Unit 3: Mobile Communication - Comprehensive Short Notes

1.0 Cellular System Fundamentals & Frequency Reuse

1.1 Concept and Need for Cellular Systems

• Definition: A cellular system divides a large geographic area into smaller regions called cells. Each cell has a base station (BS) that serves mobile users within its coverage area.

• Need:

  • Frequency Reuse: Allows the same radio channel to be used simultaneously in non-adjacent cells, dramatically increasing system capacity.

  • Handoff: Enables seamless call continuity when a user moves between cells.

  • Power Management: Low-power transmitters in cells reduce interference and battery consumption.

  • Scalability: New cells can be added to expand coverage and capacity.

1.2 Frequency Reuse Concept & Factor

• Frequency Reuse: The process of using the same set of frequencies (channel group) in different cells separated by a sufficient distance to keep co-channel interference (CCI) below an acceptable threshold.

• Reuse Ratio (N) / Cluster Size: The total number of cells in a cluster. A cluster is a group of cells where all channels are used exactly once. The pattern repeats over the service area.

  • N = i² + ij + j², where i and j are integers defining the cell coordinates.

• Channel Capacity per Cell:

  • Total available channels = C_total

  • Channels per cell = C_total / N

1.3 Cellular Layout and Geometry

• Hexagonal Cell Model: The ideal, regular hexagonal shape is used for theoretical analysis because:

  • It tessellates perfectly (no gaps/overlaps).

  • It has the minimum perimeter for a given area, minimizing the number of base stations needed for coverage.

  • All neighboring cells are equidistant.

• Locating Co-Channel Cells (N=19):

  • For a cluster size N=19, the vector from a reference cell to its first-tier co-channel cell is given by (i, j) = (3, 1) or (1, 3) etc.

  • Distance between co-channel cells (D): D = \sqrt{3N} \cdot R, where R is the cell radius.

  • For N=19: D = \sqrt{3 \times 19} \cdot R \approx 7.55 R.

  • DiagramCANVAS: Draw a hexagonal grid. Highlight a central cell (Cell 0). Using vectors (3,1) and (1,3), mark the six first-tier co-channel cells (Cells 1-6) surrounding the central cluster. Show the 19-cell cluster pattern repeating.

1.4 Co-Channel Interference (CCI)

• Definition: Interference caused by the use of the same frequency channel in two different cells that are separated by a distance D.

• Primary Cause: Inadequate frequency separation (small D/R ratio) between co-channel cells.

• Signal-to-Interference Ratio (SIR) Calculation:

  For a mobile at the edge of its serving cell, receiving desired signal from distance R and n co-channel interferers from distance D:

$$ \text{SIR} = \frac{S}{\sum_{i=1}^{n} I_i} = \frac{R^{-4}}{\sum_{i=1}^{n} D_i^{-4}} \quad \text{(using path loss exponent } \gamma = 4\text{)} $$

For a 7-cell cluster (1 desired + 6 interferers at same distance `D`):

\boxed{\text{SIR} \approx \left( \frac{D}{R} \right)^4 / 6}

> [!TIP] **Exam Tip:** SIR is a critical metric for system design. The acceptable SIR (e.g., > 18 dB for voice) determines the minimum `D/R` ratio and thus the cluster size `N`.

• Techniques to Reduce CCI:

  1. Increase D/R ratio: Use larger cluster size N (reduces capacity).

  2. Power Control: Reduce transmit power of mobiles/base stations to the minimum required for good link quality.

  3. Cell Splitting: Increase capacity by splitting large cells into smaller ones, which also increases D for a given R.

  4. Sectoring: Replace an omnidirectional antenna with several directional antennas (e.g., 120° or 60° sectors), reducing the number of co-channel interferers (n).

  5. Use of Diversity: At the receiver to combat fading, indirectly improving link budget and allowing lower powers.

2.0 Radio Wave Propagation Models

2.1 Large-Scale Path Loss (Macro Propagation)

• Free Space Propagation Model:

  • Valid for line-of-sight (LOS) in far-field.

  • Friis Equation:

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

where `d` is the T-R separation, `λ` wavelength, `c` speed of light, `f` frequency.

