Mobile phone, Bluetooth and Wi-Fi technologies

Bluetooth – short-range wireless data transmission link used to connect small devices up to a max 20-3om apart.

Wi-Fi – is a wireless technology that enables devices such as printers and laptops to be connected together to form a LAN (Local area network), and which enables laptop computers and mobile devices to connect to the internet via Wi-Fi access points

Attenuation in networking

Attenuation is the loss of signal strength in networking cables or connections. Any wave – water, sound or electromagnetic attenuates (dies away) with increasing distance from the source. Attenuation in wireless technology may look like a disadvantage but it actually has benefits.

Quantifying attenuation of an electromagnetic wave

Quantifying: express or measure the quantity of

The inverse square law

After travelling a distance of 1 unit, the power of the wave is spread out of one square. At two units or twice the distance, it is spread out over four times the area. At 3 units or 3 times the distance, it is spread out over 9 squares. So the receiving antenna at two units collects a 1/4 of the power it would at one unit. At three units, it would collect 1/9 of the power it would collect at one unit. This reduction in power in proportion to the square of the distance is called inverse square law.

Note: units of distance do not matter.

The inverse square law concerns relative power only. We cannot say what the actual relative power will be at 2km from the transmitter without further information. For example, if we knew that at 1km the power received by the antenna was 8nW, we could calculate that at 2km, the power would be 1/4 of 8nW or 2nW

the received power is proportional to 1/d²

So if the distance was 3km. the receiving power is (1/3)² or 1/9th of that collected at d=1

Q: A rambler with her mobile phone starts her walk at 1km from a mobile phone mast. By the time she is 6km from the mast, what fraction of signal power will her phone receive using reverse square law? If the power received was 0.5nW. What will the power be at 6km?

A: (1/6)² or 1/36 of the signal at 1km. If the power received was 0.5nW, the power at 6km will be 1/36 if that or 0.138 nW

If the rambler had an app, showing her signal strength received, and it was showing 0.125 nW, she would be 2km away from the mast. This is because the original signal strength at 1km was 0.5km, and 0.125 nW is a quarter of 0.5km, meaning she is double the distance away. Given the starting unit was 1km, she is now 2km away.

Inverse cube and inverse fourth power

There is additional attenuation introduced by atmosphere, weather conditions, topographical features such as natural terrain or buildings/traffic. Such situations are hard to model mathematically, but measurements have shown in urban environments, an inverse cube model (1/d)³ or inverse fourth power (1/d)4

Inverse Square Inverse Cube Inverse fourth power
power reduced by a factor of
Double distance 4 8 16
Triple distance 9 27 81
Four times distance 16 64 256
Five times distance 25 125 625

Cellular Systems

Attenuation can be advantageous for wireless communications. It means, that beyond a certain distance, devices operating on the same frequency band will not interfere with each other and so can be reused.

In mobile telephony, this is exploited by using cells. Hence the original term cellular telephony.

Note: Most cellular diagrams are represented by hexagonal shapes because hexagons tessellate, they cover a completely flat surface without leaving gaps. This is just for the convenience of representation.

Cells are clustered together to allow frequency re-use. Cells in a highly-populated area are smaller to allow for a larger number of users. I think this is why occasionally when we all flock to a certain point (such as for a fireworks display, or for a festival) we struggle for data, as the local cell is temporarily overloaded.

A seven-cell cluster is a common type of cluster, with a central cell surrounded by six adjacent cells. Each cell has a base station operating on a particular frequency. Other numbers of cell clusters are also used.

Digitisation and modulation.

How to convert a binary bitstream into a form suitable for radio transmission

Converting an analogue audio signal to digital form uses two main processes.

Sampling – to measure the instantaneous amplitude of the analogue sound at regular intervals. The results are a set of voltage levels that represent the sounds signal at the instant it was recorded.

Quantisation – divides the maximum voltage range into a number of discrete voltage bands. Each band is now represented by a number, so the result is a string of numbers, where each number represents a particular voltage of the sound.


If the sound is sampled too slowly and is a wrong impression of the original this is called aliasing

If you record audio using too low a sample rate, a kind of sampling error called aliasing can occur. With regards to audio, aliasing is defined as the misidentification of a signal frequency, which can introduce distortion or other artifacts into the recording. (accessed Feb 2022)

Aliasing is avoided by a simple rule. Sampling Theorem or Nyquist frequency. If a signal extends from very low frequencies to a maximum of B Hz, it must be sampled more frequently than 2B times per second.

The main basis in signal theory is the sampling theorem that is credited to Nyquist [1924] —who first formulated the theorem in 1928. The sampling theorem essentially says that a signal has to be sampled at least with twice the frequency of the original signal. – (accessed Feb 2022)