Statistical Wireless Channel Models

Introduction

A wireless channel is the physical medium between a transmitter and receiver. Unlike a wired link, it is affected by reflection, diffraction, scattering, atmospheric variation, mobility, and blockage. Consequently, the received signal is generally a random process rather than a deterministic attenuated copy of the transmitted signal. Statistical channel models provide mathematically tractable descriptions of these variations and are essential for designing, simulating, and evaluating wireless systems.

This chapter develops models for narrowband and wideband wireless channels. It explains multipath propagation, delay spread, Doppler spread, coherence time, coherence bandwidth, Rayleigh, Rician, and Nakagami fading, outage probability, and channel stationarity. The emphasis is on interpreting model parameters, selecting appropriate models, and recognizing their assumptions and limitations.

Learning Objectives

After completing this chapter, a learner should be able to:

1. Explain how multipath propagation produces fading and time dispersion.

2. Distinguish narrowband from wideband channel behavior.

3. Calculate delay spread, Doppler spread, coherence time, and coherence bandwidth using appropriate approximations.

4. Derive and interpret Rayleigh, Rician, and Nakagami fading models.

5. Calculate outage probability for common fading channels.

6. Explain stationarity, local stationarity, and the limits of statistical channel models.

7. Select a suitable channel model for a practical wireless link and evaluate its limitations.

1. Multipath Propagation and the Statistical Channel

1.1 Physical origin of multipath

A transmitted electromagnetic wave may reach the receiver through several paths. Large objects cause reflection; edges and corners produce diffraction; and smaller objects produce scattering. Each path can have a different attenuation, phase, angle of arrival, and propagation delay.

A complex baseband representation of a time-varying multipath channel is

\[

h(t,\tau)=\sum_{\ell=0}^{L-1} a_\ell(t)e^{j\phi_\ell(t)}\delta(\tau-\tau_\ell(t)),

\]

where \(h(t,\tau)\) is the channel impulse response, \(L\) is the number of resolvable paths, \(a_\ell(t)\) and \(\phi_\ell(t)\) are the amplitude and phase of path \(\ell\), and \(\tau_\ell(t)\) is its delay. This representation assumes that each path can be approximated as an impulse in delay. In real environments, paths may form clusters, and the channel may be represented by a continuous or finely sampled delay profile.

For transmitted complex baseband signal \(x(t)\), the received signal is

\[

y(t)=\int h(t,\tau)x(t-\tau)d\tau+n(t),

\]

where \(n(t)\) is additive receiver noise. The channel is linear but generally time-varying.

1.2 Large-scale and small-scale effects

Large-scale propagation effects vary relatively slowly with transmitter-receiver separation. Path loss describes the average decrease in received power, while shadowing represents variation caused by large obstacles. A commonly used path-loss model is

\[

PL(d)=PL(d_0)+10n\log_{10}\left(\frac{d}{d_0}\right)+X_\sigma,

\]

where \(PL(d_0)\) is path loss at reference distance \(d_0\), \(n\) is the path-loss exponent, and \(X_\sigma\) is a zero-mean Gaussian random variable in dB with standard deviation \(\sigma\). This model describes large-scale behavior and should not be confused with a small-scale fading model.

Small-scale fading is the rapid fluctuation of amplitude and phase over a short distance or time interval. It results primarily from interference among multipath components. A useful system model separates these effects as

\[

y(t)=\sqrt{P_tG(d)}\,h_s(t)x(t)+n(t),

\]

where \(G(d)\) represents large-scale power gain, \(h_s(t)\) is normalized small-scale fading, and \(P_t\) is transmitted power. The normalization is often chosen so that \(E[|h_s(t)|^2]=1\).

2. Narrowband and Wideband Channels

2.1 Narrowband channel

A channel is narrowband when its signal bandwidth \(B_s\) is sufficiently smaller than the channel’s coherence bandwidth \(B_c\). In that case, all significant frequency components of the signal experience approximately the same complex gain. The channel is frequency-flat and can be modeled as

\[

y(t)=h(t)x(t)+n(t).

\]

Although the signal may be delayed physically, the delay differences among paths are too small to cause appreciable distortion across the signal bandwidth. The principal effect is a common amplitude and phase change.

2.2 Wideband channel

A channel is wideband when \(B_s\) is comparable to or greater than \(B_c\). Different frequency components then experience different gains and phases. The channel is frequency-selective and must be represented using its impulse response or frequency response:

\[

Y(f)=H(f)x(f)+N(f),

\]

where

\[

H(f)=\int h(t,\tau)e^{-j2\pi f\tau}d\tau.

