5G Technology (EC-802 (C)) - Unit 1 Short Notes

UNIT 1: FUNDAMENTALS OF WIRELESS CHANNELS & SYSTEMS

I. INTRODUCTION TO WIRELESS COMMUNICATION SYSTEMS

Wireless Services & Requirements

• Types: Voice (circuit-switched), Data (packet-switched: email, web), Multimedia (video streaming, gaming), IoT (M2M, low-power, massive connectivity).

• Key QoS Parameters:

  • Data Rate: Peak & average throughput (bps).

  • Latency: Air-interface delay, connection setup time (ms).

  • Reliability: Packet error rate (PER), availability (e.g., 99.999% for critical IoT).

  • Coverage: Cell radius, indoor penetration.

• Economic & Social Impact: Enables ubiquitous connectivity, drives digital economy (apps, services), improves healthcare/education access, but raises privacy & spectrum allocation challenges.

[!TIP] Exam Focus: Be ready to list specific QoS requirements for different services (e.g., ultra-low latency for autonomous vehicles vs. massive connections for sensor networks).

Evolution (1G to 5G)

• Multiple Access Evolution: FDMA (1G) → TDMA (2G) → CDMA (3G) → OFDMA (4G/5G) for flexible bandwidth allocation and multipath resilience.

Fundamental Technical Challenges

1. Multipath Propagation: Causes Intersymbol Interference (ISI) and fading.

2. User Mobility: Induces Doppler shift/spread, making channel time-variant.

3. Limited Spectrum: Scarcity → need for high spectral efficiency (bps/Hz) and new bands (mmWave).

4. Noise & Interference: Additive White Gaussian Noise (AWGN), co-channel/adjacent-channel interference.

5. Security: Eavesdropping, jamming in open air medium.

II. WIRELESS CHANNEL PROPAGATION FUNDAMENTALS

Large-Scale Propagation (Path Loss & Shadowing)

• Free-Space Path Loss (FSPL):

$$ \text{FSPL}(d) = \frac{P_t}{P_r} = \left( \frac{4\pi d}{\lambda} \right)^2 = \left( \frac{4\pi d f}{c} \right)^2 $$

where \(d\) = distance, \(\lambda\) = wavelength, \(f\) = frequency, \(c\) = light speed.

> \boxed{\text{FSPL (dB)} = 20\log_{10}(d) + 20\log_{10}(f) + 20\log_{10}\left(\frac{4\pi}{c}\right)}

• Log-Distance Path Loss Model:

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

*   \(n\) = **Path Loss Exponent** (environment-dependent: 2=free space, 4=urban dense).

*   \(X_\sigma\) = **Shadowing** (log-normal random variable, zero-mean, \(\sigma\) dB std dev).

Small-Scale Propagation & Multipath Fading

• Physical Mechanisms:

  • Reflection: From surfaces (buildings, ground). Governed by Fresnel equations (depends on permittivity, angle, polarization).

  • Diffraction: Around sharp edges (knife-edge model). Loss increases with frequency.

  • Scattering: From rough surfaces (trees, walls) and small objects. Creates many reflected waves.

Delay Spread & Coherence Bandwidth

• Power Delay Profile (PDP): \(p(\tau) = \sum_{i=1}^{L} |h_i|^2 \delta(\tau - \tau_i)\), where \(h_i\), \(\tau_i\) are gain & delay of \(i^{th}\) path.

• Mean Excess Delay: \(\bar{\tau} = \frac{\sum_i |h_i|^2 \tau_i}{\sum_i |h_i|^2}\)

• RMS Delay Spread: \(\tau_{rms} = \sqrt{\bar{\tau^2} - (\bar{\tau})^2}\), where \(\bar{\tau^2} = \frac{\sum_i |h_i|^2 \tau_i^2}{\sum_i |h_i|^2}\)

• Coherence Bandwidth (\(B_c\)): Frequency range over which channel impulse response is highly correlated.

  \boxed{B_c \approx \frac{1}{5\tau_{rms}} \quad \text{to} \quad \frac{1}{\tau_{rms}}}

• Impact:

  • If \(B_s \ll B_c\) (signal bandwidth << coherence bandwidth) → Flat Fading (all freq components fade same way).

  • If \(B_s > B_c\) → Frequency-Selective Fading (ISI occurs).

