Wireless Networks and Shannon’s Law

All wireless networks (Wi-Fi, Bluetooth, 3G, LTE, etc.) operate using radio signals. Because they operate over the radio, all communication methods have a maximum channel capacity, regardless of technology. This maximum capacity was which is determined by the same underlying principles of information theory developed by Claude Shannon during World War II, known as Shannon-Hartley theorem or Shannon’s Law. Shannon’s Law states that This capacity relationship can be stated as:

$$ {C=W\log _{2}\left( 1+{S \over N} \right)} $$

where:

\(C\) is the capacity of the channel, measured in bits per second

\(W\) is the available bandwidth, measured in hertz

\(S\) is the power of the received signal, measured in watts

\(N\) is the power of the received noise, measured in watts

Shannon’s work showed that the values of \(S\), \(N\), and \(W\) set a limit upon the transmission rate — the two fundamental constraints on achievable data rates are the amount of available bandwidth and the ratio of signal to noise between the receiver and the sender.

Bandwidth

All radio communication uses a shared channel, radio waves, that is divided into frequency ranges or frequency bands. To communicate between a sender and receiver, both parties must first agree on the specific frequency they will use. Per Shannon’s model, the frequency range chosen has an effect on performance. The variable \(W\) in Shannon’s model shows that as the available bandwidth in the frequency range increases, so does the capacity of the channel. All else being equal, a doubling in frequency can double the channel capacity.

Increasing channel capacity is only one concern with radio networks because not all frequency ranges offer the same characteristics. Generally speaking, low-frequency signals can travel farther, but require larger antennas to propagate the signal. They are also generally busier and have more clients using the frequency at the same time. High-frequency signals don’t travel as far, but because they have higher bandwidth they can transfer more data at a time, requiring more (though cheaper) antennas.

All applications should perform well regardless of underlying connectivity. As a user, you should not care about the underlying technology in use, but as developers we must think ahead and architect our applications to anticipate the differences between the different types of networks.

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Signal and Noise

The second fundamental variable in Shannon’s Law is the ratio of signal to noise between the sender and receiver. This ratio is a measure of the power of the desired signal compared to the power of background noise in the frequency range. If there is a large amount of background noise, the signal needs to be stronger to carry useful information. In an ideal case, there would be no background noise or interference in a frequency range. Unfortunately, that’s not typically the case. Frequency ranges are limited, and there are now many wireless devices using the same range — we have to deal with some amount of background noise. To maximum channel capacity, then, we need to either increase the power of the signal by using stronger and more powerful radios, decrease the distance between sender and receiver to limit the effect of background noise, or do both.

Modulation

Another factor that influences the performance of wireless networks is how data is encoded and decoded during transmission. When a digital signal is sent over a radio, we need to convert binary \(1\)s and \(0\)s to analogue radio waves, using a modulation algorithm.

If you are old enough to remember dial-up modems (which stands for modulator-demodulator) you may be familiar with the process of modulation. A telephone line is designed to transfer analogue sounds, not digital bits. For a computer to communicate over such a medium the bits need to be converted into audio tones using the modem. The number of tones the modem can play per second limits the rate of the connection over the telephone line. Wireless networks work similarly, by converting a digital signal to a radio signal using by encoding different bits as radio frequencies, amplitudes, or phases using some known modulation methods.

Wireless in the Real World

Wireless use in the real world is limited by a small number of well-known variables: bandwidth and signal-to-noise ratio. These variables are encoded in Shannon’s Law and are used extensively in the design and deployment of all wireless technologies. In addition, the digital signal must be converted to an analogue signal, and the technique used can affect overall performance of the network. Frequency ranges being a shared medium are subject to many real-world factors that alter the performance and reliability of the network, including noisy neighbours, competing frequencies, and physical obstructions to the signal. If you want maximum throughput of a wireless network, you should remove any noise and interference you can control, place your receiver and sender as close as possible, increase the signal power as much possible, and use the best modulation method available.

More References

This article provides an introduction to wireless communication theory. If you want to learn more, there are several great resources to choose from:

See also

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