Upon completion of this extended tutorial, students will be able to:
Cellular networks are the backbone of mobile communications, enabling billions of users worldwide to connect seamlessly. This tutorial provides a comprehensive exploration of the fundamental architecture and operational principles of cellular systems. We begin with the foundational concept of cells and frequency reuse, which allows cellular networks to support massive numbers of subscribers with limited spectrum. We then delve into the core network architecture, location management (HLR/VLR), and handoff mechanisms that ensure service continuity as users move. We also examine capacity and coverage planning, interference management, and traffic engineering using the Erlang models. This extended version includes rigorous theoretical derivations, advanced network planning examples, and a substantial set of assessment questions. The principles covered here are essential for understanding the evolution from 1G to 5G, which will be explored in subsequent tutorials.
A cellular network consists of three main subsystems:
The cellular architecture enables seamless mobility by dividing the service area into cells, each served by a base station. A group of cells forms a location area (or tracking area), and the core network tracks the user's location at this granularity.
| Element | Role | Example (4G/5G) |
|---|---|---|
| Base Station | Provides radio coverage for a cell; performs modulation/demodulation. | eNodeB (4G), gNB (5G) |
| Mobile Switching Centre (MSC) | Circuit‑switched core for voice (2G/3G). | MSC (2G/3G) |
| Serving GPRS Support Node (SGSN) | Packet‑switched core (2G/3G). | SGSN (2G/3G) |
| Mobility Management Entity (MME) | Handles mobility, authentication, and paging in 4G/5G. | MME (4G), AMF (5G) |
| Home Location Register (HLR) | Central database of subscriber information. | HLR (2G/3G), HSS (4G/5G) |
| Visitor Location Register (VLR) | Stores subscriber info for users currently in the MSC area. | VLR (2G/3G), combined with HSS in 4G/5G |
| Gateway (SGW/PGW) | Connects to external packet networks. | SGW/PGW (4G), UPF (5G) |
A cell is the coverage area of a base station. Cells are typically modelled as hexagons for planning purposes (the hexagon provides the best approximation to a circle with no gaps and no overlaps when tessellated).
Frequency reuse is the practice of using the same frequency channels in geographically separated cells to increase capacity. The reuse factor N is the number of cells in a cluster before frequencies are reused. The cluster size N is determined by:
\( N = i^2 + ij + j^2 \)
where i and j are non‑negative integers (i ≥ j). This is the hexagonal tessellation relationship, where i and j represent the number of cells stepped to find the co‑channel cell.
Common cluster sizes: 1, 3, 4, 7, 9, 12, 13, 19. The reuse distance D (between co‑channel cells) is:
\( D = \sqrt{3N} \times R \)
where R is the cell radius (distance from center to vertex). The carrier‑to‑interference ratio (C/I) in a cellular system with reuse factor N can be approximated by:
\( \frac{C}{I} = \frac{1}{\sum_{k=1}^{M} (D_k/R)^{-\gamma}} \)
where M is the number of co‑channel interferers and γ is the path loss exponent (typically 2‑4).
In a cluster of size N, each cell is assigned a subset of the total available frequency channels. The total number of channels available per cell is:
\( N_{ch/cell} = \frac{N_{total}}{N} \)
where Ntotal is the total number of channels (or bandwidth) allocated to the operator.
The system capacity (total channels per unit area) is proportional to 1/N. A smaller reuse factor increases capacity but also increases co‑channel interference.
Example: For a 7‑cell reuse pattern, the co‑channel cells are at distances multiples of D. The C/I ratio can be calculated to ensure it meets the system requirement (e.g., 18 dB for analog systems, 10‑12 dB for digital).
Cell splitting increases capacity by reducing cell radius. When a cell is split, the new (smaller) cells reuse the same frequencies more densely, increasing capacity. The capacity increase is roughly proportional to the square of the radius reduction:
\( \text{Capacity increase} \propto \left(\frac{R_{old}}{R_{new}}\right)^2 \)
Cell splitting requires careful planning of new base station locations, antenna heights, and power levels.
