A multipath effect moving body (such as a car) travels between a building complex and an obstacle, and the intensity of the received signal is superimposed by the direct wave and the reflected wave. Multipath effects can cause signal fading. The electrical length of each path changes with time, so the phase relationship between the component fields arriving at the receiving point also changes with time. The random interference of these component fields forms the fading of the total receiving field. The phase relationship between the components is different for different frequencies. Therefore, their interference effects also vary with frequency, and this characteristic is called frequency selectivity. In broadband signal transmission, frequency selectivity may be apparent and form an intermodulation. Correspondingly, since the different paths have different delays, the signals emitted at the same time are scattered before and after the receiving points along different paths, and the narrow pulse signals are overlapped before and after.

In the channel of wireless communication, in addition to the direct wave and the ground reflected wave, the wave propagation also has scattered waves caused by various obstacles during the propagation, thereby generating a multipath effect.

The so-called multipath effect means that the amplitude of a wireless signal is rapidly fading after a short distance propagation, so that the large-scale influence is negligible, and the fading is caused by the same propagation signal propagating along two or more paths with a slight time difference. The signals arriving at the receiver interfere with each other. These waves are called multipath waves. The receiver antenna combines them into a signal whose amplitude and phase change abruptly. The degree of change depends on the strength of the multipath, the relative propagation time, and The bandwidth of the transmitted signal.

1. From the waveform point of view, the result of multipath propagation causes the determined carrier signal to become a narrowband signal whose envelope and phase are modulated, that is, a fading signal;

2. From the spectrum point of view, multipath transmission causes frequency dispersion, that is, from a single frequency to a narrowband spectrum;

3. The envelope of the signal obeys the fading of Rayleigh's law of distribution, commonly referred to as Rayleigh-type fading;

Multipath effects produce selective fading: including time selective fading, frequency selective fading, and spatially selective fading.

1. Time selective fading: a frequency diffusion of a fading process caused by a Doppler shift phenomenon;

2. Spatially selective fading: at the receiving end of a communication system (e.g., a mobile communication system), the broadening of the angle of arrival of the multipath signal to the antenna array;

3. Frequency selective fading is caused by the time spread of the transmitted code within the channel, causing intersymbol interference. From the frequency domain, the gain of a certain frequency component of the received signal spectrum is larger than the gain of other components, thereby distorting the received signal.

Coherence bandwidth is a measure of channel frequency selectivity. The smaller the ratio of the coherent bandwidth to the signal bandwidth, the stronger the frequency selectivity of the channel; conversely, the greater the ratio of the coherent bandwidth to the signal bandwidth, the weaker the frequency selectivity of the channel.

In a complex environment, the received signal may be a composite signal of a direct wave, a ground reflected wave, and a scattered wave, and the received composite field strength is a vector composite wave of each part, thereby generating a multipath effect.

In the urban areas with high buildings, since the height of the mobile station antenna is much shorter than that of the surrounding buildings, there is no line-of-sight propagation from the mobile station to the base station, which leads to fading. Even if such a line of sight propagation path exists, multipath propagation will still occur due to reflections from the ground and surrounding buildings. The incident waves arrive in different directions of propagation with different propagation delays. The signals received by the mobile station at any point in space are composed of many plane waves with randomly distributed amplitude, phase and angle of incidence. These multipath components are combined by the mobile station antenna in a vector, resulting in fading distortion of the received signal. Even if the mobile receiver is at rest, the received signal will fade due to the motion of objects in the environment in which the wireless channel is located.

At the same time each path has its own gain, phase shift and delay.

● The multipath of the wireless channel leads to the generation of small-scale fading effects, mainly as follows:

Rapid change in signal strength after short or short-term propagation;

On different multipath signals, there is random frequency modulation caused by time-varying Doppler shift;

An extension caused by multiple propagation delays (such as echo).

● Factors affecting small-scale fading are:

(1) Multipath propagation—The presence of reflections and reflections in the channel constitutes an environment that constantly consumes signal energy, resulting in changes in signal amplitude, phase, and time. These factors cause a plurality of radio waves that are temporally and spatially distinguished from each other when the transmitted wave arrives at the receiver. Random phase and multipath with different amplitudes cause signal strength fluctuations, leading to small-scale fading and signal distortion. Multipath propagation often lengthens the time it takes for the signal baseband portion to reach the receiver, causing intersymbol interference to form signal ambiguity.

(2) The motion speed of the mobile station - the relative motion between the base station and the mobile station causes random frequency modulation, which is caused by the Doppler shift phenomenon of multipath. Whether the mobile receiver is moving toward or away from the base station determines whether the Doppler shift is a positive or negative shift.

(3) The speed of movement of an environmental object - if the object in the wireless channel is in motion, it will cause a time-varying Doppler shift. If the environmental object moves at a speed greater than the mobile station, then this motion will determine the small-scale fading. Otherwise, only the influence of the moving speed of the moving station can be considered, and the influence of the moving speed of the environmental object is ignored.

(4) Signal transmission bandwidth - If the transmission bandwidth of the signal is much larger than the multipath channel bandwidth, the received signal will be distorted, but the local receiver signal strength will not fade much (ie, small-scale fading is not dominant). The channel bandwidth can be quantized by the coherence bandwidth. Here, the correlation bandwidth is a measure of the maximum frequency difference, related to the particular multipath structure of the channel. Within this range, the amplitude of the different signals maintains a strong correlation. If the transmitted signal bandwidth is narrower than the channel bandwidth, the signal amplitude will change rapidly, but the signal will not be time-distorted. Therefore, the strength of the small-scale signal and the possibility of signal blurring after short-range transmission are related to the specific amplitude, delay, and bandwidth of the transmitted signal of the multipath channel.

● Doppler shift

Since multipath is the same signal source propagating through different paths, there is a slight delay difference at the receiving point, and the superposition of vectors causes a change in signal amplitude. The extent of the change depends on the amplitude, delay, and bandwidth of the propagated signal. The time-varying of the channel causes a broadening of the signal frequency, resulting in a Doppler effect.

When the mobile station moves at a constant rate 长度 on a path of length d and endpoints X and Y, it receives a signal from the remote source S as shown:

The path difference between the radio wave starting from the source S and being received by the mobile station at point X and point Y is respectively. Here Δt is the time required for the mobile station to move from X to Y, and θ is the angle between X and Y and the incident wave. Since the distal distance is far away, it can be assumed that θ at X and Y is the same. Therefore, the phase change value of the received signal caused by the path difference is:

From this, the frequency change value can be obtained, that is, the Doppler shift fd is:

It can be seen from the above equation that the Doppler shift is related to the angle between the moving speed of the mobile station, the moving direction of the mobile station, and the incident direction of the radio wave. If the mobile station moves toward the incident wave direction, the Doppler shift is positive (ie, the receive frequency rises); if the mobile station moves back toward the incident wave direction, the Doppler shift is negative (ie, the receive frequency decreases). The signal propagates in different directions, and its multipath component causes Doppler spread of the receiver signal, thus increasing the signal bandwidth.

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