Editing Communication channel (section)

==Channel models==
Mathematical models of the channel can be made to describe how the input (the transmitted signal) is mapped to the output (the received signal). There exist many types and uses of channel models specific to the field of communication. In particular, separate models are formulated to describe each layer of a communication system.

A channel can be modeled physically by trying to calculate the physical processes which modify the transmitted signal. For example, in wireless communications, the channel can be modeled by calculating the reflection from every object in the environment. A sequence of random numbers might also be added to simulate external interference or electronic noise in the receiver.

Statistically, a communication channel is usually modeled as a [[tuple]] consisting of an input alphabet, an output alphabet, and for each pair ''(i, o)'' of input and output elements, a transition probability ''p(i, o)''. Semantically, the transition probability is the probability that the [[symbol]] ''o'' is received given that ''i'' was transmitted over the channel.

Statistical and physical modeling can be combined. For example, in wireless communications the channel is often modeled by a random attenuation (known as [[fading]]) of the transmitted signal, followed by additive noise. The attenuation term is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The noise in the model captures external interference or electronic noise in the receiver. If the attenuation term is [[Complex number|complex]] it also describes the relative time a signal takes to get through the channel. The statistical properties of the attenuation in the model are determined by previous measurements or physical simulations.

Communication channels are also studied in discrete-alphabet [[modulation]] schemes. The mathematical model consists of a transition probability that specifies an output distribution for each possible sequence of channel inputs. In [[information theory]], it is common to start with memoryless channels in which the output probability distribution only depends on the current channel input.

A channel model may either be digital or analog.

===Digital channel models===
In a digital channel model, the transmitted message is modeled as a [[digital signal]] at a certain [[protocol layer]]. Underlying protocol layers are replaced by a simplified model. The model may reflect channel performance measures such as [[bit rate]], [[bit error]]s, [[Network delay|delay]], [[delay variation]], etc. Examples of digital channel models include:
* [[Binary symmetric channel]] (BSC), a discrete memoryless channel with a certain [[bit error probability]]
* [[Binary asymmetric channel]] (BAC), similar to BSC but the probability of a flip from 0 to 1 and vice-versa is unequal
* Binary [[Burst error|bursty bit error]] channel model, a channel ''with memory''
* [[Binary erasure channel]] (BEC), a discrete channel with a certain bit error detection (erasure) probability
* [[Packet erasure channel]], where packets are lost with a certain [[packet loss]] probability or [[packet error rate]]
* [[Arbitrarily varying channel]] (AVC), where the behavior and state of the channel can change randomly

===Analog channel models===
In an analog channel model, the transmitted message is modeled as an [[analog signal]]. The model can be a [[linear]] or [[non-linear]], [[Discrete time and continuous time|time-continuous or time-discrete (sampled)]], [[memoryless]] or dynamic (resulting in [[burst error]]s), [[time-invariant]] or [[time-variant]] (also resulting in burst errors), [[baseband]], [[passband]] (RF signal model), [[Real number|real-valued]] or [[complex-valued]] signal model. The model may reflect the following channel impairments:
* [[Electronic noise|Noise]] model, for example
** [[Additive white Gaussian noise]] (AWGN) channel, a linear continuous memoryless model
** [[Phase noise]] model
* [[Interference (communication)|Interference]] model, for example [[crosstalk]] ([[co-channel interference]]) and [[intersymbol interference]] (ISI)
* [[Distortion]] model, for example a non-linear channel model causing [[intermodulation distortion]] (IMD)
* [[Frequency response]] model, including [[attenuation]] and [[phase-shift]]
* [[Group delay]] model
* Modelling of underlying [[physical layer]] [[Transmission (telecommunications)|transmission]] techniques, for example a complex-valued [[equivalent baseband model]] of [[modulation]] and [[frequency response]]
* [[Radio frequency propagation model]], for example
** [[Log-distance path loss model]]
** [[Fading]] model, for example [[Rayleigh fading]], [[Ricean fading]], log-normal shadow fading and frequency selective (dispersive) fading
** [[Doppler shift]] model, which combined with fading results in a [[time-variant system]]
** [[Ray tracing (physics)|Ray tracing]] models, which attempt to model the signal propagation and distortions for specified transmitter-receiver geometries, terrain types, and antennas
** [[Propagation graph]], models signal dispersion by representing the radio propagation environment by a graph. 
** [[Mobility model]]s, which also causes a [[time-variant system]]