Multiplexing, Spectrum Use and Channel Access

Introduction

A communication channel is a shared physical or wireless medium through which information travels. In most practical systems, the capacity of one medium is greater than the capacity required by a single user or signal at a particular instant. Multiplexing allows several independent signals to share that medium. Channel access rules determine how users coordinate their use of a shared channel, especially when simultaneous transmission would cause interference.

These ideas are central to telephone networks, optical fibre systems, cellular networks, wireless local-area networks, satellite communication, cable television, and modern broadband access. The engineer must decide how signals are separated, how much spectrum is consumed, how interference is controlled, and how capacity is allocated fairly and efficiently.

Learning Objectives

By the end of this chapter, a student should be able to:

• explain frequency-division, time-division, wavelength-division and code-division multiplexing;
• distinguish synchronous and statistical time-division multiplexing;
• describe orthogonal frequency-division multiplexing (OFDM) and its relationship to multicarrier transmission;
• explain spread-spectrum techniques, including direct-sequence and frequency-hopping systems;
• calculate basic bandwidth, bit-rate, spectral-efficiency and multiplexing quantities;
• compare channel-access methods such as random access, controlled access and scheduled access;
• assess spectrum allocation, interference, fairness and regulatory constraints; and
• select an appropriate multiplexing and access approach for a practical communication system.

1. Multiplexing as a Resource-Sharing Function

A multiplexer combines several input streams into one aggregate signal for transmission over a shared medium. At the receiving end, a demultiplexer separates the aggregate into its original streams. A logical channel may be separated from others by frequency, time, wavelength, code, spatial direction or a combination of these dimensions.

The basic arrangement is:

Figure: A multiplexer combines multiple streams and a demultiplexer recovers them at the destination.

A useful idealized capacity relationship is:

Here, R_i is the information rate assigned to channel i, and R_total is the aggregate rate, measured in bit/s. In a real system, overhead for framing, synchronization, error correction, guard bands and signalling means that useful payload rate is less than the raw aggregate rate.

2. Frequency-Division Multiplexing

In frequency-division multiplexing (FDM), each signal occupies a distinct frequency band continuously or for a long interval. Modulators translate the signals to non-overlapping carrier-frequency ranges. Band-pass filters at the receiver recover the individual components.

If channel i occupies bandwidth B_i and a guard band G_i is placed between adjacent channels, a simplified total-bandwidth estimate is:

The equation assumes that the channel bands are arranged side by side and that guard bands are counted separately. It does not include all practical filter roll-off or signalling overhead.

Traditional analogue telephone carrier systems used FDM to combine voice channels. Cable television and some satellite systems also use frequency-separated carriers. In radio, frequency allocation is a form of FDM at the system level: different services or transmitters receive different frequency ranges.

Advantages and limitations

FDM provides continuous transmission and low waiting time. It is suitable for analogue signals and for systems in which each user requires a stable portion of spectrum. Its disadvantages include guard-band waste, sensitivity to oscillator drift and intermodulation, and inefficient use when a user is silent. Filtering and linear amplification are especially important because nonlinear equipment can create energy in neighbouring channels.

FDM should be distinguished from frequency-division multiple access (FDMA). FDM is a multiplexing principle; FDMA is an access method in which different users are assigned different frequency channels.

3. Time-Division Multiplexing

Time-division multiplexing (TDM) assigns the same frequency resource to different signals at different times. A frame is divided into time slots. In synchronous TDM, each input has a predetermined slot in every frame, even if that input has no data.

Suppose there are N channels, each sampled at rate f_s samples/s, and each sample has q bits. Ignoring framing and control overhead, the payload rate is:

For a frame containing one sample from each source, the frame duration is:

The slot duration, if all slots have equal size, is T_slot = T_frame ÷ N. These relations assume that all sources contribute one sample per frame and that timing is synchronized.