\]

A wideband channel may produce intersymbol interference (ISI), because delayed copies of one symbol overlap subsequent symbols. Equalization, orthogonal frequency-division multiplexing, spread-spectrum processing, or suitable waveform design can mitigate this effect.

2.3 Resolvable multipath

For a signal of bandwidth \(B_s\), paths separated by a delay substantially larger than approximately \(1/B_s\) can often be resolved. Increasing bandwidth improves delay resolution and may transform a channel that appears flat-fading to a narrowband receiver into a frequency-selective channel for a wideband receiver.

3. Delay Dispersion and Coherence Bandwidth

3.1 Power delay profile

The power delay profile (PDP), denoted \(P(\tau)\), describes average received power as a function of excess delay. It is often estimated from measured channel impulse responses. Important parameters include mean excess delay and root-mean-square (RMS) delay spread.

The mean excess delay is

\[

\bar{\tau}=\frac{\sum_k P_k\tau_k}{\sum_kP_k},

\]

and the RMS delay spread is

\[

\sigma_\tau=\sqrt{\frac{\sum_kP_k(\tau_k-\bar{\tau})^2}{\sum_kP_k}}.

\]

Here, \(P_k\) is the average power in a path or delay bin and \(\tau_k\) is its excess delay. The units of both \(\bar{\tau}\) and \(\sigma_\tau\) are seconds.

The RMS delay spread measures temporal dispersion, not total propagation delay. It depends on the chosen measurement bandwidth, noise threshold, and delay window; therefore, measured values should always be reported with the estimation procedure.

3.2 Coherence bandwidth

Coherence bandwidth is the frequency separation over which channel responses remain strongly correlated. There is no single universal definition because the numerical value depends on the selected correlation threshold. Engineering approximations include

\[

B_c\approx\frac{1}{5\sigma_\tau}

\]

for a correlation of roughly 0.5, and

\[

B_c\approx\frac{1}{50\sigma_\tau}

\]

for a higher correlation requirement, often around 0.9. These are approximate relationships, not identities. The exact frequency correlation is obtained from the Fourier transform relationship between the PDP and the frequency correlation function under wide-sense stationary uncorrelated scattering assumptions.

If \(B_s\ll B_c\), flat fading is a reasonable approximation. If \(B_s\gg B_c\), frequency-selective fading is expected.

4. Doppler Dispersion and Coherence Time

4.1 Doppler shift

Relative motion changes the observed frequency. For a single plane wave arriving at angle \(\theta\) relative to the direction of motion, the Doppler shift is

\[

f_D=\frac{v}{\lambda}\cos\theta,

\]

where \(v\) is receiver speed, \(\lambda=c/f_c\) is wavelength, \(f_c\) is carrier frequency, and \(c\) is the speed of light. The maximum Doppler frequency is

\[

f_m=\frac{v}{\lambda}.

\]

Different paths have different arrival angles and therefore different Doppler shifts. Their combination produces Doppler spreading of a transmitted tone.

4.2 Coherence time

Coherence time indicates the time interval over which the channel remains significantly correlated. A commonly used engineering estimate is

\[

T_c\approx\frac{1}{2f_m},

\]

while alternative definitions use constants such as 0.423 or 0.5 depending on the correlation criterion and Doppler spectrum. Therefore, a coherence-time result should identify the adopted convention.

If the symbol duration is much smaller than \(T_c\), the channel is approximately slow fading over one symbol. If channel variation is significant during a symbol, the channel is fast fading and receiver tracking becomes more difficult.

4.3 Jakes or Clarke Doppler spectrum

For an isotropic two-dimensional scattering environment with a constant-speed receiver, the classical Clarke model gives the Doppler power spectral density

\[

S_h(f)=\frac{1}{\pi f_m\sqrt{1-(f/f_m)^2}},\quad |f|<f_m,

\]

and zero outside this interval. The spectrum has singular behavior near its edges in the idealized model. This model is useful for simulation but assumes isotropic scattering, a stationary environment, and a particular geometry. Real channels may have directional scattering, line-of-sight components, nonisotropic clusters, or time-varying Doppler statistics.

