Multiple Access and Cellular Network Engineering

Introduction and Context

A cellular network converts a geographically large service area into smaller coverage regions, or cells, and reuses radio resources across sufficiently separated cells. Its engineering problem is multidimensional: spectrum must be shared among users, interference must be controlled, capacity must follow spatially varying demand, and mobility must be supported without unacceptable interruption. Modern systems combine frequency-, time-, code-, space- and power-domain techniques rather than relying on one access method.

This chapter develops the engineering principles needed to compare FDMA, TDMA, CDMA, OFDMA, SDMA and NOMA; design frequency-reuse patterns; estimate capacity; and manage handover, interference and mobility. Numerical results are based on explicitly stated assumptions because cellular formulas are often valid only for particular propagation and traffic models.

Learning Objectives

After studying this chapter, a learner should be able to:

1. Explain and quantitatively compare major multiple-access methods.

2. Derive basic frequency-reuse and co-channel-interference relationships.

3. Design a preliminary cellular layout using cluster size, sectorization and channel allocation.

4. Apply Erlang B and trunking concepts to voice capacity.

5. Explain handover, mobility management and interference coordination.

6. Evaluate engineering trade-offs in contemporary multi-RAT networks.

1. Multiple Access as a Resource-Allocation Problem

Let the available radio resource be represented by time, frequency, code, spatial signature and transmit power. A multiple-access scheme assigns one or more of these dimensions to simultaneous users. The objective is not simply maximum theoretical throughput; it is reliable throughput under constraints on interference, latency, signalling overhead, terminal complexity, fairness and regulatory spectrum limits.

FDMA

In frequency-division multiple access, each user receives a distinct frequency channel, usually with guard bands. If total usable bandwidth is B, channel bandwidth is W and guard overhead per channel is g, an approximate number of channels is

M ≈ B/(W+g).

FDMA has continuous transmission and relatively simple scheduling, but guard bands reduce spectral efficiency and fixed allocation performs poorly with bursty data. Classical analogue cellular systems used FDMA; modern systems may retain frequency partitioning at a higher level.

TDMA

TDMA assigns users different time slots on a carrier. A frame contains K slots, with guard time and synchronization overhead. If slot duration is Ts and useful payload duration is Tu, the time efficiency is approximately Tu/Ts. TDMA supports discontinuous transmission and flexible scheduling, but requires accurate timing and produces delay when a user waits for its slot. GSM is a major historical example.

CDMA

CDMA allows users to overlap in frequency and time while separating them with spreading codes. For a single-user link, processing gain is approximately

Gp = Wss/Rb,

where Wss is spread-spectrum bandwidth and Rb is bit rate. In an interference-limited system, a simplified uplink capacity condition is often written

(K-1)(Eb/N0)R/Wss ≤ η,

where K is the number of simultaneous users, R is user bit rate, Wss is spread bandwidth, Eb/N0 is the required energy-per-bit to noise-density ratio, and η represents implementation and power-control margins. This is a model, not a universal capacity law. Voice activity, imperfect power control, sectorization and external interference alter the result. The near–far problem makes rapid power control essential.

OFDMA

OFDMA divides a wideband channel into orthogonal subcarriers and assigns groups of subcarriers in time to users. Orthogonality is maintained when synchronization and cyclic-prefix conditions are satisfied. A resource block is therefore a time-frequency scheduling unit rather than a permanently owned frequency. OFDMA supports frequency-selective scheduling, adaptive modulation and coding, and spatial reuse. Its costs include peak-to-average power ratio, synchronization requirements and sensitivity to inter-carrier interference.

SDMA

Space-division multiple access separates users through antenna arrays, beamforming or sectorization. In a narrowband model, a received vector can be represented as

y = Hx+n,

where H is the multiuser channel matrix. Separation is effective when user channel vectors are sufficiently distinguishable and channel state information is accurate. Massive MIMO is an advanced SDMA implementation, but pilot contamination, calibration errors and correlated channels limit ideal gains.

NOMA

Non-orthogonal multiple access deliberately superposes users in the same time-frequency resource. A downlink signal may be written

x = √(a1P)s1 + √(a2P)s2, a1+a2=1,

where users are decoded using successive interference cancellation (SIC). Power allocation normally gives a weaker channel more power, while the stronger receiver decodes and subtracts the weaker user before decoding its own signal. NOMA can improve connectivity or fairness in selected channel conditions, but error propagation, SIC complexity, pairing, control overhead and imperfect channel knowledge reduce practical gains. Orthogonal access is not automatically inferior: scheduling and MIMO can provide comparable or better performance.

