Fading

Inwireless communications,fadingis the variation of signalattenuationover variables like time, geographical position, and radio frequency. Fading is often modeled as arandom process.In wireless systems, fading may either be due tomultipath propagation,referred to as multipath-induced fading, weather (particularly rain), or shadowing from obstacles affecting thewave propagation,sometimes referred to asshadow fading.

Afading channelis a communication channel that experiences fading.

Key concepts

The presence of reflectors in the environment surrounding a transmitter and receiver create multiple paths that a transmitted signal can traverse. As a result, the receiver sees thesuperpositionof multiple copies of the transmitted signal, each traversing a different path. Each signal copy will experience differences inattenuation,delayandphase shiftwhile traveling from the source to the receiver. This can result in eitherconstructive or destructive interference,which amplifies or attenuates the signal power seen at the receiver. Strong destructive interference is frequently referred to as adeep fadeand may result in temporary failure of communication due to a severe drop in the channelsignal-to-noise ratio.

A common example of deep fade is the experience of stopping at a traffic light and hearing an FM broadcast degenerate into static, while the signal is re-acquired if the vehicle moves only a fraction of a meter. The loss of the broadcast is caused by the vehicle stopping at a point where the signal experienced severe destructive interference. Cellular phones can also exhibit similar momentary fades.

Fading channel models are often used to model the effects of electromagnetic transmission of information over the air in cellular networks and broadcast communication. Fading channel models are also used in underwater acoustic communications to model the distortion caused by the water.

Types

Slow versus fast fading

The termsslowandfastfading refer to the rate at which the magnitude and phase change imposed by the channel on the signal changes. Thecoherence timeis 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 fadingarises 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 asshadowing,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 alog-normal distributionwith a standard deviation according to thelog-distance path loss model.
Fast fadingoccurs 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 usingtime diversityto 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 anerror-correcting codecoupled 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 theDoppler spreadof 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 theDoppler 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

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

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

Block fading

Block fadingis 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 anOFDMsystem.

Selective fading

Selective fadingorfrequency selective fadingis aradio propagationanomaly caused by partial cancellation of aradio signalby itself — the signal arrives at the receiver bytwo 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 theionospheremove, separate, and combine. The two paths can both beskywaveor one begroundwave.

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 receivedaudio.

As thecarrier frequencyof a signal is varied, the magnitude of the change in amplitude will vary. Thecoherence bandwidthmeasures the separation in frequency after which two signals will experience uncorrelated fading.

Inflat 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.
Infrequency-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 asorthogonal frequency-division multiple xing(OFDM) andcode-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 narrowbandsubcarriers,each exposed to flat fading rather than frequency selective fading. This can be combated by means oferror coding,simpleequalizationor adaptivebit loading.Inter-symbol interference is avoided by introducing a guard interval between the symbols called acyclic prefix.CDMA uses therake receiverto deal with each echo separately.

Frequency-selective fading channels are alsodispersive,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.Equalizersare often deployed in such channels to compensate for the effects of theintersymbol interference.

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

The effect can be counteracted by applying somediversity scheme,for example OFDM (with subcarrierinterleavingandforward error correction), or by using tworeceiverswith separateantennasspaced a quarter-wavelengthapart, or a specially designeddiversity receiverwith two antennas. Such a receiver continuously compares the signals arriving at the two antennas and presents the better signal.

Upfade

Upfadeis a special case of fading, used to describeconstructive 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 thereceiver in phaseand 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 inwireless LANsystems.^[7]

Models

Examples of fading models for the distribution of the attenuation are:

Dispersive fadingmodels, with several echoes, each exposed to different delay, gain and phase shift, often constant. This results in frequency selective fading and inter-symbol interference. The gains may be Rayleigh or Rician distributed. The echoes may also be exposed to Doppler shift, resulting in a time varying channel model.
Nakagami fading
Log-normal shadow fading
Rayleigh fading
Rician fading
Two-wave with diffuse power (TWDP) fading
Weibull fading

Mitigation

Fading can cause poor performance in a communication system because it can result in a loss of signal power without reducing the power of the noise. This signal loss can be over some or all of the signal bandwidth. Fading can also be a problem as it changes over time: communication systems are often designed to adapt to such impairments, but the fading can change faster than the adaptations can be made. In such cases, the probability of experiencing a fade (and associated bit errors as thesignal-to-noise ratiodrops) on the channel becomes the limiting factor in the link's performance.