Statistical, or asynchronous, TDM assigns slots dynamically to active sources. Addresses or identifiers are required so that the receiver can deliver each block to the correct destination. Statistical TDM improves utilization when traffic is bursty, but it introduces queueing delay and requires buffering and control information.

Worked example: synchronous TDM

Eight digital sources each produce 64 kbit/s. A frame contains one 8-bit sample from each source, plus 16 framing bits. The payload rate is:

R_payload = 8 × 64 kbit/s = 512 kbit/s.

Each source contributes 8 bits, so the payload per frame is 64 bits. Including 16 framing bits, the frame contains 80 bits. The frame rate is 64 kbit/s ÷ 8 bit = 8,000 frames/s, and therefore the transmitted rate is:

R_total = 80 bit × 8,000 frame/s = 640 kbit/s.

The framing overhead is 128 kbit/s, or 20% of the transmitted rate. This example illustrates why useful throughput and line rate must not be treated as identical.

4. Wavelength-Division Multiplexing

Wavelength-division multiplexing (WDM) applies FDM to optical fibre. Optical carriers of different wavelengths travel through the same fibre and are combined by an optical multiplexer. At the destination, an optical demultiplexer separates them.

Because wavelength and frequency are related by:

where f is optical frequency in hertz, λ is wavelength in metres, and c is the speed of light in the medium, a wavelength channel is also a frequency channel. In fibre, the propagation speed is lower than the vacuum speed, so engineering calculations use the appropriate group velocity when precision is required.

Coarse WDM uses relatively widely separated wavelength channels. Dense WDM (DWDM) uses closely spaced channels and precise lasers, filters and amplifiers. WDM can multiply the capacity of an existing fibre without installing a new fibre. Optical add-drop multiplexers can insert or remove selected wavelengths at intermediate network nodes, while wavelength-selective switches enable reconfigurable optical networks.

Important limitations include chromatic dispersion, polarization effects, nonlinear phenomena, laser stability and the operating bandwidth of optical amplifiers. WDM is not simply “more bits without cost”: transceivers, spectral spacing, power management and signal-quality monitoring become more demanding as channel density increases.

5. Code-Division Multiplexing and Spread Spectrum

In code-division multiplexing (CDM), users occupy overlapping time and frequency resources but are distinguished by code sequences. A receiver correlates the received signal with the intended code. Ideally, codes are orthogonal or have low cross-correlation, so unwanted users contribute limited interference.

In direct-sequence spread spectrum (DSSS), each data bit is combined with a faster chip sequence. If the chip rate is R_c chips/s and the data rate is R_b bit/s, the spreading factor is:

For rectangular chips and idealized conditions, the processing gain in decibels is:

The spreading factor is dimensionless. Processing gain describes the approximate improvement obtained when despreading distributes narrowband interference over a wider decision bandwidth; it is not a guarantee of unlimited capacity or security.

In frequency-hopping spread spectrum (FHSS), the carrier changes among a sequence of frequency channels according to a shared hopping pattern. Slow hopping changes frequency less often than the symbol rate; fast hopping changes it several times during a symbol. FHSS can resist narrowband interference and makes casual interception more difficult, but synchronization is essential.

Spread spectrum has applications in cellular systems, satellite links, positioning systems and resilient wireless networks. It can provide interference tolerance and multiple-access capability. However, spreading does not eliminate the need for power control, code planning, synchronization and regulatory compliance.

6. Orthogonal Frequency-Division Multiplexing

Orthogonal frequency-division multiplexing (OFDM) divides a high-rate data stream among many low-rate subcarriers. Unlike ordinary FDM, adjacent subcarriers overlap spectrally but remain separable because their waveforms are orthogonal over the symbol interval.

For a simplified rectangular-window OFDM symbol of useful duration T_u, subcarrier spacing is:

The condition ensures that the integral of one subcarrier waveform multiplied by a different subcarrier waveform over the useful symbol interval is zero. A guard interval, often implemented as a cyclic prefix, is added to reduce inter-symbol interference caused by multipath propagation. If the useful symbol duration is T_u and the cyclic-prefix duration is T_cp, the time-efficiency factor is:

A longer cyclic prefix improves tolerance of delay spread but reduces efficiency. OFDM modulation and demodulation are efficiently implemented using the inverse fast Fourier transform and fast Fourier transform, respectively.