5. Rayleigh Fading

Rayleigh fading models a channel with many scattered components and no dominant line-of-sight path. Let the complex channel coefficient be

\[

h=h_I+jh_Q,

\]

where \(h_I\) and \(h_Q\) are independent zero-mean Gaussian random variables with equal variance. The envelope \(r=|h|\) has the Rayleigh probability density function

\[

p_R(r)=\frac{r}{\sigma^2}\exp\left(-\frac{r^2}{2\sigma^2}\right),\quad r\geq0.

\]

The corresponding cumulative distribution function is

\[

F_R(r)=1-\exp\left(-\frac{r^2}{2\sigma^2}\right).

\]

The mean-square envelope is \(E[r^2]=2\sigma^2\). If the channel is normalized to unit average power, then \(2\sigma^2=1\). The instantaneous power gain \(g=r^2\) is exponentially distributed under this normalization:

\[

p_g(g)=e^{-g},\quad g\geq0.

\]

Rayleigh fading is often a suitable first model for dense urban or indoor environments where a direct path is blocked or weak. It is less suitable when a strong deterministic component is present.

6. Rician Fading

Rician fading includes a dominant component, usually a line-of-sight path, together with diffuse scattered components. The envelope density is

\[

p_R(r)=\frac{r}{\sigma^2}\exp\left[-\frac{r^2+s^2}{2\sigma^2}\right]I_0\left(\frac{rs}{\sigma^2}\right),\quad r\geq0,

\]

where \(s\) is the amplitude of the deterministic component and \(I_0(\cdot)\) is the modified Bessel function of the first kind, order zero.

The Rician factor is

\[

K=\frac{s^2}{2\sigma^2},

\]

which is the ratio of dominant-component power to diffuse-component power. It is frequently expressed in decibels as \(K_{dB}=10\log_{10}K\). As \(K\to0\), the Rician model approaches Rayleigh fading. As \(K\) becomes large, fading becomes weaker and the channel approaches a nearly deterministic line-of-sight channel.

The Rician model assumes that the specular component and diffuse component can be meaningfully separated over the observation interval. In practical channels, the dominant component may itself vary due to blockage, antenna orientation, or movement.

7. Nakagami-m Fading

Nakagami-m fading is a flexible empirical model. If \(r\) is the envelope and \(\Omega=E[r^2]\) is its average power, the density is

\[

p_R(r)=\frac{2m^m}{\Gamma(m)\Omega^m}r^{2m-1}\exp\left(-\frac{mr^2}{\Omega}\right),\quad r\geq0,

\]

where \(m\geq 1/2\) is the shape parameter and \(\Gamma(m)\) is the gamma function. The parameter \(m\) controls fading severity. For \(m=1\), the envelope is Rayleigh. Values \(m<1epresent fading more severe than Rayleigh, while \(m>1\) represent milder fading. The model is attractive because it can fit measured data over a range of environments and has convenient mathematical properties.

Nakagami-m should not automatically be interpreted as a physical scattering mechanism. It is primarily a statistical fit. Parameter estimation may use maximum likelihood, moment matching, or sample statistics, and the estimated value depends on the measurement region and stationarity assumptions.

8. Outage Probability

Outage probability is the probability that instantaneous received quality falls below a required threshold. For a normalized flat-fading channel with average signal-to-noise ratio \(\bar{\gamma}\), instantaneous SNR is

\[

\gamma=\bar{\gamma}g,

\]

where \(g=|h|^2\) is normalized channel power gain. For Rayleigh fading, \(g\) is exponential, so

\[

P_{out}=P(\gamma<\gamma_{th})

=1-\exp\left(-\frac{\gamma_{th}}{\bar{\gamma}}\right).

\]

This expression assumes a single-branch, flat, independently sampled Rayleigh channel with perfect knowledge of the average SNR and a fixed threshold \(\gamma_{th}\). It does not include coding gain, diversity, interference, or implementation loss.

For small outage probabilities, \(\gamma_{th}/\bar{\gamma}\ll1\), the approximation

\[

P_{out}\approx\frac{\gamma_{th}}{\bar{\gamma}}

\]

follows from the first-order expansion of the exponential. The approximation should not be used when the ratio is not small.

For a target outage probability \(p\), the required average SNR in Rayleigh fading is

\[

\bar{\gamma}=\frac{\gamma_{th}}{-\ln(1-p)}.

\]

Outage probability is a link-reliability metric. It differs from average BER: two systems can have the same average error rate but different outage behavior, especially when traffic requires a minimum instantaneous rate.

