage probability within the region of interference is de ned by the probability that the active co-channel is in each of these beams. For more details the reader is referred to References [103,170 172]. It is the spatial ltering capabilities of adaptive antennas that reduce cochannel interference. In general, an adaptive array requires some information about the desired signal, such as the direction of its source, a reference signal, or a signal that is correlated with the desired signal. In situations where the precise direction of the signal is