OFDM strengths

• It converts a frequency-selective wideband channel into many approximately flat subchannels.
• Subcarriers can be adaptively loaded according to channel quality.
• Equalization is relatively simple because each subcarrier can use a one-tap correction under suitable assumptions.
• It supports flexible scheduling and combinations with multiple-input multiple-output (MIMO) antennas.

OFDM weaknesses

• The sum of many subcarriers can have a high peak-to-average power ratio (PAPR), reducing power-amplifier efficiency.
• Frequency offset and phase noise destroy orthogonality and cause inter-carrier interference.
• A cyclic prefix consumes time and carries no new payload.
• Out-of-band emissions require filtering, windowing or guard resources.

OFDM and its variants are used in Wi-Fi, digital broadcasting, broadband access and cellular systems. In uplink systems, single-carrier frequency-domain equalization and related low-PAPR waveforms may be preferred where terminal power efficiency is important.

7. Measuring Spectrum Efficiency

Spectral efficiency measures how much useful information is transmitted per unit bandwidth. A basic definition is:

where η is spectral efficiency in bit/s/Hz, R is useful data rate in bit/s, and B is occupied bandwidth in hertz. The value depends on modulation, coding, signal-to-noise ratio, interference, guard intervals, pilot symbols, control channels and implementation losses.

For an ideal additive white Gaussian noise channel, the Shannon capacity limit is:

Here, C is the theoretical maximum reliable information rate in bit/s, B is bandwidth in hertz, and S ÷ N is the dimensionless signal-to-noise power ratio. This is an upper bound under the model assumptions; it does not directly account for fading, finite block length, interference, hardware limits or protocol overhead.

The corresponding theoretical spectral-efficiency limit is:

Worked example: ideal capacity

If a channel has bandwidth 1 MHz and an SNR of 15 (linear, not 15 dB), then:

C = 1,000,000 log₂(16) = 1,000,000 × 4 = 4 Mbit/s.

This is a theoretical limit. A practical system may achieve less because of coding gaps, fading, pilot overhead and implementation constraints.

Spectrum efficiency should not be optimized in isolation. A design with high bit/s/Hz may require high power, complex signal processing or dense frequency reuse, increasing interference and cost. Energy efficiency, coverage, latency, reliability and fairness are also relevant.

8. Spectrum Allocation and Regulation

Radio spectrum is a finite public resource in the sense that uncoordinated transmitters can interfere with one another. National regulators allocate bands to services such as mobile communication, broadcasting, aviation, scientific research and satellite systems. International coordination is needed where signals cross borders or satellite orbits are involved.

Allocation occurs at several levels:

1. Allocation: a band is designated for one or more radio services.
2. Assignment: a licence, authorization or rule gives a particular organization access to specified frequencies or operating conditions.
3. Allocation within a system: an operator assigns carriers, codes, time slots or resource blocks to users.

Licensed spectrum provides interference protection but may be expensive or inflexible. Unlicensed spectrum permits shared access under technical rules such as power limits, duty-cycle restrictions and listen-before-talk procedures. Dynamic spectrum access uses sensing, databases or coordination to exploit temporarily unused frequencies. Sensing-based access must handle hidden transmitters, receiver uncertainty and the risk of harmful interference.

Regulatory decisions commonly consider coexistence, public safety, competition, rural coverage, international harmonization and efficient use. Spectrum policy is therefore both an engineering and a governance issue.

9. Channel-Access Methods

Multiplexing describes how multiple logical streams are represented on a medium. Multiple access describes how independent users obtain permission to transmit. The two are related but not identical.

