In radio technology, a radio channel is a frequency or a frequency range on which a radio signal is transmitted, e.g. B. analog voice or digital data. The bandwidth of the channel determines the amount of information that can be sent over it per unit of time. The larger the bandwidth selected, the more data can be transmitted, but the fewer channels fit (without overlapping) in a certain frequency band . In addition, the bandwidth is decisive for spatial signal fluctuations. In the case of digital transmission, one speaks of the data rate of a channel.

Depending on the intended use, channel grids were defined on certain frequency ranges . These indicate the distance from one radio channel to the next and often also its type of modulation .

## Time variance and frequency selectivity

In the case of a radio channel, there is basically multipath propagation. Propagation paths can be represented according to amount and phase (as a complex quantity). The transmission function of the radio channel can be understood as the ratio between the transmit and receive voltage. The transfer function is shown below. Here only the amount of the transmission voltage is considered, so that the phase of the reception voltage directly represents the phase of the transfer function. ${\ displaystyle {\ underline {G}} (f, t)}$

${\ displaystyle {\ underline {G}} (f, t) = {\ frac {{\ underline {U}} (f, t) _ {\ text {RX}}} {| {\ underline {U}} (f, t) _ {\ text {TX}} |}}}$

The radio channel is not an LTI (linear time-invariant) system. This comes about, for example, when the weather changes along a transmission path or when the transmitter and / or receiver move. This is why one speaks of time variance. The radio channel can be described in the time domain in such a way that if the channel is excited with a harmonic oscillation at the input, a changed signal occurs at the output. The change corresponds to an amplitude and phase modulation of this oscillation. This effect is due to the fact that the magnitude and phase of the transfer function change over time, as is also the case with the two types of modulation mentioned.

The voltage at the receiving antenna is basically frequency-dependent, which is due to physical effects, e.g. B. on the clearance attenuation . One speaks of "frequency selectivity". The English is used to describe the frequency selectivity of a radio channel in the time domain. "Power Delay Profile" with the parameter "Pulse broadening". The "Power Delay Profile" shows the time at which power from multipath signals is received. You can now calculate the average running time and see how much the “Power Delay Profile” deviates, which is given as the standard deviation. One also speaks of pulse broadening. The greater this is, ie the greater the difference in transit times of the signal arriving on several paths, the more frequency-selective a radio channel is. ${\ displaystyle \ tau}$

## Bandwidth

Basically, the following applies: the broader a signal, the less likely it will be the simultaneous cancellation of all frequencies in a point in space due to interference. This means that the reception of a broadband signal (several gigahertz bandwidth) is spatially more constant than with z. B. the rather narrow-band Bluetooth.

## Modeling

The aim of modeling a radio channel is to predict the received signal at any spatial point. Channel models can be used to calculate the impulse response . This means that the radio channel can be described correctly mathematically by a suitably good model. A basic distinction is made between four approaches to modeling:

1. Deterministic channel models
2. Stochastic channel models
3. Geometric-stochastic models
4. Simplified channel models

In the case of deterministic channel models, a realistic, three-dimensional simulation of the scenario is necessary. This includes material properties such as permittivity or electrical conductivity . The first category can be broken down into two basic approaches. The most complex method is based on the solution of Maxwell's equations in order to be able to predict the field strength in each point in space. It is easy to understand that this method requires a lot of storage space and requires good computing power. In addition, there is the ray-optical process ("ray tracing"). Possible propagation paths are searched for and the received signal is calculated taking into account diffraction, scattering and reflection. Both methods can be used in a room (e.g. living room) or on an entire radio cell (cellular network in a city).

With stochastic channel models z. For example, the “Taped Delay Line” channel model shows a direct path (without houses in between, based on the example with the radio cell). In addition, there are now pseudo-randomly delayed propagation paths. The big advantage here is the low effort: The 3D simulation is no longer necessary and the computing time required is significantly reduced compared to the models above. A filter with a finite impulse response can be used in a stochastic channel model . The impulse response of the channel is then of course a finite impulse sequence. The filter coefficients must arise in a pseudo-random manner and represent a function of time in a simulation. For the filter coefficients, the Rice distribution can be used with a direct line of sight and the Rayleigh distribution with a non-optical connection .

In a geometrical-stochastic procedure, a stochastic three-dimensional situation is generated and paths are then sought.

Very trivial approaches to solving the problem are often sufficient to calculate a radio channel. The last category includes, for example, the two-beam model, in which two beams are assumed. One direct and one indirect (reflected).