“Two-wave with diffuse power fading”的意思、由来-开放百科全书

In radio propagation, two-wave with diffuse power (TWDP) fading is a model that explains why a signal is strengthened or weakened at certain locations or times. TWDP models fading due to the interference of two strong radio signals and numerous smaller, diffuse signals.

TWDP is a generalized system using a statistical model to produce results. Other statistical methods for predicting fading, including Rayleigh fading and Rician fading, can be considered as special cases of the TWDP model. The TWDP calculation produces a number of fading cases that the older models do not, especially in areas with crowded spectrums.

Fading

The effect had been noticed from the start of radio experimentation, but was especially notable with the introduction of shortwave communications. It was identified as being due to self-interference due to multiple paths between the transmitter and receiver, which in turn led to the discovery and characterization of the ionosphere. This layer of the atmosphere is reflective, causing the signal to return to the Earth where it can reflect back into the sky, and in this way "skip" for long distances over the ground. This provided multiple paths to the receiver, with (for instance) a strong signal received after one reflection off the ionosphere and a weaker one after two reflections. The seemingly random fading effects were traced to the slow movement of billows in the ionosphere and the daily variation due to the effects of sunlight.^[2]

Modelling fading

Attempts to model the effects of fading started almost immediately after the effect was first characterized. Earlier models included simplifications in order to make the math tractable.

Rayleigh fading is named for its use of the Rayleigh distribution of the signal. This is, in effect, the 2D distribution that results from the product of X and Y components that are separately and randomly distributed according to a normal distribution. By varying the parameters of the distributions, one can model different real-world cases. This model is useful when both of the signals are roughly equal in amplitude, as is the case when there is no direct line-of-sight between the transmitter and receiver. Rician fading is similar but uses the Rice distribution instead of Rayleigh, which is characterized by two parameters, shape and scale. This system is most useful when one of the paths is stronger, especially in line-of-sight applications.

A more general solution was long sought that did not require arbitrary limits on the distributions or envelopes.^[3]^[4] The first general solution was presented in 2002 by Durgin, Rappaport, and de Wolf.^[5] The new method used the KΔ parameter to characterize the distribution.

The new system predicts a number of deep fading scenarios that are not found in the older methods, notably Rayleigh. Jeff Frolik was the first to measure TWDP fading in an aircraft fuselage, coining the term hyper-Rayleigh to denote this and other fading scenarios that result in worse-than-Rayleigh received power outages for a radio link.^[6] Subsequently, other researchers have developed alternate, improved expressions for the TWDP distribution and its statistics.^[7]^[8]

The formulation of TWDP fading has upended classical RF design by providing a new "worst case design" scenario in fading in wireless links. Thus, common performance metrics in mobile communications such as bit error rate,^[9] outage probability,^[10] diversity gains,^[11] etc. can be significantly degraded by TWDP fading. Both measurements and theoretical predictions have shown that TWDP fading becomes more common as mobile radio links increase in both frequency and density.

Channel characterization

TWDP fading arises in a radio channel characterized by two constant-amplitude waves and numerous, smaller radio waves that are randomly phased with respect to one another. A TWDP-distributed envelope R follows from the following combination of elementary random variables:

where

and

are independent uniform random variables over the interval [0,1);

and

are independent, zero-mean Gaussian random variables with standard deviation

. The two constant amplitude components are referred to as the specular components of the fading model. The

term represents the sum of numerous amplitudes and phases of smaller waves, which by the law of large numbers follows a complex Gaussian distribution.

TWDP fading PDF is characterized by three parameters: average power Ω, ratio of specular-to-diffuse power K, and disparity between specular components Δ. These three parameters are related to the amplitudes of the individual waves by

The K-factor may vary from 0 to

. A value of

corresponds to Rayleigh fading. A value of

corresponds to the type of two-wave envelope fading experienced on a transmission line with reflections. The

parameter varies from 0 to 1, with

corresponding to Rician fading and

corresponding to specular components of equal amplitude,

Unlike its special cases of Rayleigh and Rician fading, there is no simple, closed-form solution for the probability density function (PDF) of received envelope for TWDP fading. Instead, the exact PDF is the result of the following definite integral:^[12]