9.1 Random access

In random-access systems, users transmit when they have data and recover from collisions or interference. ALOHA transmits without sensing, while slotted ALOHA restricts attempts to slot boundaries. Carrier-sense multiple access (CSMA) listens before transmission. Collision detection is practical in some wired environments; collision avoidance is more appropriate in wireless systems because a transmitter generally cannot reliably listen while transmitting.

Random access is simple and effective for bursty, unpredictable traffic. Its disadvantages are collisions, variable delay and declining throughput under heavy load. Backoff algorithms reduce repeated collisions by making retransmission times partly random.

9.2 Controlled access

Polling gives a central controller permission to each station in turn. Token passing allows the station holding a token to transmit. These approaches reduce collisions and can provide bounded access time, but control traffic and token or controller failure must be managed.

9.3 Scheduled and reservation access

In scheduled access, a controller or distributed protocol assigns time-frequency resources in advance. Reservation methods are valuable for predictable latency and quality-of-service guarantees. Cellular systems commonly combine scheduling with FDM, TDM, OFDM and spatial processing. A scheduler may consider queue length, channel quality, latency, service class and fairness.

A simple fairness measure for n users is Jain’s fairness index:

Here, x_i is the allocated throughput of user i, and n is the number of users. Under nonnegative allocations, J ranges from approximately 1 ÷ n to 1; 1 indicates equal allocations. High fairness does not necessarily mean high total throughput, and equal throughput may be inappropriate when users have different requirements.

10. Integrated Design Example: A University Wireless Network

The following is an illustrative case. A university wants to provide wireless service in lecture halls, laboratories and outdoor study areas. Demand is bursty: many students access the network simultaneously at the beginning of a class, while traffic is lighter during lectures. Applications include web access, video, voice calls and campus safety systems.

Problem

A single undifferentiated channel would produce collisions and poor performance during peak demand. Walls and people create multipath propagation, and neighbouring access points may interfere. The university also operates in bands subject to regulatory power and channel rules.

Analysis

An OFDM-based wireless LAN is appropriate because its subcarriers handle frequency-selective multipath more effectively than a single high-rate carrier. A cyclic prefix reduces inter-symbol interference when its duration exceeds the significant channel delay spread. Frequency channels can be reused in separated areas, but reuse distances and transmit power must be planned to limit co-channel interference.

The access protocol should combine contention for ordinary bursty traffic with scheduling or traffic prioritization for latency-sensitive applications. Clear channel assessment and randomized backoff reduce collisions, but hidden terminals may remain when two stations cannot hear one another. Access-point placement, directional planning and, where available, coordinated scheduling help address this problem.

Approach

The design team should:

• survey the radio environment and identify overlapping networks;
• select permitted channels and transmit powers according to regulation;
• use multiple access points with carefully planned channel reuse;
• configure quality-of-service classes for voice, video and ordinary data;
• monitor utilization, retransmissions, channel occupancy and user experience;
• use authentication and encryption to prevent unauthorized access; and
• review capacity after changes in building occupancy or application demand.

Outcome

The expected outcome is not merely a higher nominal data rate. A successful deployment provides acceptable throughput at busy times, predictable service for critical applications, secure access and manageable interference. Measurements should distinguish signal strength from signal quality: a strong signal can still have poor performance if interference or contention is high.

Learning points

The case demonstrates that multiplexing, spectrum planning and channel access must be designed together. OFDM addresses the physical channel, while access control determines which station may use resources. Regulatory compliance, security, fairness and monitoring are part of the engineering solution rather than afterthoughts.

11. Challenges, Security and Ethical Considerations

Multiplexing systems face synchronization errors, oscillator drift, multipath fading, interference, congestion and equipment nonlinearity. A design should provide margins rather than assume ideal conditions. Performance claims should report useful throughput, latency, packet loss and availability, not only theoretical line rate.

Spread-spectrum and frequency-hopping methods can improve resilience, but they are not substitutes for cryptographic confidentiality and authentication. A signal that is difficult to detect is not necessarily secure. Wireless networks should use current security protocols, strong credentials, secure firmware and appropriate key management.

