Multi-way reception

Multipath propagation using the example of a radar echo; the multi-path reception creates phantom objects.

Multipath or multipath reception (engl. Multipath ) occurs at a receiver when electromagnetic waves of a transmitter of reflectors (z. B. buildings, wet leaves) are deflected in different ways and arrive at the receiver. This results in a mixing of the direct signal with the various time-shifted reflected echo signals. The level of this mixed signal is usually weaker than that of the direct path.

Particular attention must be paid to the effect of precise satellite positioning with GPS, the accuracy of which (mm ... cm) can significantly impair reflected detour signals.

causes

A signal that is transmitted via radio can take different paths from the transmitter to the receiver . Causes for this are

• Reflection of signals, e.g. B. on walls of houses,
• Refraction (refraction) of signals z. B. in the ionosphere ,
• Scattering of signals, e.g. B. on small objects such as signs,
• Diffraction of signals, e.g. B. on the edges of houses or mountains.

A so-called co - channel transmitter can also act as a further signal source.

As a result of these transmission paths of different lengths, a radio signal can arrive at a receiver multiple times and at different times. The individual echo signals that occur at the receiver have different amplitudes and transit times depending on the attenuation and path. A characteristic value for the description of such a (frequency-selective) fading channel is given by the ratio of the directly received signal power to the sum of all echo signal powers ( Rice factor ).

Measurement

The dispersion time of a radio channel measures the divergence of a square pulse. If symbols are transmitted in digital transmission with a duration that is significantly longer than the dispersion time, there is almost no fading. We speak of flat fading and a rice channel .

Effects

If the dispersion time very much larger than the symbol duration, which plays intersymbol interference negligible role and the echo signals can even be productive use by dissolving the individual signals in time and in the correct phase back together and thus the reception energy increases (multi-path diversity). The in spread spectrum , but also in terrestrial and satellite-based mobile communication systems with CDMA used -Zugriffsverfahren rake receiver operates with this method. In practice, however, the selection combining method is used much more frequently: If it is possible to resolve the individual signals in terms of time, the best signal is evaluated and the others discarded.

The digital broadcasting utilizes modern digital modulation methods , the immune to a certain degree are against multipath and this even be used for a better quality of the received signal (z. B. at COFDM that in DVB-T , DAB is used).

In the analog transmission of radio and television images, multipath effects are e.g. B. directly recognizable as ghost images. The superposition of the multipath signals with the direct signal can lead to interference which affects the signal quality. In the case of shortwave, the selective carrier loss is particularly feared.

If the correlation method is used for position determination (GPS (?)) , Short detours of the indirect paths are critical because the separation of the direct and indirect signals becomes difficult (especially if the direct signal cannot be measured). Longer detours are easier to identify and eliminate due to the large time difference.

In general, it can be said that multipath reception has a negative effect on the transmission of signals. The reason for this is the different distances covered, which cause the signal to be delayed.

${\displaystyle t={s \over c}}$

Where t is the transit time, c is the speed of light in a vacuum and s is the signal path. This formula only provides an approximate value for the normal earth atmosphere, since the speed of propagation in air is not exactly c.

Mathematical description

The following formula can also be used in the time domain for multipath reception ( impulse response ):

${\displaystyle h_{k}(t)=a_{0}\delta _{0}(t-T_{0})+a_{1}\delta _{0}(t-T_{1})}$, in which ${\displaystyle T_{1}=T_{0}+\Delta t}$

${\displaystyle a_{0}\delta _{0}(t-T_{0})}$is the direct path and the indirect path. ${\displaystyle a_{1}\delta _{0}(t-T_{1})}$

Depending on the situation, multipath reception from significantly more indirect paths is possible, which means that the following formula then applies:

${\displaystyle h_{k}(t)=a_{0}(t)\delta _{0}(t-T_{0})+\sum _{j=1}^{n}[a_{j}(t)\delta _{0}(t-T_{j})]}$

in the most general case, the path delays are also time-dependent:

${\displaystyle h_{k}(t)=a_{0}(t)\delta _{0}(t-T_{0}(t))+\sum _{j=1}^{n}[a_{j}(t)\delta _{0}(t-T_{j}(t))]}$

See also

• Multiple input multiple output , SIMO , fading (electrical engineering)

literature

• John G. Proakis, Masoud Salehi: Communication Systems Engineering . 2nd Edition. Prentice-Hall, 2002, ISBN 0-13-095007-6 .