Channel Distortion

Channel Distortion: Amplitude and Phase Distortion Effects

Communication channels introduce distortion that degrades signal quality. Understanding and correcting distortion is essential for reliable communication.

Types of Distortion

Amplitude Distortion:

• Different frequency components attenuated differently
• Frequency-selective channel: H(f) magnitude varies with f
• Results in spectral shaping (baseband distortion)

Phase Distortion:

• Different frequency components delayed differently
• Group delay not constant: τ(f) = -(1/(2π)) × dφ/df varies
• Creates intersymbol interference (ISI)

Mathematical Model

Distorted signal: y(t) = ∫ x(τ) × h(t-τ) dτ + n(t)

Channel impulse response: h(t) = Σ_k a_k × δ(t - τ_k)

• a_k = amplitude of multipath component
• τ_k = delay of k-th path
• Multiple paths cause ISI

Impulse Response Example

Intersymbol Interference (ISI)

When channel delay spread >symbol period, symbols interfere:

Output at symbol n: y(n) = h(0)×x(n) + h(1)×x(n-1) + h(2)×x(n-2) + ...

Eye Diagram: Visual representation of ISI

• Closed eye = severe ISI (high error rate)
• Open eye = low ISI (low error rate)

Equalization Techniques

Zero-Forcing (ZF) Equalizer: Inverts channel: G(f) = 1/H(f)

• Nulls channel response
• Amplifies noise in deep nulls (noise enhancement problem)

Minimum Mean-Square Error (MMSE) Equalizer: Minimizes: E[(y - x)²]

• Balances ISI reduction vs. noise amplification
• Superior to ZF at low SNR
• 3-5 dB better performance typical

Decision Feedback Equalizer (DFE): Uses previous hard decisions to cancel ISI: y(n) = [received] - Σ feedback coefficients × previous decisions

Distortion Impact on Modulation

Real-World Examples

Telephone channel (audio band-limited, dispersive):

• Amplitude: -0.5 dB at 1 kHz, -6 dB at 3 kHz
• Phase: Non-linear, causes dispersion
• ISI: ~10-20 μs delay spread

Wireless multipath:

• Delay spread: 1-10 μs typical (urban)
• Symbol period: OFDM mitigates by using many subcarriers
• OFDM subcarrier spacing >> 1/delay_spread

Interview Q&A

Q1: What is the difference between amplitude and phase distortion? A: Amplitude distortion attenuates different frequencies differently—low frequencies pass while high frequencies attenuate, creating spectral shaping. Phase distortion delays different frequencies differently (non-linear phase response), causing dispersion where signal edges blur. Both cause intersymbol interference but through different mechanisms.

Q2: Explain intersymbol interference and why it limits data rate. A: ISI occurs when channel delay spread exceeds symbol period. Previous symbols' delayed echoes overlap with current symbol, increasing noise-like interference. As data rate increases (symbol period decreases), ISI worsens. Eventually, ISI floor (error rate floor independent of SNR) appears at 10-12% of unequalized rate.

Q3: Compare zero-forcing vs. MMSE equalization. A: ZF inverts channel (G = 1/H) completely nulling ISI but amplifying noise in deep nulls—problematic at low SNR. MMSE minimizes total error (ISI + noise) finding optimal balance. MMSE reduces gain in frequency nulls rather than inverting them, trading small ISI residual for large noise reduction. MMSE is 3-5 dB superior to ZF at practical SNR levels.

Q4: What is an eye diagram and how does it relate to ISI? A: Eye diagram plots symbol-by-symbol baseband signal superimposed. Open (large) eye = low ISI, low error rate (low noise margin acceptable). Closed eye = high ISI, high error rate. Vertical opening (amplitude) shows noise immunity; horizontal opening (timing) shows timing margin. Real channels show partially-closed eyes; equalizers aim to open them.

Q5: Why does 16-QAM require better equalization than BPSK? A: BPSK has only 2 constellation points far apart (robust to distortion). 16-QAM has 16 points close together; same distortion percentage causes larger absolute errors. Distortion spread that's tolerable for BPSK (causes <10% error) might cause 30-50% error in 16-QAM. Therefore higher-order modulations require tighter equalization (better than BPSK/QPSK equalizers).

Q6: How do multicarrier systems (OFDM) mitigate channel distortion? A: OFDM uses many narrowband subcarriers (tones) with longer symbol period. If subcarrier spacing >> 1/delay_spread, each tone experiences nearly flat fading (no ISI). Cyclic prefix (padding) converts linear convolution to circular convolution, enabling one-tap per-subcarrier equalization. Simplifies equalization complexity dramatically vs. single-carrier requiring complex adaptive filters.