For a target spectral efficiency \(R\) in bits/s/Hz, an AWGN threshold is often defined as

\[

\gamma_{th}=2^R-1,

\]

because \(R=\log_2(1+\gamma)\). This threshold is an idealized capacity-based criterion and may need adjustment for coding, modulation, and implementation constraints.

9. Channel Stationarity and Statistical Validity

A channel is wide-sense stationary (WSS) over an observation interval if its mean is constant and its autocorrelation depends only on time difference, not absolute time. For a process \(h(t)\),

\[

E[h(t)]=\mu_h,

\]

and

\[

R_h(t_1,t_2)=E[h(t_1)h^*(t_2)]=R_h(t_1-t_2).

\]

The WSS assumption enables Doppler spectral analysis and simplifies parameter estimation. It is only locally valid in many mobile environments. A vehicle turning a corner, a user entering a building, or an obstruction appearing in a line-of-sight path can change the statistics.

The uncorrelated scattering (US) assumption states that channel contributions associated with distinct delays are uncorrelated. WSSUS models are widely used because they lead to tractable relationships between delay and Doppler statistics. Real channels may violate US when scattering clusters overlap in delay or when specular components create correlation.

A stationarity region is an interval in space or time over which channel statistics can be treated as approximately constant. Estimating it requires comparing local means, variances, PDPs, or correlation functions over sliding windows. Using a single model over a long route can produce biased parameter estimates and misleading performance predictions.

10. Worked Example: Classifying a Mobile Link

Consider a receiver operating at \(f_c=3.5\) GHz and moving at \(v=30\) m/s. The measured RMS delay spread is \(\sigma_\tau=1\) microsecond, and the transmitted signal bandwidth is \(B_s=10\) MHz.

The wavelength is

\[

\lambda=\frac{3\times10^8}{3.5\times10^9}=0.0857\text{ m}.

\]

The maximum Doppler frequency is

\[

f_m=\frac{30}{0.0857}\approx350\text{ Hz}.

\]

Using \(T_c\approx1/(2f_m)\),

\[

T_c\approx\frac{1}{700}=1.43\text{ ms}.

\]

Using the 0.5-correlation engineering approximation,

\[

B_c\approx\frac{1}{5(1\times10^{-6})}=200\text{ kHz}.

\]

Because \(B_s=10\) MHz is much greater than \(B_c=200\) kHz, the link is frequency-selective rather than flat-fading. The channel is likely to cause ISI unless the waveform and receiver address the delay dispersion. Whether it is slow or fast fading depends on symbol duration. For a 1 microsecond symbol, the symbol duration is below the estimated coherence time, so the channel is approximately constant during one symbol, although it changes over many symbols.

11. Applied Case: Urban 5G Link Adaptation

Background

Consider an illustrative urban 5G downlink at 3.5 GHz serving a mobile user near a group of high-rise buildings. The base station has a line of sight during some street segments but experiences blockage near intersections and buses.

Problem

A single Rayleigh, frequency-flat model predicts excessive fading during line-of-sight segments, while a single Rician model underestimates outages during blockage. The system designer must choose models for link-level simulation and adaptive modulation.

Analysis

Drive-test or channel-sounding data are divided into local spatial windows. Within each window, the measured PDP provides RMS delay spread, while envelope samples provide estimates of fading parameters. A Rician model is fitted in line-of-sight windows using the estimated \(K\)-factor. Rayleigh or Nakagami-m models are fitted in blocked windows. Doppler parameters are estimated from user speed and the measured angle-of-arrival distribution rather than assumed to be isotropic.

The bandwidth comparison determines whether the simulation should use a flat-fading coefficient or a tapped-delay-line channel. At 100 MHz signal bandwidth, even a delay spread of several hundred nanoseconds may produce frequency selectivity, so an OFDM-compatible frequency-selective model is required. The scheduler uses estimated channel quality and includes an outage margin rather than relying only on average received power.

Approach and outcome

The resulting simulator uses location-dependent channel states, correlated time evolution, and separate line-of-sight and blocked-state statistics. It evaluates throughput, outage, and handover behavior. Compared with a single global model, the state-based approach gives more realistic prediction of deep fades, modulation changes, and reliability near blockage transitions.