Comparative engineering view

FDMA and TDMA are comparatively simple but resource-fragmenting. CDMA offers universal reuse but is interference- and power-control-limited. OFDMA provides fine-grained scheduling and is dominant in broadband systems. SDMA exploits spatial selectivity and is complementary to OFDMA. NOMA increases signal-domain reuse under suitable channel disparity, but its system-level benefit depends on traffic, receiver capability and implementation losses. A fair comparison must specify bandwidth, user rates, propagation, fairness criterion, control overhead and outage target.

2. Cellular Geometry and Frequency Reuse

A regular hexagon is an analytical approximation to a radio cell. Let R be the cell radius, commonly interpreted as the distance from the site to a vertex in ideal geometry. For a conventional hexagonal layout, the reuse distance is

D/R = √(3N),

where N is the cluster size. Valid cluster sizes satisfy

N = i² + ij + j²,

for non-negative integers i and j. Thus common values include 1, 3, 4, 7, 9, 12 and 13; N=6 is not generated by this regular-lattice relation.

The reuse factor is 1/N: each cell receives approximately one-Nth of the total channel pool in a simple unsectorized plan. This is an allocation approximation; actual usable capacity also depends on control channels, guard bands, sectorization and loading.

Co-channel interference

For a first-tier approximation with six equally interfering co-channel cells, equal transmit powers, equal propagation distances and path-loss exponent n,

S/I ≈ (D/R)^n / 6 = (√(3N))^n/6.

This expression assumes a fully loaded, omnidirectional, regular layout and neglects shadowing, antenna patterns, power control and farther tiers. It should not be used as a universal interference prediction.

For N=7 and n=4:

D/R = √21 ≈ 4.583,

S/I = (√21)^4/6 = 21²/6 = 441/6 = 73.5,

or, in decibels,

10 log10(73.5) ≈ 18.66 dB.

Sectorization reduces the number and strength of dominant interferers, although it consumes antennas, increases planning complexity and can create sector-edge effects. Directional antenna patterns and downtilt must be included in a detailed link-level simulation.

3. Cellular Planning Workflow

A defensible preliminary plan follows these steps:

1. Define requirements: area, indoor/outdoor coverage, busy-hour traffic, data demand, latency, availability and regulatory limits.

2. Select propagation and link-budget assumptions, including carrier frequency, antenna heights, clutter class, shadow margin and penetration loss.

3. Estimate cell radius from coverage and verify it with field measurements or calibrated prediction.

4. Select reuse, sectorization and channel bandwidth.

5. Calculate interference and capacity under busy-hour loading.

6. Place sites according to terrain, roads, population and backhaul availability.

7. Simulate coverage, throughput, handover regions and interference.

8. Optimize parameters and validate through drive tests, crowdsourced measurements and performance counters.

Worked planning example

Suppose a legacy voice system has 120 traffic channels and requires a seven-cell cluster. With 49 cells, the number of clusters is 49/7 = 7, so the nominal channel inventory is 7×120 = 840 channel assignments. If the same area uses N=4, which is a valid cluster size because 4=2²+2(0)+0², the nominal inventory is 49×120/4 = 1470 channel assignments. Relative to the N=7 plan, the ratio is 1470/840 = 1.75, not 85.75 times. This gain is conditional: the N=4 design produces a smaller reuse distance and therefore requires an interference assessment.

Sectorization can multiply per-site frequency allocation in a planning sense. For example, three sectors may use directional antennas and separate sector channel groups, but the resulting capacity is not automatically three times the omnidirectional capacity because sector overlap, control channels, traffic imbalance and inter-sector interference consume resources.

4. Trunking and Traffic Capacity

Voice traffic is measured in erlangs: one erlang is one channel occupied continuously during the observation interval. If λ is the mean call-arrival rate and h is mean holding time in the same time unit, offered traffic is

A = λh.

For C channels and Poisson arrivals with exponentially distributed holding times, Erlang B gives the probability that an arriving call is blocked and cleared:

B(C,A) = (A^C/C!) / Σ(k=0 to C) (A^k/k!).

The model assumes no queue, statistically independent arrivals, and a suitable holding-time approximation. It is inappropriate when blocked calls retry heavily, in which case offered traffic becomes state-dependent.

