# What Is a Channel Model?

A channel model is a mathematical representation of the effects of a communication channel through which wireless signals are propagated. The channel model can represent the power loss incurred by the signal as it travels through the wireless medium. In a more general case, the channel model is the impulse response of the channel medium in the time domain or its Fourier transform in the frequency domain. The channel impulse response of a wireless communication system typically varies randomly over time.

Channel models can be classified in four categories:

1. Path loss
2. Purely stochastic
3. Spatial
4. Ray tracing

## Path Loss

Path loss channel models represent the power reduction of a transmitted signal as it traverses the wireless medium. They do not perform any filtering on the signal. These channel models are based on the medium through which the signal travels, such as free space, rain, fog, or gas. You can use the `fspl` function in MATLAB to calculate the free space path loss for a communications link.

## Purely Stochastic

Purely stochastic channel models address thermal noise generation and multipath fading channels. They do not require any knowledge of the geometry of the link being modeled. An additive white gaussian noise (AWGN) channel models the electronic noise in a receiver front end. This noise is spectrally flat, and its amplitude follows a Gaussian pdf. You can use the Communications Toolbox™ `awgn` function to simulate the addition of this noise to a signal.

A multipath fading channel exhibits delay spread, in which multiple copies of the transmitted signal arrive at the receiver. These copies typically are attenuated and phase shifted relative to the original. This channel can be modeled with an impulse response. The figure below shows a MATLAB time domain plot of a representative impulse response.

MATLAB impulse response plot.

The delay spread of a channel is the time duration between the first and last multipath components with significant energy. If the reciprocal of the delay spread is much greater than the signal bandwidth, then the fading is called frequency flat. If that reciprocal is comparable to or less than the signal bandwidth, then the fading is called frequency selective. The MATLAB figure below shows the response of a frequency selective channel with the impulse response above.

Frequency selective channel frequency response.

## Spatial

Modern wireless systems typically use beamforming to direct energy toward desired receivers and away from interferers. Beamforming requires a transceiver to use antenna arrays, giving rise to multiple-input multiple-output (MIMO) systems. Spatial channel models were developed to better represent MIMO links, since previously developed channel models did not account for array geometries and array responses. As the name suggests, these channel models enable the prediction of the angles of departure (AoD) and arrival (AoA) of signals in a wireless system. These models typically define scatterers that reflect transmitted signals to a receiver. The diagram below depicts these scatterers, also known as clusters, with two circles.

Scatterers between a transmitter and receiver.

The WINNER II channel model is one such spatial channel model (SCM), and it utilizes a cluster delay line (CDL) to model individual links and multi-link systems.

## Ray Tracing

Where spatial channel models do not explicitly specify the locations of scatterers, ray tracing channel models do. They use precise building location information to generate outdoor channel models, and precise room information to generate indoor models. One output of a ray tracing analysis is an impulse response that can be used to filter an input signal.

The figure below shows a representative point-to-point analysis between a transmitter and receiver in an actual urban environment, generated by the Communications Toolbox `raytrace` function.

Urban point-to-point analysis.

## Why Are Channel Models Important?

• They are essential to predict link performance (e.g., BER) in a single-user scenario.
• They are crucial to predict system performance (e.g., throughput, latency) in a multi-user scenario.
• They reduce the need for costly channel measurement projects.

Communications Toolbox, 5G Toolbox™, WLAN Toolbox™, LTE Toolbox™, and Phased Array System Toolbox™ provide numerous channel models in all of the above categories, for both generic and standards-based applications.

## Software Reference

#### Ray Tracing

See also: wireless communications, OFDM, massive MIMO, RF system, 5G wireless technology, 5G Toolbox, LTE Toolbox, WLAN Toolbox, Communications Toolbox, Phased Array System Toolbox, DVB-S2, Bluetooth mesh, link budget, wireless network, Bluetooth interference

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