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.