Carried traffic is

Ac = A[1-B(C,A)].

Worked Erlang example

For C=10 channels and offered traffic A=7 erlangs, recursive evaluation using

B(0,A)=1, B(c,A)=AB(c−1,A)/(c+AB(c−1,A))

gives B(10,7) ≈ 0.0791. Therefore

Ac = 7(1−0.0791) ≈ 6.45 erlangs.

The result means that approximately 7.91% of offered calls are blocked and the average occupied traffic is about 6.45 erlangs. Dimensioning should use a specified grade of service, usually a busy-hour blocking target, rather than average daily traffic.

For packet data, Erlang B is insufficient because sessions share resources dynamically and may be scheduled at variable rates. Capacity analysis should then use throughput distributions, resource-block utilization, latency percentiles, queueing models or simulation.

5. Handover and Mobility Management

A handover transfers an active connection between cells, sectors, carriers or radio-access technologies. Hard handover breaks before making the new connection; soft handover maintains overlapping links temporarily, as in some CDMA systems; make-before-break methods are also used in dual-connectivity architectures.

A practical handover decision may depend on filtered reference-signal strength or quality, hysteresis H and time-to-trigger TTT. A simplified event condition is

Qtarget − Qserving > H continuously for TTT.

Hysteresis prevents ping-pong; TTT suppresses reactions to short fades. Excessive H or TTT causes late handover and radio-link failure, whereas values that are too small increase signalling and ping-pong. Load-aware handover can move users toward lightly loaded cells, but may increase interference or reduce radio quality.

Mobility management includes measurement reporting, neighbour-cell lists, location or tracking areas, paging, authentication, context transfer and session continuity. High-speed users require larger handover margins, optimized neighbour relations and robust backhaul signalling. Inter-RAT handover must account for different coverage footprints, authentication domains and quality metrics.

6. Interference Coordination

Interference is classified as co-channel, adjacent-channel, inter-symbol, inter-carrier or inter-cell interference. Coordination mechanisms include:

• fractional frequency reuse, reserving more protected resources at cell edges;
• power control and uplink interference management;
• almost-blank or reduced-power subframes for protected users;
• coordinated scheduling and coordinated beamforming;
• dynamic spectrum sharing and carrier aggregation;
• antenna downtilt, sectorization and neighbour-relation optimization.

There is a fundamental capacity trade-off: aggressive reuse increases spectrum efficiency but reduces SINR, while protection improves edge quality at the cost of available resources. Modern systems therefore optimize weighted utility, such as

U = Σu wu log(ru),

where ru is user rate and wu is a policy weight. The logarithm illustrates proportional-fair behavior: it values aggregate throughput while preventing extreme starvation. Other objectives may prioritize emergency traffic, latency or energy efficiency.

7. Capacity Beyond Reuse Factor

Nominal channel count does not equal user capacity. A useful system-level abstraction is

Csystem ≈ Cresources × ηspectral × ηspatial × ηtime,

where the efficiencies account for modulation and coding, spatial reuse, scheduling, control overhead and outage constraints. This is not a universal capacity equation; it is a bookkeeping model for identifying losses.

For an OFDMA cell, if each resource block provides instantaneous rate rb and there are M blocks, the aggregate scheduled rate in an interval is approximately

Rcell = Σm rm,

subject to control, reference-signal, retransmission and fairness overhead. Since rm depends on SINR, modulation and coding, cell-edge users may consume many resource blocks per delivered bit. Capacity planning must therefore use a user distribution and SINR map rather than only a peak data rate.

A link budget may be expressed as

Pr(dBm)=Pt+Gt+Gr−PL(d)−Lmisc,

and a received quality estimate as

SINR = Pr/(I+N).

All powers in a linear SINR calculation must use consistent units; decibel gains and losses must be added algebraically before converting to linear power. A coverage design is valid only if the predicted SINR and received level meet the selected service threshold with the specified shadow margin.

8. Applied Case: Illustrative Urban Multi-RAT Upgrade

Background

Consider a fictional dense urban district served by a three-sector macro site and several small cells. The operator reports acceptable outdoor voice coverage but poor evening data rates near transport corridors. The macro layer has strong aggregate traffic but high cell-edge interference.

