In any communication system, the received signal will consist of the transmitted signal, attenuated as it has propagated along the transmission media and suffering from some distortion due to the characteristics of the system. In addition, unwanted signals (or noise) may occur between the transmitter and the receiver which are added to the transmitted signal. Noise is the main factor that limits the performance of a communications system.

The effect of noise on a digital signal

The effect of noise on a digital signal

There are four categories of noise:

Shannon Limit

In 1924 Harry Nyquist derived an equation expressing the maximum data rate for a noiseless channel. Nyquist proved that if an arbitrary signal is run through a low-pass filter of a given bandwidth (H), the filtered signal could be completely reconstructed by line samples taken at a rate equivalent to twice the bandwidth. Sampling the line more frequently is pointless, because the higher frequency components that such sampling could recover have already been filtered out. If the signal consists of V discrete levels, Nyquist's theorem states:

Maximum data rate = 2H log2 V bits per second

In 1948 Claude Shannon took this work further and extended it to the case of a channel subject to random (thermal) noise. According to Nyquists, a noiseless 3 KHz channel cannot transmit binary (i.e. two-level) signals at a rate exceeding 6000 bits per second. If random noise is introduced, the situation deteriorates rapidly. The amount of thermal noise present in a signal is expressed as the ratio of signal power (S) to noise power (N), and is called the signal-to-noise ratio (SNR). The ratio will become smaller as the signal propagates through the transmission medium due to attenuation of the transmitted signal. The SNR is not usually usually expressed as a ratio. Instead, the value 10 log10 S/N is used. The unit thus derived is known as a decibel (dB). A signal-to-noise ratio of 10 would be expressed as 10 dB; a ratio of 100 as 20 dB; a ratio of 1000 as 30 dB and so on. Shannon found that the maximum data rate of a noisy channel with a bandwidth of H Hz, and a signal-to-noise ratio S/N is given by:

Maximum data rate = H log2 (1+S/N) bits per second

As an example, a channel of 3000-Hz bandwidth, and a signal to thermal noise ratio of 30 dB (typical parameters for an analogue telephone line) can never transmit much more than 30,000 bps, no matter how many signal levels are used, and no matter how frequently samples are taken. Shannon's result can be applied to any channel subject to Gaussian (thermal) noise. It should also be noted that this limitation is an upper bound, and real systems will rarely achieve it.