Space Wave Propagation Questions and Answers

Q: What does the log normal shadowing term in a mobile model represent?

Buildings and terrain make the local median loss vary about the model's prediction, and that variation is well described by a log normal distribution with a standard deviation of six to ten decibels. Coverage is then quoted for a percentage of locations. Fast fading is modelled separately as Rayleigh, weather is a minor factor at these frequencies, and model uncertainty is a different thing again. Splitting variability into components with distinct statistics is what allows each to be handled with the right mathematics.

Q: When does a mobile channel follow Rician rather than Rayleigh statistics?

A dominant line of sight path adds a constant vector to the random scatter, so deep fades become much rarer and the statistics move from Rayleigh towards Gaussian as that component strengthens. The ratio of dominant to scattered power is the Rician k factor. Motion affects the rate of fading rather than its distribution, frequency and environment influence but do not define it, and two base stations are a separate situation. The presence or absence of a dominant path is what selects the distribution.

Q: What is the coherence bandwidth of a channel?

Coherence bandwidth is roughly the reciprocal of the delay spread, and a signal narrower than it fades flat while a wider one fades selectively and needs equalisation. It is a property of the propagation channel rather than of the equipment. Signal bandwidth, antenna match and receiver filtering are all equipment quantities. Comparing the signal bandwidth with the channel's coherence bandwidth immediately tells you which class of impairment the system must be designed against.

Q: What follows if the signal bandwidth exceeds the coherence bandwidth?

A wide signal sees different attenuation and phase across its own spectrum, producing intersymbol interference that must be corrected by an equaliser or avoided by using many narrow subcarriers. That is precisely why orthogonal frequency division multiplexing was adopted for broadband wireless. Flat fading is the opposite case, the channel remains usable with the right modulation, and the depth of fading is not reduced. Matching the modulation to the channel's dispersion is the central design decision in a wireless system.

Q: Why does orthogonal frequency division multiplexing suit a dispersive channel?

Dividing the band into many narrow subcarriers makes each one narrower than the coherence bandwidth, so each fades flat and can be corrected by a single complex coefficient, with a guard interval absorbing the delay spread. Power, frequency selection and cancellation are not the mechanism. Converting one difficult wideband problem into many easy narrowband ones is an idea that recurs throughout signal processing, and here it is the enabling technique for broadband wireless.

Q: What determines the cell size in a mobile network?

Cells are sized by a combination of the propagation loss at the frequency used, the traffic the cell must carry, and the practical availability of sites, and in dense areas capacity rather than coverage decides. Power and frequency both influence the loss but neither fixes the radius alone, and regulators licence spectrum rather than cell geometry. A design driven sometimes by coverage and sometimes by capacity is why urban and rural networks look so different.

Q: Why are cells smaller in a city than in the countryside?

Each cell can carry only so much traffic, so dense demand is met by dividing the area into many small cells and reusing the frequencies more often. Higher path loss from clutter reinforces the same conclusion. Regulation does not set cell size, and reflection scatters signals without neatly confining them. A network limited by capacity rather than coverage is designed by quite different reasoning, and recognising which regime applies is the first step in planning one.

31.

What is the chief limitation of the Okumura-Hata model?

A.It predicts only the median loss and cannot handle any variation
B.It cannot be used for antenna heights above ten metres
C.It applies only within the frequency and distance range it was fitted to
D.It requires a detailed terrain profile that is rarely available

Answer: C

Fitted to measurements at particular frequencies, distances and building types, it becomes unreliable outside them, which is why the COST 231 extension was derived for higher frequencies. It needs no terrain profile, which is part of its convenience, and location variability is added as a separate log normal term. Base station heights well above ten metres are within its range. Extrapolating a fitted model beyond its data is the standard way of getting a confident and wrong answer.

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32.

What does the log normal shadowing term in a mobile model represent?

A.The rapid fading caused by multipath as the mobile moves
B.The variation of loss with the time of day and the weather
C.The uncertainty in the model's own fitted coefficients
D.Variation of median loss from place to place at the same distance

Answer: D

Buildings and terrain make the local median loss vary about the model's prediction, and that variation is well described by a log normal distribution with a standard deviation of six to ten decibels. Coverage is then quoted for a percentage of locations. Fast fading is modelled separately as Rayleigh, weather is a minor factor at these frequencies, and model uncertainty is a different thing again. Splitting variability into components with distinct statistics is what allows each to be handled with the right mathematics.

Discuss in Forum

33.

What distribution describes fast fading in a mobile channel without a dominant path?

A.Rayleigh
B.Log normal, matching the shadowing statistics of the same channel
C.Uniform
D.Gaussian, because many independent contributions add together

Answer: A

With many scattered components of similar magnitude and random phase, the resultant envelope follows a Rayleigh distribution and deep fades occur frequently. When a line of sight component dominates the statistics become Rician instead. Log normal describes shadowing, the phases are indeed uniform but that is not the envelope distribution, and the in phase and quadrature components are Gaussian while their magnitude is not. Naming the correct distribution determines the fade margin required for a given outage.