Problem analysis

Counters show high physical-resource-block utilization in two sectors, repeated handovers near a street canyon, and low SINR despite adequate received signal strength. This indicates interference and congestion rather than simple coverage loss. The original neighbour list also omits a newly deployed small cell.

Approach

The operator first calibrates a propagation model with drive-test data. It adds the missing neighbour relation, adjusts antenna downtilt, and applies load-aware handover with conservative hysteresis and TTT tuning. A protected edge-resource pattern is introduced during the evening busy hour. Small cells are assigned locally reused resources, while beamforming serves users with separable spatial signatures. Backhaul and synchronization are verified before enabling coordination.

Outcome

The intervention is assessed using five-minute utilization, 5th-percentile user throughput, handover failure, ping-pong rate and dropped-session rate. A successful outcome requires improvement in the low-percentile experience without merely transferring congestion to adjacent cells. This illustrates why average throughput alone is an inadequate engineering KPI.

Learning points

1. Radio measurements must distinguish coverage, quality and capacity problems.

2. Handover optimization is coupled to interference and load.

3. Sectorization and small cells improve spatial reuse only when backhaul, synchronization and neighbour planning are adequate.

4. Changes should be validated against both mean and tail performance.

9. Limitations, Governance and Contemporary Directions

Analytical hexagonal models hide terrain, irregular site spacing and correlated shadowing. Erlang models may misrepresent retries and packet traffic. Link budgets do not predict user experience without scheduling and application demand. Simulation results are sensitive to traffic maps, propagation calibration and random seeds; reproducibility requires documented assumptions.

Spectrum use is governed by national regulators and international coordination. Engineers must observe licence conditions, exposure limits, lawful-interception requirements, emergency-service obligations and privacy law. Mobility and positioning data should be minimized, protected and retained only for legitimate purposes. AI-assisted radio optimization can learn traffic and interference patterns, but it requires monitored data quality, explainability for critical decisions, fail-safe policies and protection against adversarial or biased measurements.

Current research includes cell-free massive MIMO, integrated sensing and communications, intelligent reflecting surfaces, AI-native RAN control, energy-aware sleep modes, reconfigurable spectrum sharing and joint communication–compute orchestration. These directions do not eliminate fundamental trade-offs among bandwidth, power, interference, latency, reliability and deployment cost.

Best-Practice Checklist

• State propagation, traffic and interference assumptions before calculating capacity.
• Use only valid reuse clusters for the selected lattice model.
• Convert units consistently and distinguish offered from carried traffic.
• Validate analytical predictions with calibrated simulation and measurements.
• Optimize 5th-percentile quality, blocking, handover failures and energy—not only averages.
• Treat sectorization, MIMO, NOMA and coordination as coupled design choices.
• Document regulatory, privacy, safety and operational constraints.

Chapter Summary

Multiple access divides shared radio resources across frequency, time, code, space and power. FDMA and TDMA are structured orthogonal methods; CDMA uses spreading and power control; OFDMA enables flexible time-frequency scheduling; SDMA exploits spatial separability; and NOMA uses controlled superposition and SIC. Cellular planning combines valid hexagonal reuse patterns, link budgets, co-channel interference, sectorization and traffic demand. For a regular lattice, N=i²+ij+j² and D/R=√(3N); under a six-interferer, equal-power model, S/I≈(√(3N))ⁿ/6. Trunking calculations require explicit assumptions: Erlang B estimates blocking for loss systems, while packet networks require resource and delay models. Handover, mobility management and interference coordination are inseparable from capacity and user experience. Professional designs must be validated against measurements, tail performance, regulatory obligations and operational constraints.

Key Terms

Multiple access: Sharing radio resources among simultaneous users.

FDMA: Assignment of distinct frequency channels to users.

TDMA: Assignment of distinct time slots to users.

CDMA: Code-based spread-spectrum access.

OFDMA: Orthogonal subcarrier-based time-frequency access.

SDMA: Spatial separation using antennas or beams.

NOMA: Non-orthogonal superposition of users in a shared resource.

Cluster size: Number of cells over which a channel set is used once.

Reuse distance: Separation between co-channel cells.

Co-channel interference: Interference from cells using the same channel.

Sectorization: Division of a cell into directional antenna sectors.

Erlang: One hour-equivalent of continuous traffic occupancy.

Offered traffic: Traffic presented to a trunk group.

Carried traffic: Traffic successfully served.

Grade of service: Probability or target level of blocking or failure.