*   **Path Loss (dB):** `PL(dB) = 10\log_{10}\left(\frac{P_t}{P_r}\right) = 20\log_{10}\left(\frac{4\pi d}{\lambda}\right) - G_t - G_r`

> [!TIP] **Common Pitfall:** Free space loss increases with **square** of distance and **square** of frequency.

• Ground Reflection (Two-Ray) Model:

  • Considers direct ray and ground-reflected ray.

  • Path Loss: PL(d) ∝ d^4 (for large d), much steeper than free space (d^2).

  • Critical Distance (d_c): Distance where the two rays are in phase. For d > d_c, the d^4 law dominates.

$$ d_c = \frac{4h_t h_r}{\lambda} $$

• Mobile-to-Mobile Propagation:

  • Both antennas are low and near ground. Model similar to two-ray but with different antenna heights (h_mob << h_BS).

  • Path loss exponent often between 2 and 4.

• Foliage Losses (Empirical Models):

  • ITU Model: L_f = 0.2 f^{0.3} d^{0.6} (dB), where f in MHz, d in meters.

  • Loss depends on frequency, depth of foliage, and moisture.

• Propagation in Near-In-Distance (Close-in Reference Distance Model):

  • A practical large-scale model where path loss is measured/referenced at a close-in distance d_0 (e.g., 100m or 1km).

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

*   `γ` = path loss exponent (environment-dependent, e.g., 2 for free space, 4 for dense urban).

*   `X_σ` = zero-mean Gaussian random variable (dB) modeling **shadow fading** (log-normal distribution).

2.2 Small-Scale Multipath Propagation

• Causes: Reflection (from large objects), Diffraction (around edges), Scattering (from rough surfaces, small objects).

• Multipath Fading: Constructive/destructive interference of multiple delayed copies of the signal at the receiver.

• Time Delay Spread (τ): The spread in arrival times of multipath components.

• Dispersion Parameters:

  • Mean Excess Delay (τ̄): First moment of power delay profile.

$$ \bar{\tau} = \frac{\sum_k P_k \tau_k}{\sum_k P_k} $$

*   **RMS Delay Spread (τ_rms):** Square root of the second central moment. **Key parameter for determining frequency selectivity.**

$$ \tau_{\text{rms}} = \sqrt{\frac{\sum_k P_k (\tau_k - \bar{\tau})^2}{\sum_k P_k}} $$

2.3 Fading Characteristics

• Classification based on channel time/frequency variation:

• Clarke's Model for Flat Fading (Rayleigh Fading):

  • Assumptions: No LOS component, many scatterers, isotropic scattering, constant Doppler spectrum.

  • Model: Received signal r(t) = \text{Re}\left[ \alpha(t) e^{j2\pi f_c t} \right]

    • α(t) = complex envelope = x(t) + jy(t)

    • x(t), y(t) are independent, zero-mean Gaussian processes with same variance σ².

  • Envelope Distribution: |α(t)| follows Rayleigh distribution.

$$ p(r) = \frac{r}{\sigma^2} e^{-r^2/(2\sigma^2)}, \quad r \ge 0 $$

*   **Phase Distribution:** Uniform over `[0, 2π)`.

*   **Doppler Power Spectrum (Jakes' Spectrum):** `S(f) ∝ 1/\sqrt{1-(f/f_D)^2}` for `|f| ≤ f_D`.

• Level Crossing Rate (LCR) and Fade Statistics:

  • Level Crossing Rate (N_R): Average rate at which the fading envelope crosses a specified level R in the positive direction.

$$ N_R = \sqrt{2\pi f_D} \rho e^{-\rho^2}, \quad \text{where } \rho = R/\sigma $$

*   Used to predict how often deep fades occur.

3.0 Channel Assignment & Frequency Management

3.1 Fixed Channel Assignment (FCA)

• A fixed set of channels is permanently allocated to each cell based on the reuse plan.

• Advantage: Simple, predictable, low control overhead.

• Disadvantage: Inefficient during traffic fluctuations. A cell may run out of channels even if neighboring cells have idle ones.

