Multiplexing, Multiple Access and Multicarrier Systems

Introduction

Modern communication networks must transport many independent information streams through media whose bandwidth, power, and time are limited. Three related ideas address this requirement. Multiplexing combines several signals for transmission over a shared physical channel. Multiple access allows signals from different users to share a common network resource. Multicarrier transmission divides a wideband channel into many narrower subchannels, often improving robustness against frequency-selective fading.

These techniques are central to optical fibre systems, satellite links, cellular networks, wireless local-area networks, digital subscriber lines, and broadband radio. Their design involves trade-offs among spectral efficiency, interference, synchronization, complexity, latency, power efficiency, and implementation cost.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Distinguish multiplexing from multiple access.
2. Explain FDM, TDM, WDM, CDM, OFDM, and SC-FDMA principles.
3. Derive key bandwidth, rate, orthogonality, and capacity relationships.
4. Analyse intersymbol interference, inter-carrier interference, and multiple-access interference.
5. Select an appropriate access or multicarrier method for a practical system.
6. Evaluate contemporary implementations, limitations, and regulatory issues.

1. Multiplexing and Multiple Access

A multiplexer combines signals generated by one system or network into a composite signal. At the receiver, a demultiplexer separates them. Multiple access is a network-sharing procedure in which independently located users obtain access to a common resource. Thus, a television station may multiplex several programmes, whereas subscribers in a cellular cell use a multiple-access scheme.

The shared resource may be:

• frequency, producing frequency-division methods;
• time, producing time-division methods;
• code, producing code-division methods;
• spatial dimensions, producing space-division methods; or
• combinations of these dimensions.

A useful idealization is to represent the received signal as

where s_k(t) is the contribution of user or channel k, K is the number of simultaneous contributors, and n(t) is additive noise. In practice, the terms may be separated by frequency filters, time windows, correlation, spatial processing, or a combination of these.

1.1 Performance measures

Important measures include:

• Aggregate throughput: total successfully delivered information rate, in bit/s.
• Spectral efficiency:

where R is net information rate in bit/s and B is occupied bandwidth in hertz; therefore η is measured in bit/s/Hz.

• User fairness: the degree to which access opportunities and rates are distributed equitably.
• Outage probability: probability that a required quality measure, such as signal-to-interference-plus-noise ratio, is not achieved.
• Peak-to-average power ratio (PAPR):

This ratio is dimensionless and is often expressed in decibels as 10 log₁₀(PAPR). High PAPR reduces the efficiency of a power amplifier.

• Latency: time from information generation to delivery.

These measures can conflict. Increasing spectral efficiency may increase receiver complexity or reduce robustness; maximizing aggregate rate may reduce fairness.

2. Frequency-Division Multiplexing and Multiple Access

In frequency-division multiplexing (FDM), each signal occupies a distinct frequency band. Bandpass modulation translates channels to different carrier frequencies, and guard bands reduce overlap caused by nonideal filters.

For channel bandwidths B₁, B₂, ..., B_K and guard bands G₁, G₂, ..., G_K-1, the approximate total bandwidth is

This expression assumes adjacent channels are arranged without overlap and that the guard bands are explicitly included. FDM is simple and continuous, but guard bands reduce spectral efficiency. Frequency-division multiple access (FDMA) applies the same principle to users. A user receives a frequency channel for the duration of a connection or scheduled allocation.

Applications include analogue radio, cable television, satellite transponders, and early cellular systems. In modern systems, orthogonal frequency-division multiplexing uses closely spaced orthogonal subcarriers and therefore differs from conventional FDM: its subcarrier spectra overlap mathematically without causing interference under ideal synchronization.

3. Time-Division Multiplexing and Multiple Access

Time-division multiplexing (TDM) allocates different time intervals to different streams. In synchronous TDM, a repeating frame contains predetermined slots. If each of K channels produces R_k bit/s, the required gross rate, ignoring framing and overhead, is

When each channel has equal rate R, this becomes R_TDM = KR. Framing, synchronization, coding, and guard intervals increase the actual rate.

