Chapter 2: The Wireless Channel
Q1: What are the two types of fading in a wireless channel?
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Answer: Large-scale fading (caused by path loss and shadowing from objects) and smallscale fading (due to constructive/destructive interference of multiple signal paths).
Q2: How is the wireless channel modeled physically?
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Answer: It is modeled using electromagnetic waves, considering factors such as
reflection, diffraction, and scattering. This includes free-space models and models
accounting for ground and object reflections.
Q3: What is the role of coherence time and Doppler spread?
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Answer: Coherence time measures how long the channel remains constant, inversely
related to the Doppler spread, which indicates the rate of channel variation due to motion.
Q4: How are statistical models used for wireless channels?
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Answer: They describe channel variations using distributions like Rayleigh (for no lineof-sight) and Rician (for strong line-of-sight), alongside tap gain auto-correlation
functions.
Q5: What happens to signal power as distance increases in wireless channels?
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Answer: In free space, power decreases as 1/r21/r^2. With obstacles, it may decay faster
due to shadowing and absorption.
Q6: What is Clarke’s model in wireless channels?
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Answer: It describes multipath fading, assuming scatterers are uniformly distributed in a
circular area around the receiver.
Q7 (Mathematical): How is the coherence bandwidth related to delay spread?
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Answer: Coherence bandwidth WcW_c is approximately the reciprocal of the delay
spread TdT_d, i.e., Wc∼1/TdW_c \sim 1/T_d.
Q8: What is the significance of path loss and shadowing?
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Answer: Path loss describes the reduction in signal power as distance increases, while
shadowing accounts for random variations in received power due to obstacles.
Q9: What is the input-output model for a wireless channel?
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Answer: The wireless channel is treated as a linear time-varying system, often simplified
into a baseband equivalent model or a discrete-time baseband model.
Q10: What is the role of Additive White Gaussian Noise (AWGN) in channel models?
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Answer: AWGN represents the thermal noise inherent in communication systems,
serving as a baseline for assessing channel impairments.
Q11: How is delay spread observed in practical channels?
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Answer: Delay spread causes inter-symbol interference in time and determines
coherence bandwidth, affecting how wideband signals interact with the channel.
Q12: What are Rayleigh and Rician fading models used for?
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Answer: Rayleigh models represent environments without a strong line-of-sight
component, while Rician accounts for scenarios with a dominant line-of-sight path.
Q13 (Mathematical): How is coherence time (TcT_c) related to Doppler spread (fDf_D)?
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Answer: Tc≈1/fDT_c \approx 1 / f_D, meaning channels with higher Doppler spread
vary more rapidly in time.
Q14: What is the tap gain auto-correlation function?
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Answer: It quantifies how channel gains at different times are correlated, depending on
the Doppler spread and other channel dynamics.
Chapter 3: Point-to-Point Communication
Q1: How does fading affect uncoded transmission over wireless channels?
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Answer: Fading leads to a significant error probability, especially during deep fades,
resulting in much worse performance compared to additive white Gaussian noise
(AWGN) channels at similar signal-to-noise ratios (SNR).
Q2: What are the main types of diversity techniques in wireless communication?
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Answer: Time diversity (interleaving coded symbols), frequency diversity (spreading
signal over a wide band), and spatial diversity (using multiple antennas).
Q3: What are the benefits of multiple-input multiple-output (MIMO) systems?
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Answer: MIMO enhances reliability and capacity through spatial multiplexing and
diversity.
Q4: How does channel uncertainty impact diversity performance?
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Answer: Uncertainty increases complexity and can degrade performance in scenarios
with numerous diversity branches, as energy per path becomes difficult to estimate.
Q5 (Mathematical): What is the error probability for diversity schemes with Rayleigh
fading?
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Answer: The high-SNR error probability behaves as Pe∝SNR−LP_e \propto
\text{SNR}^{-L}, where LL is the number of independent fading paths.
Q6: What is the role of OFDM in mitigating frequency-selective fading?
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Answer: OFDM divides the bandwidth into orthogonal subcarriers, making it easier to
handle multi-path delays and achieve frequency diversity.
Q7 (Mathematical): What is the high-SNR performance for uncoded detection in Rayleigh
fading?
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Answer: The error probability is approximately proportional to Pe∝1/SNRP_e \propto
1/\text{SNR}, much worse than exponential decay in AWGN channels.
Q8: How does antenna diversity improve reliability?
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Answer: By using multiple receive or transmit antennas, signals from different paths are
combined, reducing the likelihood of deep fades affecting all paths simultaneously.
Q9: What is the principle behind space-time coding?
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Answer: It uses both spatial and temporal domains to encode data, enhancing reliability
and enabling diversity in MIMO systems.
Q10: How is time diversity achieved with repetition coding?
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Answer: Information is transmitted multiple times across different time intervals to
reduce the impact of deep fades on reliability.
Q11: How does OFDM mitigate inter-symbol interference (ISI)?
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Answer: By converting a frequency-selective fading channel into a set of flat-fading subchannels, OFDM reduces ISI and simplifies equalization.
Q12: What is the impact of channel estimation on communication?
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Answer: Accurate channel estimation allows coherent detection, which significantly
outperforms non-coherent detection in terms of error probability.
Q13: What challenges arise with non-coherent detection?
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Answer: Non-coherent detection avoids explicit channel estimation but suffers from
higher error rates and limited ability to exploit diversity.
Q14 (Mathematical): What is the diversity gain with LL independent paths in Rayleigh
fading?
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Answer: The error probability decays as Pe∝SNR−LP_e \propto \text{SNR}^{-L},
illustrating that increasing diversity reduces the error rate more rapidly.
Q15: How does GSM leverage time diversity?
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Answer: GSM interleaves coded symbols across multiple frames, exploiting variations in
the channel to reduce the likelihood of burst errors.
Q16: How does frequency diversity improve performance?
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Answer: By spreading the signal over a wide frequency band, independent fades across
different frequencies provide resilience against frequency-selective fading.
Q17: How does spatial diversity differ between transmit and receive configurations?
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Answer: Transmit diversity requires coordinated signaling (e.g., Alamouti codes), while
receive diversity uses multiple antennas to directly combine incoming signals.
Q18 (Mathematical): What is the relationship between channel capacity and diversity in
MIMO systems?
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Answer: Capacity grows linearly with the minimum of the number of transmit (ntn_t)
and receive (nrn_r) antennas, i.e., C∝min⁡(nt,nr)C \propto \min(n_t, n_r).