3.2 Dynamic Channel Assignment (DCA) / Non-Fixed Channel Assignment

• Channels are not permanently assigned to cells. A channel is allocated to a call on demand from the pool of available channels.

• Algorithms:

  • Borrowing: A cell can borrow a channel from a neighboring cell if all its own are busy, with MSC coordination.

  • Channel Segregation: Cells learn which channels are "good" (low interference) through usage and preferentially assign them.

• Comparison: DCA vs. FCA:

  | Feature | FCA | DCA | | :--- | :--- | :--- | | Complexity | Low | High (real-time computation) | | Capacity | Fixed, lower on average | Higher, adapts to traffic | | Interference | Controlled by plan | Requires dynamic CCI avoidance | | Overhead | Minimal | Significant signaling |

3.3 Frequency Management in Cellular Systems

• The process of allocating the total radio spectrum (C_total channels) to cells in a service area.

• Involves:

  1. Determining the cluster size N (based on required SIR).

  2. Assigning channel groups to cells within a cluster (e.g., 1, 2, ..., N).

  3. Repeating the cluster pattern.

  4. Managing adjacent channel interference by ensuring non-adjacent channels in the same cell are separated by guard bands.

3.4 Trunking and Grade of Service (GoS)

• Trunking: The concept of sharing a limited pool of channels (trunks) among a large number of users to achieve statistical multiplexing gain.

• Grade of Service (GoS): The probability that a user's call will be blocked (if no channel available) or delayed (in queued systems). For voice, typical GoS = 0.02 (2% blocking probability).

• Erlang B Formula (Conceptual): Relates offered traffic load A (in Erlangs), number of channels C, and blocking probability P_b.

$$ P_b = \frac{A^C / C!}{\sum_{k=0}^{C} A^k / k!} $$

Used to determine `C` needed for a given `A` and `P_b`.

4.0 Handoff and Mobility Management

4.1 Necessity and Types of Handoff

• Necessity: To maintain an active call when a mobile station (MS) moves out of the coverage area of its current serving base station (BS).

• Types:

  1. Intra-cell Handoff: Handoff within the same cell (e.g., due to rapid fading or load balancing). May involve changing carrier frequency or time slot.

  2. Inter-cell Handoff: Handoff between base stations of different cells in the same system (most common).

  3. Inter-system Handoff: Handoff between base stations of different cellular systems (e.g., GSM to CDMA, or to a different operator's network).

4.2 Handoff Decision Strategies

• Mobile-Assisted Handoff (MAHO):

  • MS continuously measures signal strength (or quality) of its serving BS and neighboring BSs.

  • MS reports these measurements to the current BS/MSC at regular intervals.

  • Network (MSC) makes the handoff decision based on these reports.

  • Advantage: Reduces network measurement overhead, faster decisions. Used in GSM, IS-95.

• Network-Controlled Handoff (NCHO):

  • Network (BSs/MSC) continuously monitors the signal strength of all active mobiles.

  • Decision is made entirely by the network.

  • Advantage: Centralized optimization.

  • Disadvantage: High network signaling load, slower response. Used in early analog systems (e.g., AMPS).

4.3 Queuing Concept in Handoff

• Handoff Request Queuing: If no channel is available in the target cell at the exact moment of handoff request, the request can be queued for a short time (T_queue).

• Handoff Prioritization: Handoff requests for ongoing calls are given higher priority than new call attempts. If a channel becomes free, it is assigned first to a queued handoff request.

• Goal: Minimize forced termination probability (call drop) at the cost of slightly increased new call blocking probability.

4.4 Handoff Procedures in Specific Systems

• GSM: Uses MAHO. MS measures 6 strongest surrounding BSs (using BA list from BCCH). Reports via MEASUREMENT REPORT on SACCH. MSC evaluates and initiates handoff via HANDOVER COMMAND.

• CDMA (IS-95): Uses softer handoff (between sectors of same BS) and hard handoff (between different BSs). MS continuously measures Pilot signal strengths (Ec/Io). Active set management by MSC.