Statistical or asynchronous TDM assigns slots according to demand. It improves utilization when sources are bursty but requires buffering, addressing, queue management, and variable delay. Time-division multiple access (TDMA) assigns users scheduled slots. Guard times compensate for propagation-delay differences and oscillator uncertainty.

A slot duration must be sufficiently large to transmit the assigned data and any control information. If a frame has duration T_f and user k receives T_k seconds, its long-term duty fraction is T_k/T_f, subject to scheduling constraints.

4. Wavelength-Division and Space-Division Multiplexing

Wavelength-division multiplexing (WDM) is FDM in the optical domain. Independent optical carriers with wavelengths λ₁, λ₂, ..., λ_K propagate through one fibre. Dense WDM uses closely spaced wavelengths and requires stable lasers, accurate wavelength filters, and control of nonlinear optical effects.

Because optical frequency and wavelength are related by

where f is optical frequency in hertz, λ is wavelength in metres, and c is the speed of light in vacuum (approximately 3 × 10⁸ m/s), equal wavelength spacing does not correspond exactly to equal frequency spacing over a broad range. Engineering channel plans therefore commonly specify frequency spacing.

Space-division multiplexing (SDM) separates signals by physical propagation paths or spatial modes. Examples include multiple fibres, multicore fibre, antenna arrays, and multiple-input multiple-output (MIMO) radio. SDM can multiply capacity, but coupling between modes, calibration, channel estimation, and hardware cost become important.

5. Code-Division Multiple Access

In code-division multiple access (CDMA), users share time and frequency but are distinguished by spreading waveforms. A data symbol is multiplied by a higher-rate spreading sequence. If the spreading factor is N, then, in a simplified system, one information symbol is represented by N chips.

For normalized spreading sequences c_i and c_j, ideal orthogonality requires

and a nonzero self-correlation for i = j. Orthogonality is generally degraded by multipath propagation, timing errors, and unequal received powers. The resulting interference is called multiple-access interference (MAI).

CDMA offers frequency reuse of one and soft capacity: adding users gradually increases interference rather than exhausting a fixed set of slots. However, power control is essential. A strong nearby transmitter can overwhelm a weak distant transmitter, the classical near–far problem. RAKE receivers can combine resolvable multipath components when the spreading waveform and channel permit it.

6. Orthogonal Frequency-Division Multiplexing

6.1 Principle

OFDM divides a high-rate stream into N lower-rate parallel streams transmitted on orthogonal subcarriers. If the useful OFDM symbol duration is T_u, the subcarrier spacing is

For subcarrier indices k and l, the complex exponentials are orthogonal over the useful interval when k ≠ l:

This orthogonality allows subcarrier spectra to overlap while maintaining ideal demodulation in a synchronized, time-invariant channel.

An inverse discrete Fourier transform (IDFT) generates the time-domain samples. At the receiver, a discrete Fourier transform (DFT) recovers subcarrier symbols. Fast Fourier transform algorithms make implementation efficient, with computational complexity approximately proportional to N log₂ N, rather than N² for a direct transform.

6.2 Cyclic prefix

Multipath causes delayed replicas and intersymbol interference (ISI). OFDM commonly inserts a cyclic prefix (CP), formed by copying the final samples of an OFDM symbol to its beginning. If the channel impulse response has maximum significant delay τ_max, the CP duration T_cp should satisfy

under the usual assumption of a quasi-static channel during one symbol and correct synchronization. The CP converts linear convolution into circular convolution, allowing one-tap frequency-domain equalization on each subcarrier.

The useful-data efficiency due solely to the CP is

This neglects pilots, null subcarriers, cyclic-prefix processing loss, coding, and other overheads. For example, if T_u = 66.7 μs and T_cp = 4.7 μs, then η_CP ≈ 66.7/71.4 ≈ 0.934, or about 93.4% before other overheads.

