## Example 2.3

#### A digital cellular telephone system is required to work at a bandwidth efficiency of 4 bits/second/Hz in order to accommodate sufficient users to make it profitable. What is the minimum Eb/N0 ratio that must be planned for in order to ensure that users on the edge of the coverage area receive error-free communication?
If the operator wishes to double the number of users on his existing network, how much more power must the base-station and handsets radiate in order to maintain coverage and error-free communication?

### Solution

#### The Shannon–Hartley theorem can be written as: C/B = log2[1 + Eb.C/N0.B]
Now, the bandwidth efficiency is required to be C/B = 4 bits/second/Hz, thus:
4 = log2[1 + 4Eb/N0]
Therefore:
Eb/N0 = (24 – 1) / = 3.75 or 5.74 dB.
In order to double the number of users for the same operating bandwidth, the bandwidth efficiency of the system must be increased to 8 bits/second/Hz. This means that the Eb/N0 value must rise to:
Eb/N0 = (28 – 1) / 8 = 31.87 or 15 dB
Thus the transmitted power must increase by a factor of 15.03 – 5.74 = 9.29 dB.