 Hello everyone, welcome to a video lecture on interference and system capacity. I am K.R. Biradhar, Assistant Professor, Department of Electronics and Telecommunication Engineering, Walsh and the Institute of Technology, Shalapur. Let us start with the learning outcomes first. At the end of this video, students will be able to explain interference in cellular system. Introduction. Interference is the major limiting factor in the performance of cellular system. If there is any increase in interference, we will degrade the cellular system performance. The various sources of interference are, it could be another mobile in the same cell or maybe call is in progress in the neighboring cell or other base stations operating in the same frequency band or it may non-cellular system leaks energy into the cellular frequency band. There are two major sources of interference in cellular system. Those are co-channel interference also known as CCI. Second one, adjacent channel interference also known as ACI. Co-channel interference is caused due to the cells that reuse the same set of frequency. These cells use the same frequency set or called co-channel cells. Adjacent channel interference is caused due to the signals that are adjacent in frequency. Concentration interference and system capacity. We have seen the concept of frequency reuse that means there are several cells that use the same set of frequencies that is in co-channel cells which will introduce co-channel interference. We have seen the concept of frequency reuse that means there are several cells that use the same set of frequencies that is in co-channel cells which will introduce co-channel interference. There is a way to reduce co-channel interference that is co-channel cell must be separated by a minimum distance. When the size of the cell is approximately same, co-channel interference is independent of the transmitted power. Concentration interference depends on or a function of radius of the cell R and distance between center of the nearest co-channel cell. Increasing the ratio Q is equal to capital D divided by capital R where capital D is the distance between center of the nearest co-channel cell and R is the radius of the cell. Increasing the ratio interference is reduced that means increasing the distance between co-channel cells and decreasing the radius of the cell where Q is called co-channel reuse ratio. For a hexagonal geometry Q is equal to capital D divided by capital R which is equal to square root of 3 into capital N where N is called the cluster size. A small value of Q provides large capacity of cellular system and also large value of Q improves the signal transmission quality, smaller value of co-channel interference. A trade-off must be made between these two objectives. On the table we can understand that for i is equal to 1 and j equal to 1 for large capacity with less value of Q whereas i is equal to 1 and j equal to 3 increases cluster size and also capacity decreases with increase in value of Q. In other words we can conclude that as we increase the cluster size at the same time decrease the capacity of the cellular system and increase the value of Q. Let small i0 be the number of co-channel interfering cells. The signal to interference ratio S i r for a mobile receiver can be expressed as S by i is equal to S divided by summation i equal to 1, 2, i0, ii where S is the desired signal power, ii be the interference power caused by the ith transferring co-channel cell base station. The average reshoot power at a distance D from the transmitting antenna is approximated by P suffix r is equal to P suffix 0 into D divided by D suffix 0 raise to minus N. Here small n is the path loss exponent which ranges from 2 to 4. When the transmitting power of each base station is equal the signal to interference ratio for a mobile can be expressed as or can be approximated as S by i is equal to r raise to minus N divided by summation i equal to 1, 2, i0, di raise to minus N where r is the radius of the cell. D is the distance between co-channel cells. Consider only the first layer of interfering cells. The signal to interference ratio is given by S by i is equal to D divided by r raise to N both are capital divided by i0 which is equal to square root of 3 into capital N whole raise to small n divided by i0. Here i0 is equal to 6 because it is a 6 layer or first layer consists of 6 cells. Adjacent channel interference interference from adjacent infrequency to the desired signal that means interference occurred due to adjacent channels because these channels will have similar frequency. In perfect receiver filters allow nearby frequencies to leak into the pass band that is why we need to use a perfect filter so that we can avoid maximum possible adjacent channel interference. Interference degrade seriously due to near for effect. The figure shows that without using a proper filter we can find there is a unwanted signal which has a signal amplitude almost same as the desired signal amplitude. But when you have a proper filter the interference can be reduced and almost negligible therefore adjacent channel interference can be minimized through careful filtering and channel assignment. Give the frequency separation between each channel in a given cell as large as possible. A channel separation greater than 6 is needed to bring the adjacent channel interference to an acceptable level. In this slide we shall see a problem for a given path loss exponent n is equal to 4 find the frequency reuse factor and the cluster size that should be used for maximum capability. The signal to interference ratio of 15 dB is minimum required for satisfactory forward channel performance of a cellular system. There are 6 co-channel cells in the first tire and all of them are at the same distance from the mobile pass the video and try to solve this problem thank you. I think you might have solved this problem let us see the answer for this problem path loss exponent for the system is given which is n equal to 4. Let us consider a 7 cell reuse pattern that means here n is equal to 7. Frequency reuse factor Q is equal to capital D divided by capital R which is equal to square root of 3n here n is equal to 7 that means square root of 3 into 7 is equal to square root of 21 which is approximately equal to 4.583. The signal to noise interference ratio is given by S by i is equal to 1 by 6 into 4.583 raise to n 4.583 already we have calculated which is a Q raise to n that is equal to 70.3. In dB it can be expressed with a value of 18.66 dB since this is greater than the required signal to interference ratio which is 15 dB therefore, a system with cluster size n equal to 7 can be used. If let us consider 4 cell reuse pattern here n is equal to 4 Q is equal to D by R which is equal to square root of 3 into n which is equal to square root of 12 which is equal to 3.46 dB S by i equal to 13 dB since this is less than the required signal to interference ratio therefore, n is equal to 4 cannot be used. These are the references I refer to prepare the above presentation thank you.