6.3 OFDM limitations

OFDM is sensitive to carrier-frequency offset and timing errors. A frequency offset destroys subcarrier orthogonality and produces inter-carrier interference (ICI). Its large PAPR results from the possible constructive addition of many subcarriers. Power amplifiers must operate with back-off or use linearization, reducing energy efficiency.

Other concerns include CP overhead, pilot overhead, sensitivity to narrowband interference, and spectral leakage when the waveform is abruptly truncated. Windowing, filtering, tone reservation, clipping with compensation, selected mapping, and coding can reduce PAPR, although each introduces trade-offs.

7. Multiuser OFDMA and SC-FDMA

Orthogonal frequency-division multiple access (OFDMA) assigns different subsets of OFDM subcarriers to different users. A scheduler can adapt assignments according to channel quality, traffic demand, latency, and fairness. Resource allocation may occur in time, frequency, and spatial dimensions simultaneously.

If user i receives subcarrier set S_i, disjoint allocation requires

in an ideal orthogonal allocation. Practical systems reserve pilots, guard subcarriers, synchronization signals, and control regions.

Single-carrier frequency-division multiple access (SC-FDMA), also called DFT-spread OFDM, applies a DFT precoding stage before subcarrier mapping. It retains frequency-domain equalization and flexible scheduling while generally producing lower PAPR than ordinary OFDM. This makes it attractive for power-limited terminals, although the receiver and scheduler are more constrained than in some OFDMA arrangements.

8. Capacity and Resource Allocation

For an additive white Gaussian noise channel of bandwidth B, received signal power S, and noise power N, Shannon capacity is

where C is in bit/s and S/N is a dimensionless signal-to-noise ratio. The formula assumes ideal coding, arbitrarily long codewords, Gaussian noise, and a channel that is adequately represented by the model. It is an upper bound, not a guaranteed practical rate.

For parallel orthogonal subchannels,

where B_k, S_k, and N_k are the bandwidth, signal power, and noise power associated with subchannel k. If the transmitter knows channel conditions and can vary power subject to a total-power constraint, water-filling allocates more power to favourable subchannels. In practical systems, discrete modulation and coding, regulatory limits, fairness, and control overhead replace ideal continuous allocation.

Worked example: OFDM resource calculation

An OFDM system has 1024 subcarriers, subcarrier spacing 15 kHz, and a cyclic prefix of 4.7 μs. The useful symbol duration is

T_u = 1/(15,000) = 66.67 μs.

The total symbol duration is approximately 71.37 μs, so the symbol rate per subcarrier is about 14,012 symbols/s. If 600 subcarriers carry data, each uses 16-QAM, and coding rate is 3/4, the ideal coded data rate before pilots and other overhead is

The four bits per 16-QAM symbol and the coding rate are assumed constant on every data subcarrier. The result excludes control symbols, pilots, guard bands, retransmissions, and implementation losses.

9. Practical System Design

A design process should begin with traffic and channel requirements rather than with a preferred waveform.

1. Characterize the channel: bandwidth, delay spread, Doppler spread, fading statistics, interference, and regulatory mask.
2. Define service requirements: peak and guaranteed rates, latency, reliability, mobility, and user density.
3. Select the sharing dimension: frequency, time, code, space, or a hybrid.
4. Choose waveform parameters: subcarrier spacing, symbol duration, CP length, modulation, coding, pilots, and guard intervals.
5. Design synchronization: carrier, timing, sampling, frequency offset, and network timing.
6. Evaluate implementation: PAPR, converter resolution, amplifier efficiency, memory, processing, and thermal limits.
7. Test under realistic conditions: mobility, nonlinearity, adjacent-channel interference, burst traffic, and multiuser loading.

The CP should not simply be made very long: it improves multipath tolerance but decreases efficiency. Similarly, narrow subcarrier spacing improves resistance to delay spread but increases symbol duration and may increase sensitivity to Doppler-induced ICI. A system therefore requires a numerology appropriate to its propagation environment.

10. Applied Case: Illustrative 5G-Style Broadband Cell

Background. Consider an illustrative urban broadband cell serving mobile users with different speeds, channel qualities, and traffic types. The base station has a multi-antenna array and a wideband OFDM-based air interface.