Doppler Shift & Doppler Spread

• Doppler Shift (single path): \(f_d = \frac{v}{\lambda} \cos\theta = f_c \frac{v}{c} \cos\theta\)

  • \(v\) = mobile speed, \(\theta\) = angle between mobile direction and incident wave.

• Maximum Doppler Spread: \(f_{d,\max} = \frac{v}{\lambda} = f_c \frac{v}{c}\)

• Coherence Time (\(T_c\)): Time duration over which channel impulse response is correlated.

  \boxed{T_c \approx \frac{1}{f_d} \quad \text{(often approximated as } T_c \approx \frac{9}{16\pi f_{d,\max}} \text{ for Jakes' model)}}

• Impact: High \(v\) → large \(f_d\) → fast channel variation → need faster tracking (shorter training intervals).

Classification of Fading

• Small-Scale Fading Distributions:

  • Rayleigh: No dominant line-of-sight (LOS) component. PDF of envelope \(r\): \(p(r) = \frac{r}{\sigma^2} e^{-r^2/(2\sigma^2)}\), \(r \ge 0\).

  • Rician: With dominant LOS component (power \(K\)). PDF: \(p(r) = \frac{r}{\sigma^2} e^{-(r^2 + A^2)/(2\sigma^2)} I_0\left(\frac{rA}{\sigma^2}\right)\), where \(A\) = LOS amplitude, \(K = A^2/(2\sigma^2)\).

[!TIP] Common Pitfall: Confusing conditions for flat/frequency-selective (compare \(B_s\) vs \(B_c\)) and slow/fast fading (compare \(T_s\) vs \(T_c\)). Always state the condition clearly.

III. CHANNEL MODELING AND CHARACTERIZATION

Stochastic Channel Modeling

• WSSUS Model (Wide-Sense Stationary Uncorrelated Scattering):

  • Assumptions:

    1. WSS: Channel statistics (power) invariant to time shift.

    2. US: Scattering components with different delays are uncorrelated.

  • Condensed Parameters: Fully described by Delay Power Spectrum \(S(\tau)\) (PDP) and Doppler Power Spectrum \(S(f_d)\).

  • Significance: Simplifies analysis; basis for standard models (e.g., tapped-delay line).

Narrowband, Wideband, and Directional Models

Time-Variant Two-Path Model

• Simple model: \(h(t, \tau) = \alpha_1(t)\delta(\tau) + \alpha_2(t)\delta(\tau - \Delta\tau)\)

• Captures ISI (from \(\Delta\tau\)) and time-variance (from \(\alpha_i(t)\)).

• Used to illustrate concepts like delay spread and Doppler effects analytically.

Channel Measurement and Sounding

• Purpose: Obtain PDP/Doppler spectrum, validate models.

• Time-Domain:

  • Pulse Sounding: Transmit short pulse, measure received pulse shape. Simple but low SNR.

  • Spread Spectrum Sliding Correlator: Transmit PN sequence, correlate at receiver. Good SNR, high resolution.

• Frequency-Domain: Use vector network analyzer to measure \(S_{21}(f)\) over bandwidth, then IFFT to get PDP.

Doppler Power Spectral Density (Doppler Spectra)

• Clarke's Model (Isotropic): Uniform AoA in horizontal plane. PSD: \(S(f_d) \propto \frac{1}{\sqrt{f_{d,\max}^2 - f_d^2}}\) for \(|f_d| < f_{d,\max}\).

• Jakes' Model: Practical simulation of Clarke's. Uses sum of sinusoids with specific phases/frequencies.

• Shape: U-shaped (Clarke) for isotropic scattering; asymmetric if dominant LOS or non-uniform AoA.

IV. WIRELESS TRANSCEIVER ARCHITECTURE & PERFORMANCE

Block Diagram of a Wireless Link

Transmitter: Source → Channel Encoder → Interleaver → Modulator → Up-converter → Power Amp → Antenna

Channel: Wireless Fading Channel (with AWGN)

Receiver: Antenna → LNA → Down-converter → Equalizer → Demodulator → Deinterleaver → Channel Decoder → Sink

• Key Blocks:

  • Power Amplifier (PA): Efficiency critical (non-linear → distortion).

  • Low-Noise Amplifier (LNA): Sets noise figure (NF) of receiver.