5.0 Multiple Access Techniques

5.1 Frequency Division Multiple Access (FDMA)

• Principle: The total available bandwidth B_T is divided into C non-overlapping frequency bands (channels), each assigned to a user for the duration of the call.

• Channel Allocation:

$$ \text{Number of Channels } (C) = \frac{B_T - (C \cdot B_{guard})}{B_c} $$

where `B_c` is channel bandwidth, `B_guard` is guard band between adjacent channels.

> [!TIP] **Exam Calculation:** Given `B_T = 12.5 MHz`, `B_guard = 10 kHz`, `B_c = 30 kHz`:

> 

$$ > C = \frac{12.5 \times 10^6 - C \times 10 \times 10^3}{30 \times 10^3} > \Rightarrow C(1 + 10/30) = 12.5e6 / 30e3 > \Rightarrow C \times (4/3) = 416.67 > \Rightarrow \boxed{C \approx 312 \text{ channels}} > $$

5.2 Time Division Multiple Access (TDMA)

• Principle: Users share the same frequency channel but are assigned unique time slots in a repeating frame.

• Frame Structure (GSM example): One frame = 8 time slots (TS0-TS7). Each slot carries a burst (~0.577 ms). One user is assigned a specific slot in each frame.

• Advantage over FDMA: Fewer frequency synthesizers needed at BS, can support more users per carrier.

5.3 Code Division Multiple Access (CDMA)

• Spread Spectrum Multiple Access (DS-CDMA):

  • Each user's data is multiplied by a unique, high-rate pseudo-noise (PN) code (chip sequence).

  • Chip Rate (R_c) >> Data Rate (R_b).

  • Processing Gain (PG): The ratio of spread bandwidth to original data bandwidth.

  \boxed{PG = \frac{R_c}{R_b} = \frac{\text{Chip Rate}}{\text{Data Rate}}}

  • At receiver, correlation with the correct PN code despreads the signal, compressing interference from other users (who appear as noise) into a wider bandwidth.

• CDMA System Description (IS-95):

  • Forward Channel (BS → MS): Uses Walsh codes (orthogonal) for channelization. Pilot, Sync, Paging, Traffic channels.

  • Reverse Channel (MS → BS): Uses PN codes (quasi-orthogonal) for channelization and identification. Access, Traffic channels.

  • PN Codes: Long PN sequence (2^42-1 chips) for user identification (code phase). Short PN sequence (2^15 chips) for orthogonal Walsh code generation.

• Power Control in CDMA (Near-Far Problem):

  • Problem: A nearby user's signal can overwhelm a distant user's signal at the BS because all users transmit on the same frequency.

  • Solution: Rigorous power control to make all received signals at the BS have approximately equal power.

  • Open Loop Power Control: MS estimates path loss from received BS pilot power and sets its initial transmit power.

  • Closed Loop Power Control: BS measures Eb/Nt (bit energy to total noise+interference density) and sends power adjustment commands (up/down) to the MS every 1.25 ms (800 bps).

• Bit Error Probability for CDMA:

  For a single user in a single-path AWGN channel with K-1 other interferers, the approximate BER for BPSK is:

$$ P_e \approx Q\left( \sqrt{\frac{2E_b}{N_0} \cdot PG \cdot \frac{1}{K-1}} \right) $$

where `PG` is processing gain, `K` is total number of users.

> [!TIP] **Exam Calculation (IS-95):** Given `K=20`, `B_channel=1.25 MHz`, `R_c=1.2288 Mcps`, `R_b=13 kbps`, `PN length=32768 (2^15)`, `Eb/N0=7.8 dB`.

> 1. **Processing Gain:** `PG = R_c / R_b = 1.2288e6 / 13e3 ≈ 94.53` (or `10log10(94.53) ≈ 19.75 dB`).

> 2. **BER:** `Eb/N0 = 7.8 dB = 6.03 (linear)`.

>    `K-1 = 19`.

>    Argument = `sqrt(2 * 6.03 * 94.53 / 19) = sqrt(60.1) ≈ 7.75`.

>    `P_e = Q(7.75) ≈ 4.4e-15` (extremely low).