Problem. Users near the cell edge experience lower signal-to-interference-plus-noise ratio, fast-moving users experience channel variation, and video traffic creates bursty demand. A fixed allocation would waste resources or provide poor fairness.

Analysis. The scheduler divides the available time–frequency grid into resource blocks. Channel-state information estimates which users have favourable conditions on each block. However, maximizing instantaneous throughput would repeatedly favour users with strong channels. A fairness-aware scheduler therefore balances channel quality with historical service. The CP is selected to exceed the relevant delay spread, while the subcarrier spacing is chosen as a compromise between delay robustness and Doppler tolerance.

Approach. The system uses adaptive modulation and coding, hybrid automatic repeat request, OFDMA scheduling, link adaptation, and multiuser MIMO. Edge users receive robust coding and lower-order modulation. Users with stable channels may receive higher-order modulation. Beamforming provides spatial separation, while reference signals support channel estimation. Power-amplifier back-off and digital predistortion limit distortion from high-PAPR downlink signals.

Outcome. Compared with fixed equal allocation, adaptive scheduling improves aggregate throughput and maintains a defined fairness target. Performance remains dependent on channel-estimation accuracy, feedback delay, interference coordination, and the overhead of reference signals.

Learning points. No multiple-access method is universally optimal. The practical result depends on propagation, traffic, hardware, control overhead, and the fairness objective. Orthogonality is a system condition—not merely a mathematical property—and is lost when synchronization and channel assumptions fail.

11. Limitations, Governance, and Contemporary Developments

Multiplexing and access systems operate within national spectrum regulations, licensing conditions, emission masks, and standards-essential intellectual-property frameworks. Spectrum allocation must protect incumbent users and safety-critical services. Network operators should document scheduler policies, especially where resource allocation affects emergency access or service discrimination.

Security is also relevant. Shared wireless media are vulnerable to eavesdropping, spoofing, jamming, and denial-of-service attacks. Physical-layer separation does not replace cryptographic confidentiality and authentication. Measurements and AI-assisted scheduling must be monitored for biased performance across locations, devices, or user groups. Training data, model drift, explainability, and fail-safe operation matter when machine learning controls radio resources.

Contemporary research includes cell-free massive MIMO, intelligent reflecting surfaces, integrated sensing and communications, non-terrestrial networks, sub-THz communications, OTFS-like delay–Doppler waveforms, and AI-assisted resource allocation. These approaches may improve coverage or adaptability, but they introduce difficult questions involving synchronization, hardware impairments, scalability, energy consumption, and reproducible evaluation. Claims of improvement should therefore be assessed using common channel models, realistic overhead, statistical confidence, and end-to-end energy and latency—not peak physical-layer throughput alone.

Best Practices

• State channel and synchronization assumptions explicitly.
• Separate gross bit rate from net application throughput.
• Include pilots, guard intervals, coding, control, and retransmission overhead.
• Report both spectral efficiency and energy efficiency.
• Evaluate fairness, outage, latency, and reliability alongside peak rate.
• Test amplifier nonlinearity and PAPR with realistic hardware.
• Select CP and subcarrier spacing from measured propagation conditions.
• Use standards-compliant spectrum masks and coexistence procedures.
• Treat AI-based scheduling as a controlled engineering component with monitoring and fallback modes.

Chapter Summary

Multiplexing combines independent signals, while multiple access enables independent users to share network resources. FDM and FDMA separate signals in frequency; TDM and TDMA separate them in time; WDM applies frequency separation to optical carriers; CDMA uses spreading sequences and correlation; and SDMA exploits spatial separation. OFDM divides a wideband channel into orthogonal subcarriers, with the IDFT/DFT pair enabling practical implementation. A cyclic prefix protects against multipath when it exceeds the significant channel delay spread, but it consumes efficiency. OFDMA supports flexible multiuser scheduling, whereas SC-FDMA generally reduces terminal PAPR.