  • Equalizer: Compensates for channel distortion (ISI).

Antennas for Mobile Stations

• Common Types:

  • Monopole/Dipole: Simple, omnidirectional, quarter/half-wave.

  • Patch (Microstrip): Low-profile, conformal, directional (often used in phones).

• Key Parameters:

  • Impedance Matching: \(Z_{ant} = 50\Omega\) (standard) for max power transfer.

  • Polarization: Linear (vertical/horizontal) vs. circular (better for mobile orientation).

  • Gain & Efficiency: \(G = \eta D\) (D = directivity, \(\eta\) = efficiency). Small size → low gain.

  • Size Constraint: \(\sim \lambda/4\) minimum for efficient radiation at given \(f\).

Modulation & Demodulation Impact

• Bandwidth Efficiency (\(\eta_b\)): \(\eta_b = \frac{\log_2(M)}{B T_s}\) (bps/Hz). Higher \(M\) → higher \(\eta_b\) but needs higher SNR.

• Power Efficiency: SNR required for target BER. Coherent (PSK, QAM) > Non-coherent (FSK) in power efficiency.

• Example Comparison:

  • QPSK: \(\eta_b = 2\) bps/Hz, coherent.

  • MSK (GMSK): \(\eta_b = 1\) bps/Hz, constant envelope (non-linear PA friendly), smoother spectrum.

AWGN Channel Model

• Assumptions: Linear, time-invariant, additive white Gaussian noise (flat spectrum, Gaussian stats).

• Significance: Fundamental baseline for error probability analysis.

• Error Probability (for coherent BPSK):

  \boxed{P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)}

  where \(Q(x) = \frac{1}{\sqrt{2\pi}}\int_x^\infty e^{-t^2/2} dt\).

V. MITIGATION TECHNIQUES FOR FADING CHANNELS

Diversity Techniques

• Fundamental: Provide multiple independent (or partially correlated) signal replicas tocombine, reducing fade probability.

• Microdiversity vs. Macrodiversity:

  | Feature | Microdiversity | Macrodiversity | | :--- | :--- | :--- | | Scale | Within a cell/small area (cm-m) | Between base stations (km) | | Correlation | High (small separation) | Low (large separation) | | Purpose | Combat small-scale fading (fast) | Combat large-scale shadowing (slow) | | Example | Multiple antennas at BS (MIMO) | Soft handoff, cooperative BSs |

• Diversity Types:

  • Time: Repeat transmission in different time slots (requires \(T_c\) separation).

  • Frequency: Transmit on different frequencies (requires \(B_c\) separation).

  • Space: Multiple antennas (most common).

  • Polarization: Orthogonal polarizations (vertical/horizontal).

  • Angle: Using directional antennas with different AoA.

• Combining Methods:

  • Selection Combining (SC): Pick branch with highest SNR. Simple, suboptimal.

  • Equal Gain Combining (EGC): Co-phasing, equal weighting. Medium complexity.

  • Maximal Ratio Combining (MRC): Weight by SNR. Optimal, requires channel estimation.

Equalization

• Need: To remove ISI caused by frequency-selective fading (\(B_s > B_c\)).

• Classification:

  | Type | Linear | Nonlinear | | :--- | :--- | :--- | | | Zero-Forcing (ZF) | Decision Feedback (DFE) | | | Inverts channel (H⁻¹). Amplifies noise at deep fades. | Uses past decisions to cancel post-cursor ISI. No noise amplification, but error propagation. | | | MMSE | Maximum Likelihood (Viterbi) | | | Minimizes MSE (noise+fading trade-off). | Optimal sequence estimation (MLSE). High complexity (2^L states for L taps). |

• Fractional Spaced Equalizer (FSE):

  • Structure: Taps spaced at \(T_s/2\) (or other fraction) instead of \(T_s\).

  • Advantage: Avoids timing sensitivity, better performance when sampling clock offset exists. Can be implemented as two \(T_s\)-spaced filters (polyphase).

• Blind vs. Decision-Directed Equalization:

  | Aspect | Blind Equalization | Decision-Directed (DD) | | :--- | :--- | :--- | | Training | No known sequence; uses signal statistics (e.g., constant modulus). | Uses initial training sequence, then switches to decisions. | | Convergence | Slower, may converge to local minima. | Faster after training, but can drift if decisions wrong. | | When Preferred | When training overhead is costly, or channel varies slowly after initial convergence. | Standard in most systems (e.g., GSM, LTE) for reliable start. |

[!TIP] Exam Key: For equalizer comparison, always state the objective (invert channel, minimize MSE, cancel ISI) and main drawback (noise amplification, error propagation, complexity).