> \boxed{\text{Processing Gain} \approx 94.5 \text{ (19.75 dB)}}

> \boxed{P_e \approx 4.4 \times 10^{-15}}

• Advantages of CDMA over FDMA/TDMA:

  • Soft Capacity: Capacity increases gradually with decreased Eb/Nt (graceful degradation).

  • Soft Handoff: MS can be in contact with multiple BSs simultaneously, combining signals (diversity gain).

  • Low Interference: Spread spectrum and power control reduce interference to other systems.

  • Security & Privacy: PN codes provide inherent encryption.

  • 抗干扰能力: Resistant to narrowband interference and jamming.

5.4 Frequency Hopped Multiple Access (FHMA)

• Principle: The carrier frequency of a user changes (hops) according to a pseudorandom sequence known to both transmitter and receiver.

• Slow Frequency Hopping (SFH):

  • Several symbols are transmitted on the same frequency hop (N_sym_per_hop > 1).

  • Benefit: Frequency diversity (mitigates flat fading on a hop).

• Fast Frequency Hopping (FFH):

  • Frequency changes within a symbol (N_sym_per_hop < 1, often << 1).

  • Benefit: Averaging of interference (if interference is narrowband and constant, it only hits some hops).

• Working of FHSS: Transmitter and receiver synchronize to hop through a large set of frequencies (M frequencies) in a predetermined order (PN sequence). Only the intended pair knows the sequence.

6.0 GSM (2G) System Architecture & Channels

6.1 GSM Network Architecture (Block Diagram)

• Mobile Station (MS): Mobile phone + SIM card.

• Base Station Subsystem (BSS):

  • Base Transceiver Station (BTS): Radio equipment (transceivers, antennas) for a cell.

  • Base Station Controller (BSC): Controls multiple BTSs. Manages radio resources, handoffs, frequency hopping.

• Network and Switching Subsystem (NSS):

  • Mobile Switching Center (MSC): Core switch. Call routing, mobility management, interfacing to PSTN/other networks.

  • Home Location Register (HLR): Database of all subscribers (permanent data, current location).

  • Visitor Location Register (VLR): Temporary database for subscribers currently in the MSC area.

  • Equipment Identity Register (EIR): Database of valid mobile equipment (IMEI).

  • Authentication Center (AuC): Generates authentication parameters (RAND, SRES, Kc).

• Operation and Support Subsystem (OSS): Network monitoring, maintenance, billing.

  • DiagramCANVAS: Draw a block diagram with MS connected via Um interface to BTS. Multiple BTS connect to BSC via Abis. BSC connects to MSC via A interface. MSC connects to HLR/VLR/AuC/EIR (often co-located) via various interfaces. PSTN connects to MSC. Show OSS connected to all.

6.2 GSM Interfaces

• Um: Air interface between MS and BTS.

• Abis: Between BTS and BSC. Standardized (ETSI).

• A: Between BSC and MSC. Carries traffic and signaling (TCAP/MAP over SS7).

• Ater: Between BSC and Transcoder (for rate adaptation).

• Iu/C/D: (For GPRS/UMTS later).

6.3 GSM Channel Types

• Traffic Channels (TCH): Carry encoded voice/data.

  • TCH/F: Full Rate (13 kbps).

  • TCH/H: Half Rate (6.5 kbps).

• Control Channels (CCH): Carry signaling/synchronization.

  • Broadcast (BCH): BCCH (Cell info), CCCH (Common), DCCH (Dedicated).

  • Common Control (CCCH): PCH (Paging), AGCH (Access Grant), RACH (Random Access - uplink).

  • Dedicated Control (DCCH): SDCCH (Stand-alone Dedicated Control), SACCH (Slow Associated Control - linked to TCH/FACCH), FACCH (Fast Associated Control - steals TCH slots).

6.4 GSM Frame Structure

• Multiframe: Two types:

  1. 26-Multiframe (Traffic): 26 TDMA frames (26x8=208 slots). 25 frames for traffic (TCH/SDCCH), 1 frame for control (FACCH/SACCH).

  2. 51-Multiframe (Control): 51 TDMA frames (51x8=408 slots). Used for BCCH, CCCH, SDCCH.