The effects of fading can be combated by usingdiversityto transmit the signal over multiple channels that experience independent fading and coherently combining them at the receiver. The probability of experiencing a fade in this composite channel is then proportional to the probability that all the component channels simultaneously experience a fade, a much more unlikely event.

Diversity can be achieved in time, frequency, or space. Common techniques used to overcome signal fading include:

Besides diversity, techniques such as application ofcyclic prefix(e.g. inOFDM) andchannel estimationandequalizationcan also be used to tackle fading.

References

^Tse, David; Viswanath, Pramod (2006).Fundamentals of Wireless Communication(4 ed.). Cambridge (UK): Cambridge University Press. p. 31.ISBN 0521845270.
^Ahlin, Lars; Zander, Jens; and Slimane, Ben;Principles of Wireless Communications,Professional Publishing Svc., 2006, pp. 126-130.
^Biglieri, Ezio;Caire, Giuseppe;Taricco, Giorgio (1999). "Coding for the Fading Channel: a Survey". In Byrnes, Jim S. (ed.).Signal Processing for Multimedia.IOS Press. p. 253.ISBN 978-90-5199-460-5.
^Médard, Muriel;Tse, David N. C."Spreading in block-fading channels"(PDF).Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers.34th Asilomar Conference on Signals, Systems and Computers, Oct 29 – Nov 1, 2000, Pacific Grove, CA, USA. Vol. 2. pp. 1598–1602.doi:10.1109/ACSSC.2000.911259.ISBN 0-7803-6514-3.Retrieved2014-10-20.
^Sklar, Bernard (July 1997)."Rayleigh fading channels in mobile digital communication systems.I. Characterization".IEEE Communications Magazine.35(7): 90–100.doi:10.1109/35.601747.
^Lehpamer, Harvey;Microwave transmission networks: planning, design, and deployment,McGraw-Hill, 2010,ISBN 0-07-170122-2,page 100
^Lewis, Barry D.; Davis, Peter T.;Wireless networks for dummies,For Dummies, 2004,ISBN 0-7645-7525-2,page 234

Literature

T.S. Rappaport,Wireless Communications: Principles and practice,Second Edition, Prentice Hall, 2002.
David Tse and Pramod Viswanath,Fundamentals of Wireless Communication,Cambridge University Press, 2005.
M. Awad, K. T. Wong[1]^{[permanent dead link‍]}& Z. Li,An Integrative Overview of the Open Literature's Empirical Data on the Indoor Radiowave Channel's Temporal Properties,[2]IEEE Transactions on Antennas & Propagation, vol. 56, no. 5, pp. 1451–1468, May 2008.
P. Barsocchi,Channel models for terrestrial wireless communications: a survey,CNR-ISTItechnical report, April 2006.

External links

Fading due to multipath effect

[1] Tse, David; Viswanath, Pramod (2006).Fundamentals of Wireless Communication(4 ed.). Cambridge (UK): Cambridge University Press. p. 31.ISBN 0521845270.

[2] Ahlin, Lars; Zander, Jens; and Slimane, Ben;Principles of Wireless Communications,Professional Publishing Svc., 2006, pp. 126-130.

[3] Biglieri, Ezio;Caire, Giuseppe;Taricco, Giorgio (1999). "Coding for the Fading Channel: a Survey". In Byrnes, Jim S. (ed.).Signal Processing for Multimedia.IOS Press. p. 253.ISBN 978-90-5199-460-5.

[4] Médard, Muriel;Tse, David N. C."Spreading in block-fading channels"(PDF).Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers.34th Asilomar Conference on Signals, Systems and Computers, Oct 29 – Nov 1, 2000, Pacific Grove, CA, USA. Vol. 2. pp. 1598–1602.doi:10.1109/ACSSC.2000.911259.ISBN 0-7803-6514-3.Retrieved2014-10-20.

[5] Sklar, Bernard (July 1997)."Rayleigh fading channels in mobile digital communication systems.I. Characterization".IEEE Communications Magazine.35(7): 90–100.doi:10.1109/35.601747.

[6] Lehpamer, Harvey;Microwave transmission networks: planning, design, and deployment,McGraw-Hill, 2010,ISBN 0-07-170122-2,page 100

[7] Lewis, Barry D.; Davis, Peter T.;Wireless networks for dummies,For Dummies, 2004,ISBN 0-7645-7525-2,page 234

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