Learning points

1. Model selection must reflect propagation state, not only carrier frequency.

2. Delay spread determines whether a flat or frequency-selective model is appropriate.

3. A fitted distribution is meaningful only over a declared stationarity region.

4. Temporal correlation matters when evaluating retransmissions, scheduling, and tracking.

5. Average SNR alone is insufficient for reliability engineering.

12. Practical Modelling Workflow and Limitations

A defensible channel-modelling workflow is:

1. Define the scenario, frequency, antenna configuration, bandwidth, mobility, and performance metric.

2. Separate large-scale path loss and shadowing from small-scale fading.

3. Measure or obtain the PDP and estimate delay spread.

4. Estimate Doppler behavior from mobility and scattering geometry.

5. Determine local stationarity regions.

6. Select flat- or frequency-selective representation.

7. Select a fading distribution using physical knowledge and goodness-of-fit tests.

8. Preserve temporal and spatial correlation in simulation.

9. Validate predictions against independent measurements.

10. Report assumptions, thresholds, parameter-estimation methods, and confidence intervals.

Statistical models have important limitations. A Rayleigh or Rician distribution describes marginal amplitude behavior but does not by itself specify temporal correlation, spatial correlation, polarization, antenna coupling, or frequency correlation. Independent fading samples can substantially overestimate diversity and underestimate outage duration. The same fitted distribution can arise from different physical environments, so statistical fit alone does not establish physical validity.

In modern systems, geometry-based stochastic models, ray tracing, measurement-driven models, and hybrid models are often combined. Machine learning can assist in classifying propagation states, estimating channel parameters, or generating samples. However, learned models require representative training data, careful validation, and safeguards against extrapolation. They should not obscure physical assumptions or replace uncertainty analysis.

13. Design and Governance Considerations

Channel models affect spectrum planning, coverage claims, emergency-service reliability, infrastructure investment, and fairness of performance evaluation. Models should therefore be documented and reproducible. Measurements should represent relevant environments, mobility patterns, device orientations, and user groups. Regulatory or standards-based evaluations may prescribe channel models, but engineering studies should state when a prescribed model is unsuitable for a particular deployment.

Privacy is relevant when channel sounding uses location traces or identifiable user trajectories. Data collection should minimize personal information, control access, and follow applicable data-protection requirements. Safety-critical applications should use conservative reliability targets and test unusual but plausible blockage and mobility conditions rather than relying only on average performance.

Chapter Summary

Wireless channels are random, time-varying systems created by multipath propagation, mobility, and environmental variation. The channel impulse response describes path amplitudes, phases, and delays, while its frequency response describes frequency-selective behavior. Narrowband signals experience approximately one complex channel gain when signal bandwidth is much smaller than coherence bandwidth; wideband signals resolve delay dispersion and may suffer ISI.

RMS delay spread characterizes temporal dispersion and is related approximately to coherence bandwidth. Maximum Doppler frequency is determined by velocity and wavelength, while coherence time describes the duration of significant temporal correlation. Rayleigh fading models diffuse multipath without a dominant component, Rician fading includes a specular component measured by the \(K\)-factor, and Nakagami-m provides a flexible empirical description controlled by parameter \(m\).

Outage probability quantifies the chance that instantaneous SNR falls below a required threshold. Stationarity assumptions, including WSS and WSSUS, make analysis tractable but are usually valid only locally. Reliable professional modelling requires scenario-specific parameter estimation, preservation of correlation, validation against measurements, and explicit reporting of assumptions and limitations.

Key Terms

Multipath propagation: Arrival of a transmitted signal through multiple reflected, diffracted, or scattered paths.

Channel impulse response: Channel response as a function of time and propagation delay.

Power delay profile: Average received power distributed over excess delay.

Mean excess delay: Power-weighted average excess propagation delay.

RMS delay spread: Square root of the power-weighted delay variance.

Coherence bandwidth: Frequency interval over which channel responses are strongly correlated.

Doppler shift: Frequency shift caused by relative motion between transmitter, receiver, and propagation paths.

Doppler spread: Range of Doppler frequencies produced by multipath motion.

Coherence time: Time interval over which the channel remains significantly correlated.

Flat fading: Fading in which the signal bandwidth is much smaller than coherence bandwidth.

Frequency-selective fading: Fading in which different signal frequencies experience different gains.

Rayleigh fading: Diffuse multipath fading without a dominant specular component.

Rician fading: Fading containing a dominant component and diffuse scattering.

Rician K-factor: Ratio of dominant-component power to diffuse-component power.

Nakagami-m fading: Flexible envelope model controlled by shape parameter \(m\).

Outage probability: Probability that instantaneous link quality falls below a specified threshold.

Wide-sense stationarity: Constant mean and autocorrelation dependent only on time difference.

