Question

(30 pts) Assume that a circular cell has 57 channels and a cell radius of 10 km. The transmit power of the base station in this cell is 32 W. The path loss exponent in this cell is assumed to be 4. The grade of service is established to be a probability of blocking of 5% (assuming blocked calls are cleared). Assume the average call length is two minutes, and each user averages two calls per hour. Further, assume the cell has just reached its maximum capacity and must be split into four new microcells to provide four times the capacity in the same area. a) (5 pts) What is the current user capacity of this cell? b) (10 pts) What is the radius and transmit power of the new cells? c) (5 pts) How many channels are needed in each of the new cells to maintain frequency reuse stability in the system? d) (10 pts) If traffic is uniformly distributed, what is the new traffic carried by each new cell? Will the probability of blocking in these new cells be below 0.1% after the split? Assume 57 channels are used at the original base station and the split cells.

Please solve it in one hour !!!

Answer 1

Answer -

   Given,

   $\small \mu$ = 2 calls/hour

   H = 2 minute/call

GOS = 5%

C = 57 channels

So,

     $\small A_{\mu}=\mu.H$

   $\small A_{\mu}=\left ( \frac{2}{60} \right ).2=0.0667Erlangs$

From Erlang B chart, we have,

A = 50 Erlangs

Hence, current user capacity is,

     
А U 50 0.0667 750

current user capacity = 750 users.

(b) Since the 4 new cells must cover the the area of the old cell, the radius of the new cells must be half the radius of the old cell.

Given,

   Radius of old cell = 10 km

So,

   Radius of new cell = radius of old cell / 2 = 5 km

To maintain the same SNR, the power at the edge of the new cells must equal the power at the edge of the original cell.

Transmit power of old cell = 32 W

So,

   Transmit power of new cell = Transmit power of old cell / 24

   Transmit power of new cell = 32 / 16

   Transmit power of new cell = 2 W

(c) To maintain frequency reuse stability in the system, 4 cells are neede. So, 4 x 57 = 228 channels are needed in new cells.

(d) Now,

New traffic carried by each new cell = Traffic carried by old cell / number of new cells

   New traffic carried by each new cell = 50 / 4 = 12.5 Erlangs.

  For C = 57 channels, GOS = 0.1 % from Erlang B chart, we have,

A $\small \approx$ 38 >> 12.5 Erlangs.

  Therefore, the probability of blocking in these new cells will be below 0.1%.