• Superframe: 26 x 51 = 1326 TDMA frames (or 51 x 26). Repeats every ~6.12 seconds. Contains all information for location update.

• Hyperframe: 2048 x 1326 TDMA frames = 2,715,648 frames ≈ 3 hours 28 minutes. Repeats all encryption sequences (A5) and frequency hopping sequences.

6.5 GSM Radio Subsystem (RSS) Overview

• The part of GSM dealing with radio transmission between MS and BSS.

• Includes: MS, BTS, BSC, and the Um interface.

• Functions: RF management, channel allocation, handoff control, transmission/reception, encryption.

7.0 Capacity Enhancement Techniques

7.1 Cell Splitting

• Concept: Subdivide a congested cell into smaller cells (microcells/picocells), each with its own base station and reduced transmit power/radius R.

• Implementation:

  • New, smaller cells are added within the original cell.

  • New cluster size N may be kept same (if D also reduced proportionally) or increased.

  • Challenge: Requires additional sites, backhaul, and careful frequency planning to avoid increased CCI.

7.2 Sectoring

• Concept: Replace a single omnidirectional antenna at a BS site with several directional antennas, each covering a sector (typically 120° or 60°).

• Effect:

  • Reduces the number of co-channel interferers (n) in the SIR formula. For 120° sectors, n reduces from 6 to 2.

  • Allows use of the same frequency channels in all sectors of the same site (if using different antenna polarizations or sufficient isolation).

  • Increases capacity by a factor of 3 (for 120° sectors) if channel set per sector is reduced.

• Disadvantage: Requires more antennas and transceivers per site.

7.3 Microcell Zone Concept

• A cell is divided into zones (e.g., 3 zones), each served by a separate zone controller and directional antenna at the same cell site.

• All zones share the same pool of frequencies.

• Benefit: Reduces handoff latency and channel acquisition time within the macrocell, as MS may stay within the same cell site while moving between zones.

• Capacity Gain: Similar to sectoring, but with common channel pool.

7.4 Other Techniques

• Overlay/Underlay Cell:

  • Overlay Cell: Large macrocell covering a wide area, using high power.

  • Underlay Cell: Small cell (microcell) within the macrocell, using low power and different frequency set to avoid interference.

  • Allows high capacity in hot spots without affecting macrocell coverage.

• Range Expansion: Using lower transmission powers or more sensitive receivers to allow cells to serve mobiles at greater distances, potentially increasing coverage but also interference.

8.0 Key Parameters, Definitions & Calculations

8.1 Coherence Bandwidth (B_c)

• Definition: The range of frequencies over which the channel impulse response is essentially flat (constant magnitude and linear phase). It is inversely related to the RMS delay spread (τ_rms).

• Calculation / Relation:

  • Approximate definitions:

    1. B_c ≈ 1/(5 τ_rms) (for correlation > 0.9)

    2. B_c ≈ 1/(50 τ̄) (using mean excess delay)

  • Condition for Flat Fading: Signal bandwidth B_signal << B_c.

  • Maximum Symbol Rate for Minimal ISI:

$$ R_{sym} \le \frac{1}{2 \tau_{\text{rms}}} \quad \text{or} \quad R_{sym} \le B_c $$

> [!TIP] **Exam Problem (Jun 2025):** Given `B_c = 100 kHz`, `f_c = 900 MHz`.

> `R_{sym,max} = B_c = 100 \text{ kbaud}` (or `1/(2τ_rms)` if `τ_rms` is derived from `B_c`).

> \boxed{R_{sym, \max} = 100 \text{ ksymbols/sec}}

8.2 Doppler Spread (f_D) and Coherence Time (T_c)

• Doppler Spread (f_D): The range of frequencies over which the received Doppler spectrum is non-zero. f_D = v / λ (maximum Doppler shift), where v is MS speed, λ wavelength.

• Coherence Time (T_c): The time duration over which the channel impulse response is approximately invariant. It is inversely proportional to f_D.

  • Approximate: T_c ≈ \sqrt{9}/(16\pi f_D) or T_c ≈ 1/f_D.