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34.

When does a mobile channel follow Rician rather than Rayleigh statistics?

A.When two base stations are received at equal strength
B.When a strong direct component is present alongside the scatter
C.When the mobile is stationary rather than moving
D.When the frequency is above one gigahertz in an urban area

Answer: B

A dominant line of sight path adds a constant vector to the random scatter, so deep fades become much rarer and the statistics move from Rayleigh towards Gaussian as that component strengthens. The ratio of dominant to scattered power is the Rician k factor. Motion affects the rate of fading rather than its distribution, frequency and environment influence but do not define it, and two base stations are a separate situation. The presence or absence of a dominant path is what selects the distribution.

Discuss in Forum

35.

What is the coherence bandwidth of a channel?

A.The range of frequencies over which the antenna is well matched
B.The bandwidth of the receiver's intermediate frequency filter
C.The band over which the channel response is nearly constant
D.The bandwidth occupied by the transmitted signal after modulation

Answer: C

Coherence bandwidth is roughly the reciprocal of the delay spread, and a signal narrower than it fades flat while a wider one fades selectively and needs equalisation. It is a property of the propagation channel rather than of the equipment. Signal bandwidth, antenna match and receiver filtering are all equipment quantities. Comparing the signal bandwidth with the channel's coherence bandwidth immediately tells you which class of impairment the system must be designed against.

Discuss in Forum

36.

What follows if the signal bandwidth exceeds the coherence bandwidth?

A.The signal is attenuated uniformly across its whole bandwidth
B.The channel becomes unusable at any data rate whatever
C.The fading becomes slower and less deep than it would otherwise be
D.The channel fades selectively and equalisation is needed

Answer: D

A wide signal sees different attenuation and phase across its own spectrum, producing intersymbol interference that must be corrected by an equaliser or avoided by using many narrow subcarriers. That is precisely why orthogonal frequency division multiplexing was adopted for broadband wireless. Flat fading is the opposite case, the channel remains usable with the right modulation, and the depth of fading is not reduced. Matching the modulation to the channel's dispersion is the central design decision in a wireless system.

Discuss in Forum

37.

Why does orthogonal frequency division multiplexing suit a dispersive channel?

A.Each subcarrier is narrow enough to fade flat
B.It transmits at a lower power and so suffers less fading
C.It uses only frequencies at which the channel response is flat
D.It eliminates multipath by cancelling the delayed components

Answer: A

Dividing the band into many narrow subcarriers makes each one narrower than the coherence bandwidth, so each fades flat and can be corrected by a single complex coefficient, with a guard interval absorbing the delay spread. Power, frequency selection and cancellation are not the mechanism. Converting one difficult wideband problem into many easy narrowband ones is an idea that recurs throughout signal processing, and here it is the enabling technique for broadband wireless.

Discuss in Forum

38.

What is the purpose of a guard interval in such a system?

A.It provides time for the transmitter to switch between subcarriers
B.It absorbs the delay spread so symbols do not overlap
C.It separates the transmissions of different users in time
D.It allows the receiver to measure the noise floor between symbols

Answer: B

Extending each symbol with a cyclic prefix longer than the channel's delay spread means the delayed copies of the previous symbol have died away before the useful part begins, so intersymbol interference is eliminated. The cost is a proportion of the transmitted time and power. User separation, noise measurement and switching are separate functions. Buying a clean channel with a fraction of the throughput is a bargain worth making when the alternative is a complex equaliser.

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39.

What determines the cell size in a mobile network?

A.The frequency band, which fixes the range independently of anything else
B.The regulator, who specifies the radius of each cell in the licence
C.Path loss, traffic capacity and the available site locations
D.The transmitter power alone, which fixes the coverage radius

Answer: C

Cells are sized by a combination of the propagation loss at the frequency used, the traffic the cell must carry, and the practical availability of sites, and in dense areas capacity rather than coverage decides. Power and frequency both influence the loss but neither fixes the radius alone, and regulators licence spectrum rather than cell geometry. A design driven sometimes by coverage and sometimes by capacity is why urban and rural networks look so different.

Discuss in Forum

40.

Why are cells smaller in a city than in the countryside?

A.Path loss is lower in cities so signals travel further
B.Regulations forbid large cells in built up areas
C.Buildings reflect the signal and confine it to a small area
D.Traffic density requires more capacity in the same area

Answer: D

Each cell can carry only so much traffic, so dense demand is met by dividing the area into many small cells and reusing the frequencies more often. Higher path loss from clutter reinforces the same conclusion. Regulation does not set cell size, and reflection scatters signals without neatly confining them. A network limited by capacity rather than coverage is designed by quite different reasoning, and recognising which regime applies is the first step in planning one.

Discuss in Forum

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