Sectorization divides a cell into sectors using directional antennas (typically 3 sectors, 120° each, or 6 sectors, 60° each). Each sector can use different frequency channels, effectively increasing the reuse factor and reducing interference. Sectorization provides a capacity gain proportional to the number of sectors, but with increased hardware complexity.
Location management tracks the location of mobile devices so that the network can find them for incoming calls. It consists of:
The trade‑off is between paging load (large location area) and location update load (small area). The network uses location areas (LAs) in 2G/3G and tracking areas (TAs) in 4G/5G. The HLR (Home Location Register) stores the permanent subscriber data, while the VLR (Visitor Location Register) stores the subscriber's current location (at the LA/TA level).
Handoff (or handover) is the process of transferring an ongoing call/data session from one cell to another as the user moves. Types of handoff:
The handoff decision is based on measurements of signal strength (RSRP), signal quality (RSRQ), and hysteresis (to prevent ping‑pong). The handoff threshold and hysteresis are critical for avoiding excessive handoffs and ensuring good quality.
Handoff latency is critical for VoIP and real‑time services. 4G LTE targets less than 50 ms, and 5G URLLC targets less than 10 ms.
Cellular network planning involves determining the number of cells (base stations) required to meet coverage and capacity targets.
Coverage planning: Use propagation models (Okumura‑Hata, 3GPP TR 38.901) to estimate the maximum cell radius based on transmit power, antenna gains, receiver sensitivity, and path loss. A fade margin is added for shadowing.
Capacity planning: Use traffic models (Erlang B for loss systems, Erlang C for queuing systems) to estimate the number of traffic channels required per cell. The Erlang B formula is:
\( P_b = \frac{A^C / C!}{\sum_{k=0}^{C} A^k / k!} \)
where A is the offered traffic (in Erlangs), C is the number of channels, and Pb is the blocking probability (e.g., 1%).
Co‑channel interference is the dominant limit in cellular systems. Techniques to manage interference:
A city requires coverage for 5 million people over 100 km². Using 3GPP UMa model, the cell radius is 500 m. Number of cells ≈ area / (πR²) × 1.21 (hexagon factor) = 100 / (π×0.25) × 1.21 ≈ 154 cells. With 3‑sector sites, ~52 sites. Capacity planning uses Erlang B with 2% blocking.
For a stadium with 50,000 users, mmWave (28 GHz) cells have radius ~50 m. Requires ~200 small cells. Massive MIMO and beamforming are used to handle the high capacity.
A rural area uses 900 MHz with cell radius of 10 km. Fewer cells are needed, but backhaul and power are challenges.
Test your understanding of cellular network fundamentals.
Q1. Define a cell in the context of cellular networks. Why are cells modelled as hexagons?
A cell is the geographic coverage area of a base station. Cells are modelled as hexagons because hexagons tessellate perfectly without gaps or overlaps, and best approximate the circular coverage of an omnidirectional antenna.
Q2. What is frequency reuse, and why is it essential in cellular networks?
Frequency reuse is the practice of using the same frequency channels in geographically separated cells. It is essential because it allows many users to share limited spectrum, dramatically increasing network capacity.
Q3. What is the relationship between the cluster size N and the reuse distance D? Write the formula.
D = √(3N) × R, where R is the cell radius. This gives the distance between co‑channel cells.
Q4. Calculate the cluster size N for i = 2 and j = 1 using N = i² + ij + j².
N = 4 + 2 + 1 = 7. This is the standard 7‑cell reuse pattern.
Q5. What is the difference between hard handoff and soft handoff?
Hard handoff is break‑before‑make: the connection to the old cell is broken before the new one is established. Soft handoff is make‑before‑break: the device connects to the new cell while still connected to the old one, providing seamless continuity.
Q6. What is the role of the Home Location Register (HLR) in a cellular network?
The HLR is a central database that stores permanent subscriber information, including service profiles, location (at the VLR level), and authentication data.
Q7. What is the purpose of the Visitor Location Register (VLR)?
The VLR stores subscriber information for users currently in the MSC area (or tracking area). It allows the network to locate a subscriber for incoming calls without querying the HLR every time.
Q8. Explain the concept of location areas (LAs) or tracking areas (TAs) in mobility management.
