Multiple Access and the Cellular Principle

1. An analog cellular system has 250 duplex channels available (250 channels in each direction). To obtain acceptable transmission quality, the relation between reuse distance (D) and cell radius (R) has to be at least D/R = 7. The cell structure is designed with a cell radius of R = 2km.

During a busy hour, the traffic per subscriber is on average one call of 2-minute duration. The network setup is modeled as an Erlang-B loss system with the blocking probability limited to 3%.

(a) Calculate the following:

(i) The maximal number of subscribers per cell.

(ii) The capacity of the network in Erlangs/km2. (Assume that the cell area is Acell= πR2.)

(b) The analog system above is modernized for digital transmission. As a consequence, the channel separation has to be doubled - i.e., only 125 duplex are now available. However, digital transmission is less sensitive to interference and acceptable quality is obtained for D/R = 4. How is the capacity of the network affected by this modernization (in terms of Erlangs/km2)?

(c) To increase the capacity of the network in B, the cells are made smaller, with a radius of onlyR = 1 km. How much is capacity increased (in terms of Erlangs/km2) and how many more BSs are required to cover the same area?

2. A system specifies a blocking level to be less than 5% for 120 users each with an activity level of 10%. When a user is blocked, it is assumed to be cleared immediately - i.e., the system is anErlang-B system. Assume two scenarios: (i) one operator and (ii) three operators. How many channels are needed for the two scenarios?