Handover: Transfer of an active connection between serving resources.

Hysteresis: Decision margin preventing rapid handover reversals.

Time-to-trigger: Required duration of a handover condition.

SINR: Signal-to-interference-plus-noise ratio.

Interference coordination: Techniques that manage interference across cells.

Review Questions

Short Answer Questions

1. Why does OFDMA support frequency-selective scheduling?

2. State the valid-cluster-size relation for a regular hexagonal cellular model.

3. Distinguish offered traffic from carried traffic.

4. What are hysteresis and time-to-trigger used for?

5. Why is power control important in CDMA uplinks?

Long Answer Questions

1. Compare FDMA, TDMA, CDMA, OFDMA, SDMA and NOMA in terms of resource dimension, synchronization, interference and implementation complexity.

2. Derive the reuse-distance and first-tier co-channel-interference relationships under their stated assumptions.

3. Explain a complete cellular planning workflow from requirements to field validation.

4. Discuss Erlang B assumptions and explain why they are inadequate for bursty packet data.

5. Evaluate sectorization, fractional frequency reuse and coordinated scheduling as interference-management strategies.

Analytical / Application Questions

1. A seven-cell reuse plan uses 120 channels and covers 49 cells. Calculate nominal channel assignments and compare them with a valid N=4 plan; discuss the interference trade-off.

2. For N=7 and path-loss exponent n=4, calculate D/R and S/I in linear and decibel form using the six-interferer approximation.

3. An urban operator has high utilization, low edge SINR and excessive ping-pong handovers. Propose a measurement-led intervention and specify performance metrics for acceptance.

Multiple Choice Questions with Answers

Question 1

Which access method assigns users flexible groups of orthogonal subcarriers in time-frequency resources?

A. FDMA

B. OFDMA

C. Pure CDMA

D. Analog FM broadcasting

Correct Answer: B. OFDMA

Question 2

Which cluster size is valid under N=i²+ij+j² for a regular hexagonal lattice?

A. 2

B. 5

C. 7

D. 8

Correct Answer: C. 7

Question 3

For N=7 and path-loss exponent n=4, using six equal first-tier interferers, what is S/I?

A. 18.7 dB approximately

B. 13.7 dB approximately

C. 23.3 dB approximately

D. 6.0 dB approximately

Correct Answer: A. 18.7 dB approximately

Question 4

What is the principal purpose of handover hysteresis?

A. To increase thermal noise

B. To prevent rapid back-and-forth handovers

C. To eliminate all co-channel interference

D. To assign a permanent frequency to every user

Correct Answer: B. To prevent rapid back-and-forth handovers

Question 5

A system has 120 channels and 49 cells. Comparing valid cluster sizes N=7 and N=4, what are the nominal channel assignments and their ratio?

A. 840 and 1470; ratio 1.75

B. 840 and 480; ratio 0.57

C. 120 and 49; ratio 2.45

D. 1470 and 840; ratio 0.50

Correct Answer: A. 840 and 1470; ratio 1.75

Question 6

For offered traffic of 7 erlangs and 10 channels, Erlang B is approximately 0.079. What is the carried traffic?

A. 0.55 erlang

B. 5.96 erlangs

C. 6.45 erlangs

D. 7.91 erlangs

Correct Answer: C. 6.45 erlangs

Question 7

Which condition is most central to effective CDMA uplink operation?

A. No power control is required

B. Near-far effects are managed by power control

C. Every user occupies a unique frequency

D. Users cannot overlap in time

Correct Answer: B. Near-far effects are managed by power control

Question 8

In downlink NOMA, successive interference cancellation generally allows a receiver to do what?

A. Decode and subtract a superposed signal before decoding its own signal

B. Convert every channel into a separate fibre

C. Remove the need for channel estimation

D. Guarantee zero outage for all users

Correct Answer: A. Decode and subtract a superposed signal before decoding its own signal

Question 9

Which metric is most directly associated with the ratio of desired signal power to interference-plus-noise power?

A. Erlang

B. SINR

C. Cluster size

D. Holding time

Correct Answer: B. SINR

Question 10

Which statement about the Erlang B model is correct?

A. It assumes blocked calls wait in an unlimited queue

B. It models a loss system in which blocked calls are cleared

C. It applies only when all channels are permanently occupied

D. It directly predicts OFDMA packet latency distributions

Correct Answer: B. It models a loss system in which blocked calls are cleared