A location/tracking area is a group of cells where a mobile device can move without updating its location to the network. When the device crosses a LA/TA boundary, it performs a location update. This reduces signalling overhead compared to updating at every cell.
Q9. What is cell splitting, and how does it increase capacity?
Cell splitting reduces the cell radius, creating more cells in the same area. Since frequencies are reused more densely, capacity increases approximately as (R_old / R_new)².
Q10. What is sectorization, and what is its impact on frequency reuse?
Sectorization divides a cell into sectors using directional antennas (e.g., 3 sectors). Each sector can use different frequencies, effectively increasing the reuse factor and reducing co‑channel interference.
Q11. What is the Erlang B formula used for in cellular planning?
The Erlang B formula estimates the probability of call blocking given the offered traffic (Erlangs) and the number of traffic channels. It is used to determine the number of channels needed for a target blocking probability.
Q12. What is the difference between fixed and dynamic channel assignment?
Fixed channel assignment allocates a fixed set of channels to each cell permanently. Dynamic channel assignment allocates channels on demand from a central pool, adapting to traffic variations.
Q13. What is co‑channel interference (CCI), and why is it a key limiting factor in cellular networks?
CCI is interference from cells using the same frequency channels. It is the dominant limit in cellular networks because it directly impacts the SINR and thus the capacity and quality of service.
Q14. What is fractional frequency reuse (FFR), and how does it help manage interference?
FFR uses different reuse factors for cell‑edge and cell‑centre users. Cell‑edge users use a higher reuse factor (e.g., 3) to reduce interference, while cell‑centre users use a lower reuse factor (e.g., 1).
Q15. Explain the concept of "ping‑pong" in handoff and how it is mitigated.
Ping‑pong is the rapid switching between two cells due to signal fluctuations near a cell boundary. It is mitigated by using a hysteresis margin (a threshold offset) and a time‑to‑trigger to avoid unnecessary handoffs.
Q16. What is the difference between horizontal and vertical handoff?
Horizontal handoff is between cells of the same technology (e.g., LTE to LTE). Vertical handoff is between different technologies (e.g., LTE to Wi‑Fi).
Q17. What is the purpose of paging in cellular networks?
Paging is the process of broadcasting a message across a location/tracking area to find a mobile device when an incoming call arrives.
Q18. What is the typical carrier‑to‑interference (C/I) requirement for digital cellular systems?
For digital systems (e.g., GSM, LTE), the C/I requirement is typically 10‑12 dB (lower than analog, which required 18 dB) due to digital modulation and error correction.
Q19. What is the maximum number of co‑channel interferers in a hexagonal cellular system with 7‑cell reuse?
In a 7‑cell reuse pattern, there are 6 co‑channel cells in the first tier (at distance D), so the number of interferers is typically 6 (first tier). Additional tiers contribute less.
Q20. What is the role of the Mobility Management Entity (MME) in LTE/4G?
The MME handles mobility management, authentication, paging, and tracking area updates. It is the control‑plane node in the LTE core (EPC).
Q21. What is the difference between a location update and a paging procedure?
A location update is initiated by the mobile device to inform the network of its current location area. Paging is initiated by the network to locate a device for an incoming call.
Q22. How does the Erlang B blocking probability change as the offered traffic increases for a fixed number of channels?
As offered traffic increases, the blocking probability increases non‑linearly (the system becomes congested). For a fixed number of channels, there is a maximum offered traffic that can be supported for a given blocking probability.
Q23. What is the significance of the path loss exponent γ in the C/I calculation for cellular systems?
The path loss exponent (γ) determines how quickly signal strength decays with distance (typically 2‑4). A higher γ means that signals decay faster, which can reduce co‑channel interference from distant cells.
Q24. What is the purpose of ICIC (Inter‑Cell Interference Coordination) in LTE?
ICIC coordinates the allocation of frequency and power resources between neighbouring cells to mitigate interference at the cell edge, improving performance for edge users.
Q25. What is a "make‑before‑break" handoff and which systems use it?
Make‑before‑break (soft handoff) establishes the new connection before breaking the old one. It is used in CDMA‑based systems (IS‑95, WCDMA) and provides seamless service continuity.