VI. ADVANCED TOPICS & SYNTHESIS

Derivation of Rayleigh Distance for Antennas

• Concept: Distance beyond which angular beamwidth is constant; far-field region.

• Expression: For antenna with largest dimension \(D\) and wavelength \(\lambda\):

  \boxed{R_{ray} = \frac{2D^2}{\lambda}}

• For Square Aperture with Gain \(G\): \(G = \frac{4\pi A}{\lambda^2} = \frac{4\pi D^2}{\lambda^2}\) (for square, \(A = D^2\)). So \(D^2 = \frac{G\lambda^2}{4\pi}\).

  Substitute: \(R_{ray} = \frac{2}{\lambda} \cdot \frac{G\lambda^2}{4\pi} = \frac{G\lambda}{2\pi}\).

• Example: \(G = 20\) dB = 100, \(\lambda = 0.03\) m (10 GHz) → \(R_{ray} = \frac{100 \times 0.03}{2\pi} \approx 0.48\) m.

Impact of Frequency-Dispersive Fading on Error Probability

• Mechanism: Delay spread → frequency-selective fading → some subcarriers (in OFDM) or frequency components experience deep fades.

• Effect on BER: For flat fading, BER averaged over Rayleigh/Rician distribution. For frequency-selective, ISI causes additional errors even if average SNR is high. Requires equalization or multi-carrier modulation (OFDM) to convert to flat fading per subcarrier.

• Key Relationship: If \(B_s > B_c\), system performance degrades significantly without mitigation; BER floor may appear.

Comparative Analysis (Exam Favorites)

1. Blind vs. Decision-Directed Equalization:

   • Blind: No training needed → bandwidth efficient. Convergence slower, may not converge to optimal solution. Used in non-stationary channels or where training is expensive.

   • DD: Fast convergence after training. Reliable start but may drift if decision errors occur (error propagation). Standard in most systems.

2. Microdiversity vs. Macrodiversity:

   • Micro: Small-scale (antennas close). Combats fast fading (Rayleigh). High correlation if spacing < \(\lambda/2\). Used in MIMO, antenna arrays at BS.

   • Macro: Large-scale (BSs far apart). Combats slow shadowing. Low correlation. Used in soft handoff, cooperative networks.

3. Spectral Efficiency: MSK vs. QPSK

   • QPSK: \(\eta_b = 2\) bps/Hz. Coherent detection. Requires linear PA (sensitive to non-linearities).

   • MSK: \(\eta_b = 1\) bps/Hz. Constant envelope → non-linear PA friendly. Smoother spectrum (lower sidelobes). More robust to non-linearities but lower rate.

Short Note Topics (From Past Papers)

• Antennas for Mobile Stations: Focus on size constraints (fractional wavelength), omnidirectional pattern (unless beamforming), low cost, durability. Common: monopole (whip), PIFA (planar inverted-F), patch. Key params: impedance matching (50Ω), VSWR < 2, efficiency > 50%.

• Data Services in Cellular Communication: Contrast with voice: packet-switched, bursty traffic, asymmetric (DL > UL), QoS classes (conversational, streaming, interactive, background). Requires efficient packet scheduling, HARQ, adaptive modulation.

• TDMA and CDMA Systems:

  • TDMA (2G GSM): Time slots per carrier. Synchronization critical. Simple receiver, but high overhead for bursty data. Vulnerable to frequency-selective fading (needs equalizer).

  • CDMA (3G UMTS): Spread spectrum, all users same band. Rake receiver combines multipaths. Soft capacity, robust to fading (processing gain). Requires precise power control, complex receiver.

[!TIP] Final Exam Strategy: For 7-mark questions, provide definition → key formula → implications/impact. For 14-mark derivations, show step-by-step with clear assumptions (e.g., for Rayleigh distance: start from far-field definition \(R > 2D^2/\lambda\)). Always connect channel parameters to system design (e.g., "large \(\tau_{rms}\) → frequency-selective → need OFDM or equalizer").