• Condition for Slow Fading: Symbol period T_sym >> T_c.

• Condition for Fast Fading: T_sym < T_c.

8.3 Incident Angle and Slope Angle in Hilly Terrain Propagation

• Used in empirical models for propagation over hilly terrain.

• Incident Angle (θ_i): The angle at which the direct ray strikes the hilltop (from the transmitter side).

• Slope Angle (θ_s): The angle of the hill's slope relative to the horizontal.

• Calculation (from past paper Nov 2023):

  • Given: Hill height H = 100 m, BS antenna height h_t = 50 m, MS antenna height h_r = 3 m, path length d = 5 km.

  • Incident Angle: tan(θ_i) ≈ (H - h_t) / (d/2) (assuming symmetric path and hill at midpoint).

    θ_i = tan^{-1}((100-50)/(5000/2)) = tan^{-1}(50/2500) ≈ 1.145°.

  • Slope Angle: tan(θ_s) ≈ H / (d/2) = 100 / 2500 = 0.04.

    θ_s = tan^{-1}(0.04) ≈ 2.29°.

  \boxed{\theta_i \approx 1.15^\circ, \quad \theta_s \approx 2.29^\circ}

8.4 Antennas

• Cell Site Antennas:

  • Types: Directional (sectoring: 65°, 90°, 120°), Omnidirectional.

  • Height: Typically 30-100 m on towers/buildings.

  • Patterns: Carefully designed to cover the cell sector while minimizing interference to adjacent cells.

• Mobile Antennas:

  • Typically omnidirectional, short monopoles (λ/4).

  • Often use diversity (two antennas spaced λ/2 apart) to combat fading.

9.0 Advanced Topics (Short Note Scope)

9.1 Multiple Input Multiple Output (MIMO) System

• Concept: Use of multiple antennas at both transmitter (Mx) and receiver (Nx) to create multiple spatial channels.

• Benefits:

  1. Capacity Increase: Multiplexing gain. Channel capacity increases linearly with min(M, N) in rich scattering environments (C ∝ min(M,N) log(SNR)).

  2. Diversity Gain: Improves reliability by providing multiple independent fading paths.

  3. Beamforming: Directional transmission/reception to increase SNR and reduce interference.

• Challenges: Complex signal processing (e.g., V-BLAST, STBC), channel estimation, correlation between antenna elements.

9.2 Orthogonal Frequency Division Multiplexing (OFDM)

• Principle:

  • High-rate data stream is split into many parallel low-rate sub-streams.

  • Each sub-stream modulates a subcarrier that is orthogonal to others (subcarrier spacing = 1/T_symbol).

  • Orthogonality prevents ICI even with overlapping spectra.

• Advantages:

  • Combats ISI: Long symbol duration (T_symbol) makes τ_rms << T_symbol, so flat fading per subcarrier. Cyclic Prefix (CP) added to absorb delay spread.

  • Spectral Efficiency: Orthogonal subcarriers are closely spaced.

  • Simple Equalization: One-tap equalizer per subcarrier (in frequency domain).

  • Robust to Selective Fading: Only some subcarriers may be deep faded; coding/interleaving across subcarriers provides diversity.

• Used in: Wi-Fi (802.11a/g/n/ac/ax), 4G LTE (downlink), 5G NR, DVB-T, DSL.

9.3 Diversity Techniques

• Goal: Provide the receiver with multiple independent (or partially correlated) copies of the same signal to combat fading.

• Spatial Diversity (Antenna Diversity):

  • Use two or more antennas separated by ≥ λ/2 to receive independent fading signals.

  • Combining Techniques: Selection Combining (pick best), Maximal Ratio Combining (weighted sum), Equal Gain Combining.

• Other Types:

  • Time Diversity: Same signal transmitted at different times (e.g., interleaving, repetition). Requires T_sep > T_c.

  • Frequency Diversity: Same signal transmitted on different frequencies. Requires Δf > B_c.

  • Polarization Diversity: Use orthogonal polarizations (vertical/horizontal) from same location.

  • Angle Diversity: Use directional antennas pointing in different directions.

END OF UNIT 3 NOTES