Spectrum access also raises fairness and public-interest concerns. Automated scheduling can favour users with favourable channel conditions unless fairness constraints are included. Dynamic access databases and sensing systems may reveal location or operational information. Monitoring must follow privacy laws and institutional policies. Emergency, accessibility and rural-coverage requirements may justify allocations that do not maximize short-term commercial revenue.

Artificial intelligence can assist spectrum prediction, anomaly detection, beam selection and traffic scheduling. However, models may be trained on incomplete measurements, may encode unfair allocation policies, and may respond unpredictably to adversarial signals. AI-controlled radio systems require validation, human oversight, logging, fail-safe behaviour and compliance with spectrum rules.

12. Best-Practice Design Principles

1. Define the traffic model, including burstiness, latency, reliability and mobility.
2. Separate payload rate from raw line rate and include all overheads.
3. Select multiplexing dimensions that match the medium: wavelength for fibre, frequency and time for radio, and code or spatial separation where justified.
4. Use guard intervals, pilots, synchronization and error control based on measured channel conditions.
5. Plan interference and coexistence before maximizing nominal capacity.
6. Match channel access to traffic: contention for light bursty loads and scheduling or reservation for predictable service.
7. Measure fairness, energy use, latency and coverage in addition to throughput.
8. Apply authentication, encryption, secure management and privacy controls.
9. Observe national and international spectrum regulations.
10. Monitor deployed systems continuously because traffic, devices and interference change over time.

Chapter Summary

Multiplexing enables multiple signals to share a communication medium. FDM separates users by frequency, TDM by time, WDM by optical wavelength, and CDM by spreading codes. Synchronous TDM is simple but can waste slots; statistical TDM improves utilization for bursty traffic at the cost of buffering and delay. OFDM uses orthogonal overlapping subcarriers and a cyclic prefix to manage multipath, but it introduces synchronization and peak-power challenges.

Spread spectrum increases signal bandwidth to obtain processing gain and interference resilience, but it does not provide unlimited capacity or cryptographic security. Spectral efficiency is measured in bit/s/Hz, while Shannon capacity provides an ideal upper bound under specified assumptions. Spectrum allocation involves engineering, regulation and public-interest decisions. Channel access may be random, controlled, reserved or scheduled, and practical systems often combine several approaches.

Effective design evaluates capacity, interference, delay, fairness, reliability, energy use, security and compliance together. The central professional skill is selecting and coordinating multiplexing and access mechanisms for the actual traffic and propagation environment.

Key Terms

Multiplexing: Combining multiple information streams for transmission over a shared medium.

Demultiplexing: Separating an aggregate signal into its constituent streams.

FDM: Multiplexing by assigning distinct frequency bands to signals.

TDM: Multiplexing by assigning different time intervals to signals.

Synchronous TDM: TDM with predetermined recurring slots.

Statistical TDM: TDM that assigns slots dynamically to active sources.

WDM: Optical multiplexing using different wavelengths in one fibre.

CDM: Multiple access using distinguishing code sequences.

DSSS: Spread spectrum in which data is combined with a high-rate chip sequence.

FHSS: Spread spectrum in which the carrier hops among frequencies.

OFDM: Multicarrier transmission using orthogonal, overlapping subcarriers.

Cyclic prefix: A copied end portion of an OFDM symbol used as a guard interval.

Spectral efficiency: Useful data rate divided by occupied bandwidth.

Processing gain: Ratio of spread bandwidth or chip rate to original information bandwidth or data rate.

Guard band: Unused frequency separation that limits adjacent-channel interference.

Random access: Channel access in which users contend for transmission opportunities.

Polling: Controlled access in which a coordinator grants transmission permission.

Co-channel interference: Interference from another system using the same channel.

Jain’s fairness index: A measure of equality among resource allocations.

Dynamic spectrum access: Use of sensing, databases or coordination to share spectrum adaptively.

