The signal to interference ratio (SIR), is the quotient between the average received modulated carrier power (C) and the average received co-channel interference power (I).

The signal to noise ratio (SIR), also known as the carrier to interference ratio (CIR), which is the signal to noise  ratio (SNR) of a modulated signal before modulation. By using directional antennas, a given cell will receive interference and transmit with only a fraction of available co-channel cells. The technique for decreasing co-channel interference and thus increasing system capacity by using directional antennas is called sectoring.

The factor by which the co-channel interference is reduced depends on the amount of sectoring used. A cell is normally portioned into three 120̊ sectors or six 60̊ sectors as shown in fig.

Let us assume 7 cell reuse in cellular system in which an average call last 2 minutes and the probability of blocking is to be 1% and assuming that every subscriber makes 1 call per hour on average. for the case of 120̊ sectors, the no. of interferers in the first tier is reduced from 6 to 2 because of only 2 of the 6 co-channel cells receive interference with a particular sectored channel group.

Now employing 120̊ sectoring, as we know there are 19 channels per antenna sector because of (57/3 antennas)

Where, traffic channels= 57

And, sector= 3

Therefore, antenna sector= 57/3 = 19 channels.

For the same probability of blocking and average call length, it can be found from the Erlang B Distribution that each sector can handle 11.2 Erlang or 336 calls per hour.

Since, each cell = 3 sectors

Cell capacity= 3 x 336 = 1008 calls per hour

Trunk efficiency= 24%

Which amounts to a 24% decreaseswhen compared to the unsectored case.

Thus, sectoring decreases the truck efficiency while improving the S/I for each user in the system. It can be found that using 60̊ sectors improves the S/I even more