Apply your knowledge to these cellular planning and analysis problems.
Exercise 1: A cellular system has a total of 1000 voice channels. Using a 7‑cell reuse pattern, how many channels are available per cell? If each cell has 3 sectors, how many channels per sector?
Channels per cell = 1000 / 7 ≈ 142.86 ≈ 142 channels per cell (assuming integer allocation). With 3 sectors, channels per sector ≈ 142 / 3 ≈ 47 channels per sector.
Exercise 2: Calculate the reuse distance D for a cell radius R = 2 km and cluster size N = 7. If the path loss exponent γ = 4, what is the approximate C/I ratio considering only the 6 first‑tier co‑channel cells?
D = √(3×7) × 2 = √21 × 2 ≈ 4.58 × 2 = 9.16 km. C/I = 1 / (6 × (D/R)^(-γ)) = 1 / (6 × (4.58)^(-4)) = 1 / (6 × 1/440) = 1 / 0.0136 ≈ 73.5 linear, which is about 18.7 dB. This is approximate; actual may be lower due to other factors.
Exercise 3: A cell has 30 channels. The average call duration is 120 seconds, and each user generates 2 calls per hour. What is the offered traffic per user in Erlangs? How many users can be supported with a blocking probability of 2% (use the Erlang B table, assume C = 30, P_b = 0.02 gives A ≈ 25 Erlangs)?
Traffic per user = call rate × holding time = (2/3600) × 120 = 0.0667 Erlangs. With A = 25 Erlangs, number of users = 25 / 0.0667 ≈ 375 users.
Exercise 4: A cellular network has a target blocking probability of 2%. The offered traffic per cell is 30 Erlangs. How many channels are required per cell? Use the Erlang B formula or table. (Erlang B: for P_b = 0.02, A = 30, C ≈ 40).
Using Erlang B table or calculator, for A = 30 Erlangs and P_b = 0.02, C ≈ 40 channels. (Interpolation: at C=40, A for 2% blocking is about 33; but with 30 Erlangs, C=38-40).
Exercise 5: A mobile device is moving at 60 km/h. It needs to hand off from one cell to another. The measurement period is 200 ms, and the handoff latency is 50 ms. How far does the device move during the handoff process? Is this acceptable for a cell radius of 500 m?
v = 60 km/h = 16.67 m/s. Total time = measurement (200 ms) + handoff (50 ms) = 250 ms = 0.25 s. Distance = 16.67 × 0.25 = 4.17 m. This is small compared to 500 m, so acceptable.
Exercise 6: A city has an area of 200 km² and needs 2000 channels. Using a 4‑cell reuse pattern and a cell radius of 2 km, how many cells are needed? How many channels per cell? What is the total capacity?
Area per cell = (3√3/2) × R² ≈ 2.598 × 4 = 10.39 km². Number of cells ≈ 200 / 10.39 ≈ 19.25 → 20 cells (or 19, but must cover area). Channels per cell = 2000 / 4 = 500. Total capacity = 20 × 500 = 10,000 channels (but this is not realistic; we need to consider sectorization and traffic).
Exercise 7: Explain the difference between a location area (LA) and a cell. Why is the LA larger than a cell?
A cell is the coverage area of a single base station. A location area is a group of cells where a mobile device can move without performing location updates. The LA is larger to reduce the number of location updates (signalling overhead), at the cost of more paging when an incoming call arrives.
Exercise 8: A cell uses 3‑sectorization. Each sector has a directional antenna with a gain of 15 dBi. Compared to an omnidirectional antenna with 10 dBi gain, what is the effective increase in received power for a user in the main beam?
Gain increase = 15 - 10 = 5 dB. This improves the link budget and allows for either greater range or better SINR. However, the sector antenna only covers 120°, so the cell is effectively split.
Exercise 9: A cellular system uses 900 MHz with a cell radius of 5 km in a rural area. The path loss exponent is 3.5. The transmitter power is 40 dBm, antenna gains are 5 dBi each, and receiver sensitivity is -100 dBm. Calculate the fade margin. Is the link adequate for a 10 dB fade margin?