Uncorrelated scattering: Assumption that contributions associated with different delays are uncorrelated.

Intersymbol interference: Symbol distortion caused by delayed signal components overlapping neighboring symbols.

Stationarity region: Spatial or temporal interval over which channel statistics are approximately constant.

Review Questions

Short Answer Questions

1. What physical mechanisms produce multipath propagation?

2. Define RMS delay spread and explain its significance.

3. What is the difference between flat fading and frequency-selective fading?

4. What does the Rician K-factor represent?

5. Why are channel statistics often considered locally stationary rather than globally stationary?

Long Answer Questions

1. Derive the relationship between the multipath impulse response and the frequency response, and explain its implications for a wideband system.

2. Compare Rayleigh, Rician, and Nakagami-m fading models, including their parameters, assumptions, and appropriate applications.

3. Explain coherence bandwidth and coherence time, including why their numerical estimates depend on correlation conventions.

4. Develop the Rayleigh outage probability expression for a normalized flat-fading channel.

5. Discuss the assumptions and limitations of WSSUS channel models in practical mobile environments.

Analytical / Application Questions

1. A 2.6 GHz receiver moves at 15 m/s and measures an RMS delay spread of 2 microseconds. Estimate maximum Doppler frequency, coherence time using \(1/(2f_m)\), and coherence bandwidth using \(1/(5\sigma_\tau)\). Classify a 20 MHz signal as flat or frequency-selective.

2. A normalized Rayleigh channel has average SNR of 12 dB and requires an instantaneous SNR of 5 dB. Calculate its outage probability and interpret the result.

3. Design a measurement and modelling procedure for a high-speed railway link. Specify how you would estimate delay spread, Doppler spread, stationarity regions, and the appropriate fading distribution.

Multiple Choice Questions with Answers

Question 1

A channel is most appropriately treated as frequency-flat when:

A. The signal bandwidth is much greater than the coherence bandwidth

B. The signal bandwidth is much smaller than the coherence bandwidth

C. The Doppler frequency is greater than the carrier frequency

D. The RMS delay spread is zero in every practical environment

Correct Answer: B. The signal bandwidth is much smaller than the coherence bandwidth

Question 2

If the RMS delay spread is 1 microsecond, the approximation Bc ≈ 1/(5στ) gives:

A. 2 kHz

B. 20 kHz

C. 200 kHz

D. 5 MHz

Correct Answer: C. 200 kHz

Question 3

For a receiver moving at speed v, the maximum Doppler frequency is:

A. vλ

B. λ/v

C. v/fc

D. v/λ

Correct Answer: D. v/λ

Question 4

Rayleigh fading is most appropriate when:

A. A strong deterministic line-of-sight component dominates

B. There are many scattered components and no dominant component

C. The channel has no multipath propagation

D. The signal bandwidth is exactly equal to the carrier frequency

Correct Answer: B. There are many scattered components and no dominant component

Question 5

The Rician K-factor is the ratio of:

A. Noise power to signal power

B. Diffuse-component power to dominant-component power

C. Dominant-component power to diffuse-component power

D. Maximum Doppler power to average received power

Correct Answer: C. Dominant-component power to diffuse-component power

Question 6

For normalized Rayleigh fading, the instantaneous power gain is distributed as:

A. Uniform

B. Exponential

C. Gaussian with zero variance

D. Deterministic

Correct Answer: B. Exponential

Question 7

A normalized Rayleigh channel has average SNR 10 and outage threshold 2. Its outage probability is:

A. 1 − exp(−0.2)

B. 1 − exp(−5)

C. exp(−0.2)

D. 2 exp(−10)

Correct Answer: A. 1 − exp(−0.2)

Question 8

In Nakagami-m fading, increasing m above 1 generally indicates:

A. More severe fading than Rayleigh fading

B. Milder fading than Rayleigh fading

C. A zero-power channel

D. An increase in Doppler frequency only

Correct Answer: B. Milder fading than Rayleigh fading

Question 9

Under wide-sense stationarity, the channel autocorrelation depends on:

A. Absolute time only

B. The carrier frequency only

C. Time difference rather than absolute time

D. The transmitted data symbols only

Correct Answer: C. Time difference rather than absolute time

Question 10

A principal consequence of large delay spread in a wideband system is:

A. Guaranteed absence of ISI

B. Frequency-selective fading and possible ISI

C. Removal of Doppler spread

D. Conversion of all fading into path loss

Correct Answer: B. Frequency-selective fading and possible ISI