# Wireless & Mobile Communications Questions & Answers – Rayleigh and Ricean Distribution

This set of Wireless & Mobile Communications Multiple Choice Questions & Answers (MCQs) focuses on “Rayleigh and Ricean Distribution”.

1. Which of the following distribution is used for describing statistical time varying nature of received envelope of multipath component?
a) Log normal distribution
b) Levy distribution
c) Rayleigh distribution
d) Gaussian distribution

Explanation: Rayleigh distribution is the most common distribution for statistical modelling. It is used to describe the statistical time varying nature of the received envelope of a flat fading signal. It also describes the envelope of an individual multipath component.

2. Envelope of the sum of two quadrature Gaussian noise signal obeys _________ distribution.
a) Rayleigh
b) Inverse Gaussian
c) Nakagami
d) Gamma

Explanation: It is well known that the envelope of the sum of two quadrature Gaussian noise signal obeys Rayleigh distribution. This fading distribution could be applied to any scenario where there is no line of sight path between transmitter and receiver antennas.

3. For a Rayleigh fading signal, mean and median differ by _______
a) 2 dB
b) 10 dB
c) 0.55 dB
d) 100 dB

Explanation: The mean and median differ by only 0.55 dB in a Rayleigh fading signal. The differences between the rms values and the other two values are higher.

4. It is easy to compare different fading distributions using mean values instead of median values.
a) True
b) False

Explanation: By using median values instead of mean values, it is easy to compare different fading distributions which may have widely varying means. Median is used in practice since fading data is measured in the field and a particular distribution cannot be assumed.

5. For a nonfading signal component present, the small scale fading envelope distribution is ____________
a) Rayleigh
b) Gaussian
c) Log normal
d) Ricean

Explanation: The small scale fading envelope is Ricean when there is a dominant stationary (nonfading) signal component, such as line of sight propagation path. In such a situation, random multipath components arriving at different angles are superimposed on a stationary dominant signal.
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6. Ricean distribution degenerates to ________ distribution when the dominant component fades away.
a) Log normal
b) Gamma
c) Rayleigh
d) Gaussian

Explanation: Ricean distribution degenerates to Rayleigh distribution when the dominant component fades away. As the dominant signal becomes weaker, the composite signal resembles a noise signal which has an envelope that is Rayleigh.

7. The envelope of a bandpass noise is __________
a) Uniformly distributed
b) Rayleigh
c) Ricean
d) Gaussian

Explanation: The envelope of only bandpass noise is Rayleigh distribution. Rayleigh distribution is a continuous probability density function for positive random variables.

8. The envelope of a sinusoid plus bandpass noise has __________
a) Uniformly distributed
b) Rayleigh
c) Ricean
d) Gaussian

Explanation: The envelope of a sinusoid plus bandpass noise has Ricean distribution. In probability theory, Ricean distribution is the probability distribution which has magnitude of a circular bivariate normal random variable with potentially non-zero mean.

9. What do you call an attenuation that occurs over many different wavelengths of the carrier?

Explanation: Slow fading does not vary quickly with the frequency. It originates due to effect of mobility. Slow fading is the result of signal path change due to shadowing and obstructions such as tree or buildings etc.

10. Which of the reception problems below that is not due to multipath?
c) Random Doppler shift

Explanation: Slow fading arises when the coherence time of the channel is large relative to the delay requirement of the application. Slow fading is 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.

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