Fading

The terms slow and fast fading refer to the rate at which the magnitude and phase change imposed by the channel on the signal changes. The coherence time is a measure of the minimum time required for the magnitude change or phase change of the channel to become uncorrelated from its previous value.

• Slow fading arises when the coherence time of the channel is large relative to the delay requirement of the application.[1] In this regime, the amplitude and phase change imposed by the channel can be considered roughly constant over the period of use. Slow fading can be caused by events such as shadowing, where a large obstruction such as a hill or large building obscures the main signal path between the transmitter and the receiver. The received power change caused by shadowing is often modeled using a log-normal distribution with a standard deviation according to the log-distance path loss model.
• Fast fading occurs when the coherence time of the channel is small relative to the delay requirement of the application. In this case, the amplitude and phase change imposed by the channel varies considerably over the period of use.

In a fast-fading channel, the transmitter may take advantage of the variations in the channel conditions using time diversity to help increase robustness of the communication to a temporary deep fade. Although a deep fade may temporarily erase some of the information transmitted, use of an error-correcting code coupled with successfully transmitted bits during other time instances (interleaving) can allow for the erased bits to be recovered. In a slow-fading channel, it is not possible to use time diversity because the transmitter sees only a single realization of the channel within its delay constraint. A deep fade therefore lasts the entire duration of transmission and cannot be mitigated using coding.

The coherence time of the channel is related to a quantity known as the Doppler spread of the channel. When a user (or reflectors in its environment) is moving, the user's velocity causes a shift in the frequency of the signal transmitted along each signal path. This phenomenon is known as the Doppler shift. Signals traveling along different paths can have different Doppler shifts, corresponding to different rates of change in phase. The difference in Doppler shifts between different signal components contributing to a signal fading channel tap is known as the Doppler spread. Channels with a large Doppler spread have signal components that are each changing independently in phase over time. Since fading depends on whether signal components add constructively or destructively, such channels have a very short coherence time.

In general, coherence time is inversely related to Doppler spread, typically expressed as

${\displaystyle T_{c}\approx {\frac {1}{D_{s}}}}$

where ${\displaystyle T_{c}}$ is the coherence time, ${\displaystyle D_{s}}$ is the Doppler spread. This equation is just an approximation,[2] to be exact, see Coherence time.

Block fading is where the fading process is approximately constant for a number of symbol intervals.[3] A channel can be 'doubly block-fading' when it is block fading in both the time and frequency domains.[4] Many wireless communications channels are dynamic by nature, and are commonly modeled as block fading. In these channels each block of symbol goes through a statistically independent transformation. Typically the slowly-varying channels based on jakes model of Rayleigh spectrum [5] is used for block fading in an OFDM system.

Selective fading or frequency selective fading is a radio propagation anomaly caused by partial cancellation of a radio signal by itself — the signal arrives at the receiver by two different paths, and at least one of the paths is changing (lengthening or shortening). This typically happens in the early evening or early morning as the various layers in the ionosphere move, separate, and combine. The two paths can both be skywave or one be groundwave.

Selective fading manifests as a slow, cyclic disturbance; the cancellation effect, or "null", is deepest at one particular frequency, which changes constantly, sweeping through the received audio.

As the carrier frequency of a signal is varied, the magnitude of the change in amplitude will vary. The coherence bandwidth measures the separation in frequency after which two signals will experience uncorrelated fading.

• In flat fading, the coherence bandwidth of the channel is larger than the bandwidth of the signal. Therefore, all frequency components of the signal will experience the same magnitude of fading.
• In frequency-selective fading, the coherence bandwidth of the channel is smaller than the bandwidth of the signal. Different frequency components of the signal therefore experience uncorrelated fading.

Since different frequency components of the signal are affected independently, it is highly unlikely that all parts of the signal will be simultaneously affected by a deep fade. Certain modulation schemes such as orthogonal frequency-division multiplexing (OFDM) and code-division multiple access (CDMA) are well-suited to employing frequency diversity to provide robustness to fading. OFDM divides the wideband signal into many slowly modulated narrowband subcarriers, each exposed to flat fading rather than frequency selective fading. This can be combated by means of error coding, simple equalization or adaptive bit loading. Inter-symbol interference is avoided by introducing a guard interval between the symbols called a cyclic prefix. CDMA uses the rake receiver to deal with each echo separately.

Frequency-selective fading channels are also dispersive, in that the signal energy associated with each symbol is spread out in time. This causes transmitted symbols that are adjacent in time to interfere with each other. Equalizers are often deployed in such channels to compensate for the effects of the intersymbol interference.

The echoes may also be exposed to Doppler shift, resulting in a time varying channel model.

The effect can be counteracted by applying some diversity scheme, for example OFDM (with subcarrier interleaving and forward error correction), or by using two receivers with separate antennas spaced a quarter-wavelength apart, or a specially designed diversity receiver with two antennas. Such a receiver continuously compares the signals arriving at the two antennas and presents the better signal.

Upfade is a special case of fading, used to describe constructive interference, in situations where a radio signal gains strength.[6] Some multipath conditions cause a signal's amplitude to be increased in this way because signals travelling by different paths arrive at the receiver in phase and become additive to the main signal. Hence, the total signal that reaches the receiver will be stronger than the signal would otherwise have been without the multipath conditions. The effect is also noticeable in wireless LAN systems.[7]