Path loss at 5 km using Okumura‑Hata or simplified: L = 32.4 + 20log₁₀(900) + 10×3.5×log₁₀(5) = 32.4 + 59.1 + 10×3.5×0.699 = 91.5 + 24.47 = 115.97 dB. Received power = 40 + 5 + 5 - 115.97 = -65.97 dBm. Fade margin = -65.97 - (-100) = 34.03 dB. Adequate for 10 dB margin.
Exercise 10: A network uses a tracking area (TA) with 10 cells. Each cell has an average of 50 location updates per hour. What is the total location update load? If each update takes 200 bytes, what is the signalling bandwidth required?
Total location updates = 10 × 50 = 500 updates/hour = 0.139 updates/s. Data rate = 0.139 × 200 × 8 = 222 bps. This is negligible signalling overhead.
Exercise 11: What is the effect of increasing the cluster size N on the system capacity and C/I ratio? Provide a qualitative analysis.
Increasing N increases the reuse distance (D), which improves C/I (lower interference) but reduces capacity (fewer channels per cell). There is a trade‑off: N must be large enough to meet the C/I requirement but small enough to provide adequate capacity.
Exercise 12: A mobile device is in a soft handoff region between two cells. The signal strengths from Cell A and Cell B are -80 dBm and -85 dBm, respectively. The handoff margin is 3 dB. Will the device hand off to Cell B? Why or why not?
Cell A is stronger (-80 dBm > -85 dBm). The device will not hand off to Cell B because the difference (5 dB) is greater than the handoff margin (3 dB). Handoff typically occurs when the target is stronger than the current by the margin.
Independent study and advanced analysis problems.
HW1. Derive the relationship between the cluster size N and the C/I ratio in a hexagonal cellular system. Assume a path loss exponent γ and only the first tier of interferers. Explain how this relationship guides the choice of N.
C/I = 1 / (Σ (D/R)^(-γ)) with D = √(3N)R. For 6 interferers, C/I = 1 / (6 (√(3N))^(-γ)) = (3N)^(γ/2) / 6. Given a target C/I, N must be at least ((6×C/I)^(2/γ)) / 3. This shows that larger N gives better C/I but reduces capacity (channels per cell = total/N).
HW2. Research the concepts of "cell breathing" and "power control" in CDMA systems. How do they differ from the frequency‑based systems (GSM/LTE)?
In CDMA, all cells use the same frequency (reuse factor 1). Power control adjusts the transmit power of each user so that all users are received at the same power level. Cell breathing refers to the shrinking of the cell coverage as the number of users increases (due to rising interference). Unlike GSM/LTE, CDMA is interference‑limited, not noise‑limited, so capacity is determined by the total interference, not fixed channels.
HW3. Analyse the trade‑offs between location update frequency and paging load. Derive the optimal location area size to minimise total signalling overhead.
Assume a device crosses LA boundaries at rate λ (updates per time) and receives calls at rate μ (pages per time). The total signalling cost is proportional to λ × update_cost + μ × (size of LA) × page_cost. The optimal LA size balances the cost of updates (which increase with crossing frequency) and paging (which increases with LA size). The solution depends on mobility and call arrival rates.
HW4. Compare and contrast the handoff mechanisms in GSM (hard handoff), WCDMA (soft handoff), and LTE (hard handoff with make‑before‑break using RRC).
GSM: hard handoff, measured by mobile (MAHO), network‑controlled. WCDMA: soft handoff (make‑before‑break), mobile‑assisted, with active set. LTE: hard handoff, but with X2 interface for fast data forwarding; handover is network‑controlled with UE measurements. LTE handoff is fast (<50 ms) and supports SON (Self‑Organizing Networks).
HW5. Explain the concept of "fractional frequency reuse" (FFR) and its application in LTE. Derive the capacity gain achieved by FFR over a standard reuse‑1 system.
FFR divides the spectrum into a cell‑centre band (reuse 1) and a cell‑edge band (higher reuse). Edge users use the higher reuse band to reduce interference, improving their SINR. The capacity gain depends on the fraction of spectrum allocated to the edge band and the SINR improvement. FFR can increase cell‑edge throughput by up to 50‑100% compared to full reuse‑1, at the cost of some spectral efficiency for centre users.
