Channel Interference and Noise

Transmission-channel impairments

A transmission channel changes the signal between the sender and receiver. The analysis distinguishes multiplicative disturbances, which change the signal amplitude or phase, from additive disturbances, which add an unwanted component to it.

Multiplicative disturbances

A multiplicative disturbance can be represented as the input signal multiplied by a time-dependent function. For an input x(t), the output has the form y(t) = a(t)x(t), so the effect depends on the instantaneous signal value and the transmission-path parameters.

Types of Distortion

• Linear distortion: This type changes the signal's amplitude or phase as a function of frequency. A linear time-invariant path does not create new frequency components. Examples include fading in wireless channels or changes in cable attenuation due to temperature.
• Non-linear distortion: This occurs when the signal passes through a non-linear component, such as an overdriven amplifier. The component generates new, unwanted frequency components.
  • Harmonic distortion: If the input signal has a frequency $f$, new signals appear at integer multiples of this frequency ($2f, 3f, 4f, ...$).
  • Intermodulation distortion: If the input signal contains two or more frequencies ($f_1, f_2$), new frequencies that are sums and differences of the originals ($f_1 \pm f_2, 2f_1 \pm f_2$) are created.

Additive disturbances

An additive disturbance occurs when an unwanted component is added to the useful signal. The sum of such components is commonly called noise, and it can originate outside or inside the communication system.

External noise sources

• Interference: Disturbances from other telecommunication systems or electrical devices, such as crosstalk from adjacent cables and interference from electric motors.
• Atmospheric noise: Caused by natural phenomena such as lightning. It is impulsive and is especially relevant in lower radio bands, including frequencies below approximately 30 MHz.
• Cosmic noise: Electromagnetic radiation from the Sun, the Milky Way, and other strong extraterrestrial sources. It is relevant to satellite communications and radio astronomy.

Internal noise sources

• Thermal noise (Johnson-Nyquist noise): Caused by the random thermal motion of charge carriers, including electrons, in conductive materials. Over the band being analyzed it can be modeled as white noise. Its power is given by:
  $P_N = k \cdot T \cdot B$
  Where $k$ is Boltzmann's constant, $T$ is the absolute temperature in Kelvin, and $B$ is the bandwidth in Hertz. For a matched resistive source model, the formula gives the noise power available in that band.
• Shot noise: Arises in semiconductor devices from the discrete nature of electric current and the statistical variation of carrier flow.
• Flicker noise (1/f noise): Its power spectral density is approximately inversely proportional to frequency. It usually dominates at low frequencies in semiconductor devices.