Imperfections of the Transmission Channel

No transmission channel is perfect. As a signal travels from sender to receiver, it is inevitably degraded by various unwanted effects. These impairments can be broadly categorized into two types: multiplicative disturbances, which alter the signal itself, and additive disturbances, which mix the signal with unwanted noise.

Multiplicative Disturbances (Distortions)

Multiplicative disturbances occur when the output signal is the result of the input signal being multiplied by some time-varying disturbance function. The effect of the disturbance depends on the instantaneous value of the signal itself. They are mainly caused by changing parameters of the transmission path.

Types of Distortion

• Linear Distortion: This type alters the signal's amplitude or phase differently for different frequencies but does not create new frequencies. 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 (like an overdriven amplifier). It's particularly problematic as it generates new, unwanted frequency components in the signal.
  • 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 (Noise)

Additive disturbances occur when an unwanted signal is added to the useful signal. This is the most common category of impairment, collectively known as noise. It originates from sources both outside and inside the communication system.

External Noise Sources

• Interference: Disturbances from other telecommunication systems or electrical devices (e.g., crosstalk from adjacent cables, interference from electric motors).
• Atmospheric Noise: Caused by natural phenomena like lightning. It is impulsive and primarily affects lower radio frequencies (below 30 MHz).
• Cosmic Noise: Electromagnetic radiation from space (e.g., from the Sun or other galaxies), mainly relevant to satellite communications and radio astronomy.

Internal Noise Sources

• Thermal Noise (Johnson-Nyquist Noise): The most fundamental noise source, caused by the random thermal motion of charge carriers (electrons) in all conductive materials. It is often 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.
• Shot Noise: Arises in semiconductor devices due to the discrete nature of electric current, which consists of individual electrons arriving randomly.
• Flicker Noise (1/f Noise): A type of noise whose power spectral density is inversely proportional to the frequency. It is significant only at very low frequencies in semiconductor devices.