HW6. Research the role of the Serving Gateway (SGW) and Packet Data Network Gateway (PGW) in the LTE Evolved Packet Core (EPC). How do they support mobility and session continuity?
The SGW routes user‑plane data and acts as a local mobility anchor when the UE moves between eNodeBs within the same SGW service area. The PGW provides connectivity to external packet networks (Internet, IMS) and serves as a global mobility anchor (for UE moving between SGWs). Both support bearer management and QoS.
HW7. Analyse the impact of the path loss exponent on the frequency reuse factor. For a given C/I target, how does γ affect the required N?
From C/I ≈ (3N)^(γ/2) / 6, solving for N gives N ≈ (6 × C/I)^(2/γ) / 3. A larger γ means that interference decays faster, so a smaller N is needed to achieve the same C/I. Thus, in environments with high path loss exponent (e.g., urban), smaller reuse factors (like 1 or 3) can be used.
HW8. Describe the operation of the 4‑way handshake in LTE for establishing a security context during handoff. How does it differ from the initial attachment?
During handoff, the target eNodeB derives a new security key (KeNB*) from the current KeNB using a key derivation function. The 4‑way handshake (or a simpler 2‑way for X2 handoff) establishes the new security association. This is faster than the full AKA (Authentication and Key Agreement) used during initial attachment.
HW9. Write a critical evaluation of the statement: "With large bandwidth and massive MIMO, cell planning for 5G becomes trivial." Discuss the challenges that remain.
While 5G offers more spectrum (including mmWave) and advanced techniques like massive MIMO, cell planning remains complex. mmWave requires dense small cells and beamforming alignment. Massive MIMO introduces new challenges in channel estimation, interference coordination, and backhaul. Additionally, planning must account for diverse service requirements (eMBB, URLLC, mMTC) and coexistence with 4G.
HW10. Derive the blocking probability for a system with C channels and offered traffic A using the Erlang B formula. How does the blocking probability behave as A approaches C?
Erlang B: P_b = (A^C / C!) / Σ_{k=0}^C (A^k / k!). As A approaches C, the blocking probability increases significantly. For a loss system, when A > C, many calls are blocked. The system can support a maximum offered traffic approximately equal to C for low blocking (e.g., <5%).< /p>
HW11. Compare the location management strategies in GSM (using HLR/VLR) and 5G (using UDM, AMF, and AUSF). How has the architecture evolved to support more subscribers and services?
GSM uses a hierarchical HLR/VLR structure with circuit‑switched and packet‑switched domains. 5G uses a service‑based architecture (SBA) with the UDM (Unified Data Management) for subscription data, AMF (Access and Mobility Function) for mobility, and AUSF (Authentication Server Function). This modular architecture supports network slicing, edge computing, and more flexible deployment.
HW12. Design a cellular network plan for a suburban area of 50 km² with 5000 users, each generating 0.05 Erlangs, target blocking probability 1%. Determine the number of cells, channels per cell, and site requirements. Assume a 4‑cell reuse pattern and a cell radius of 1.5 km. Use the Erlang B table.
Total traffic = 5000 × 0.05 = 250 Erlangs. Area per cell = 2.598 × (1.5)² = 5.85 km². Number of cells = ceil(50 / 5.85) = 9 cells. Traffic per cell = 250 / 9 ≈ 27.8 Erlangs. Erlang B with P_b = 0.01, A = 28 → C ≈ 40 channels per cell. With 4‑cell reuse, total channels = 40 × 4 = 160 (per cell, but this is the number for the whole system). Each cell needs 40 channels. Total system channels = 40 × 9 = 360 channels. Sites: 9 sites (assuming 3 sectors per cell, but with 4‑cell reuse, each site may have multiple cells).
This extended tutorial covered the fundamental principles of cellular network architecture and operation, including:
These foundational principles are essential for understanding the evolution of cellular technologies from 1G to 5G, which will be explored in the next tutorial.
© COMP347 – Unit 7: Wireless and Mobile Networks (Extended Tutorial 6)