Numerous techniques have been proposed to approximate the TWDP PDF in closed form or evaluate its statistics directly.^[5]^[7]^[8]

References

1. ^{{cite web |url=http://www.radio-electronics.com/info/propagation/multipath/multipath-fading.php |title=Multipath Fading |website=Radio-Electronics}}
2. ^{{cite web |url=https://radiojove.gsfc.nasa.gov/education/educ/radio/tran-rec/exerc/iono.htm |title=The Effects of Earth's Upper Atmosphere on Radio Signals |website=NASA}}
3. ^{{Cite journal|last=W.R. Bennett|date=April 1948|title=Distribution of the sum of randomly phased components|url=|journal=Quarterly Journal of Applied Mathematics|volume=5|issue=|doi=|pmid=|access-date=|via=}}
4. ^{{Cite journal|last=R. Esposito and L.R. Wilson|date=March 1973|title=Statistical properties of two sine waves in Gaussian noise|url=|journal=IEEE Transactions on Information Theory|volume=19|issue=2|doi=10.1109/tit.1973.1054978|pages=176–183}}
5. ^¹{{Cite journal |first1=Gregory |last1=Durgin |first2= Theodore |last2=Rappaport |first3=David |last3=de Wolf |date=2002 |title=New analytical models and probability density functions for fading in wireless communications |journal=IEEE Transactions on Communications |volume=50 |issue=6 |doi=10.1109/tcomm.2002.1010620 |pages=1005–1015}}
6. ^{{Cite journal|last=Frolik|first=Jeff|date=April 2007|title=A Case for Considering Hyper-Rayleigh Fading Channels |url=http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4155662 |journal=IEEE Transactions on Wireless Communications|volume=6|issue=4|doi=|pmid=|access-date=|via=}}
7. ^¹{{Cite journal|last=S.A. Saberali and N.C. Beaulieu|date=September 2013 |title=New Expressions for TWDP Fading Statistics |journal=IEEE Wireless Communications Letters|volume=2|issue=6|pages=643–646|doi=10.1109/WCL.2013.090313.130541|pmid=}}
8. ^¹{{Cite journal|last=M. Rao, F.J. Lopez-Martinez, M.S. Alouini, A. Goldsmith|date=January 2015|title=MGF Approach to the Analysis of Generalized Two-Ray Fading Models|url=http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7001066 |journal=IEEE Transactions in Wireless Communications|volume=14|issue=5|doi=|pmid=|access-date=|via=}}
9. ^{{Cite journal|last=S.H. Oh and K.H. Li|date=July 2005|title=BER performance of BPSK receivers over two-wave with diffuse power fading channels|url=http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1512105&queryText=TWDP%20BER&sortType=asc_p_Publication_Year|journal=IEEE Transactions on Wireless Communications|volume=4|issue=4|doi=|pmid=|access-date=|via=}}
10. ^{{Cite journal|last=Y. Lu, X. Wang, J. Lu|date=May 2011|title=Outage Probability of Cooperative Relay Systems in Two-Wave with Diffuse Power Fading Environments|url=http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5956119&queryText=TWDP%20outage%20probability&sortType=asc_p_Publication_Year|journal=Vehicular Technology Conference (VTC Spring), 2011 IEEE 73rd|volume=|issue=|pages=1–4|doi=10.1109/VETECS.2011.5956119|pmid=|access-date=|via=|isbn=978-1-4244-8332-7}}
11. ^{{Cite journal|last=W.S. Lee and S.H. Oh|date=December 2007|title=Performance of dual switch-and-stay diversity NCFSK systems over two-wave with diffuse power fading channels|url=http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4449556&queryText=diversity%20TWDP&sortType=asc_p_Publication_Year|journal=Information, Communications & Signal Processing, 2007 6th International Conference on|volume=|issue=|pages=1–5|doi=10.1109/ICICS.2007.4449556|pmid=|access-date=|via=|isbn=978-1-4244-0982-2}}
12. ^{{Cite book|title=Space-Time Wireless Channels|last=Durgin|first=Gregory|publisher=Pearson|year=2003|isbn=|location=Upper Saddle River, NJ|pages=|via=}}