Review Questions

Short Answer Questions

1. What is the difference between multiplexing and multiple access?
2. Why are guard bands used in FDM systems?
3. State one advantage and one limitation of statistical TDM.
4. What purpose does the cyclic prefix serve in OFDM?
5. Why does spectrum regulation matter in wireless communication?

Long Answer Questions

1. Compare FDM, TDM, WDM and CDM in terms of resource dimension, synchronization, applications and limitations.
2. Explain OFDM operation and discuss orthogonality, cyclic prefixes, PAPR and frequency offset.
3. Describe DSSS and FHSS, including their interference-resistance mechanisms and limitations.
4. Explain Shannon capacity and spectral efficiency, and discuss why practical systems operate below theoretical limits.
5. Compare random, controlled and scheduled channel access for a network carrying both bursty data and real-time traffic.

Analytical / Application Questions

1. A system combines twelve sources, each producing 32 kbit/s. Each frame adds 24 framing bits to 12 source samples of 8 bits each. Calculate the payload rate, frame rate and total line rate.
2. An OFDM symbol has a useful duration of 80 μs and a cyclic prefix of 20 μs. Calculate the subcarrier spacing and time-efficiency factor. State the assumption used for the spacing calculation.
3. Design a high-level spectrum and access plan for a crowded university campus. Justify your choices of multiplexing, channel reuse, access control, monitoring metrics, security and regulatory safeguards.

Multiple Choice Questions with Answers

Question 1

Which multiplexing technique assigns separate frequency bands to different signals?

A. Frequency-division multiplexing

B. Time-division multiplexing

C. Code-division multiplexing

D. Statistical polling

Correct Answer: A. Frequency-division multiplexing

Question 2

In synchronous TDM, what happens to a source’s slot when the source has no data?

A. It is always assigned to another source

B. It may remain unused

C. It changes into a guard band

D. It becomes a new frequency channel

Correct Answer: B. It may remain unused

Question 3

WDM is most directly associated with which transmission medium?

A. Twisted-pair copper only

B. Coaxial cable only

C. Optical fibre

D. Acoustic cable

Correct Answer: C. Optical fibre

Question 4

If a DSSS system has a chip rate of 2 Mchip/s and a data rate of 100 kbit/s, what is its spreading factor?

A. 2

B. 10

C. 20

D. 200

Correct Answer: C. 20

Question 5

For an OFDM useful symbol duration of 50 μs, what is the ideal subcarrier spacing under the relation ∆f = 1 ÷ T_u?

A. 2 kHz

B. 20 kHz

C. 50 kHz

D. 500 kHz

Correct Answer: B. 20 kHz

Question 6

What is the principal purpose of a cyclic prefix in OFDM?

A. To increase the carrier frequency

B. To reduce inter-symbol interference from multipath

C. To encrypt the payload

D. To eliminate all noise

Correct Answer: B. To reduce inter-symbol interference from multipath

Question 7

Which access method allows users to contend and recover from collisions or interference?

A. Random access

B. Fixed wavelength assignment

C. Optical filtering

D. Permanent circuit allocation

Correct Answer: A. Random access

Question 8

A channel has bandwidth 1 MHz and linear SNR 3. According to Shannon’s ideal formula, its capacity is closest to which value?

A. 1 Mbit/s

B. 2 Mbit/s

C. 3 Mbit/s

D. 4 Mbit/s

Correct Answer: B. 2 Mbit/s

Question 9

Which statement about spectral efficiency is correct?

A. It is measured in joules per bit only

B. It is useful data rate divided by occupied bandwidth

C. It is always equal to signal power

D. It excludes the effects of coding and overhead in every practical measurement

Correct Answer: B. It is useful data rate divided by occupied bandwidth

Question 10

Which approach is generally most suitable when predictable latency and quality-of-service guarantees are required?

A. Uncoordinated ALOHA only

B. Scheduled or reservation access

C. Random transmission without backoff

D. Unfiltered overlapping carriers

Correct Answer: B. Scheduled or reservation access