System performance must be assessed through spectral efficiency, capacity, latency, fairness, reliability, interference, and energy efficiency. Shannon capacity is an ideal upper bound. Real systems require synchronization, channel estimation, coding, pilots, guard resources, amplifier linearity, and regulatory compliance. The appropriate technique is determined by propagation conditions, traffic, mobility, hardware constraints, and service objectives.

Key Terms

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

Multiple access: A method by which independent users share a communication resource.

FDM: Frequency-division multiplexing using separate frequency bands.

FDMA: Assigning frequency channels to different users.

TDM: Time-division multiplexing using separate time intervals.

TDMA: Assigning scheduled time slots to users.

WDM: Optical multiplexing using distinct wavelengths.

CDMA: Multiple access using spreading sequences and correlation.

OFDM: Transmission using mutually orthogonal subcarriers.

OFDMA: Assignment of OFDM subcarriers or resource blocks to users.

SC-FDMA: DFT-spread multicarrier access with reduced PAPR characteristics.

Subcarrier: One orthogonal frequency component in a multicarrier waveform.

Cyclic prefix: Repeated symbol suffix inserted to combat multipath.

ISI: Interference between successive transmitted symbols.

ICI: Interference between nominally orthogonal subcarriers.

PAPR: Ratio of peak signal power to average signal power.

Spectral efficiency: Net information rate per unit bandwidth.

Multiple-access interference: Interference caused by simultaneous users.

Water-filling: Power-allocation principle for parallel channels with unequal quality.

MIMO: Use of multiple transmit and receive antennas for spatial processing.

Review Questions

Short Answer Questions

1. Distinguish multiplexing from multiple access.
2. Why are guard bands used in conventional FDM?
3. State the orthogonality condition for two spreading sequences.
4. What is the purpose of a cyclic prefix in OFDM?
5. Define PAPR and explain why it matters in transmitter design.

Long Answer Questions

1. Explain FDM, TDM, WDM, CDMA, and OFDM, comparing their resource dimensions, advantages, and limitations.
2. Derive the relationship between OFDM subcarrier spacing and useful symbol duration, and discuss the role of the cyclic prefix.
3. Explain OFDMA scheduling and the trade-off between throughput and fairness.
4. Discuss the causes and mitigation methods of PAPR in multicarrier systems.
5. Explain Shannon capacity and discuss why practical systems operate below the theoretical bound.

Analytical / Application Questions

1. A system has 20 channels of 25 kHz each and 19 guard bands of 2 kHz each. Calculate the approximate occupied bandwidth and explain the principal efficiency limitation.
2. An OFDM channel has a maximum significant multipath delay of 3 μs. Evaluate whether a 2 μs cyclic prefix is adequate, and state the likely consequence if it is not.
3. Design a qualitative multiple-access strategy for a mobile cell containing low-rate sensors, high-rate stationary users, and high-mobility users. Justify the choice of time, frequency, spatial, and coding dimensions.

Multiple Choice Questions with Answers

Question 1

Which technique separates channels primarily by assigning distinct time intervals?

A. FDM

B. TDM

C. WDM

D. CDMA

Correct Answer: B. TDM

Question 2

For ideal OFDM orthogonality, the subcarrier spacing is related to useful symbol duration by which expression?

A. ∆f = T_u

B. ∆f = 2T_u

C. ∆f = 1/T_u

D. ∆f = T_u²

Correct Answer: C. ∆f = 1/T_u

Question 3

The main purpose of a cyclic prefix is to

A. increase carrier frequency

B. combat multipath-induced intersymbol interference

C. eliminate the need for channel coding

D. reduce the number of subcarriers

Correct Answer: B. combat multipath-induced intersymbol interference

Question 4

If 600 data subcarriers use 16-QAM and coding rate 3/4, how many coded information bits are conveyed per OFDM symbol before other overheads?

A. 1,200

B. 1,800

C. 2,400

D. 3,200

Correct Answer: C. 2,400

Question 5

Which problem is especially associated with CDMA systems having unequal received powers?

A. Near–far problem

B. Aliasing problem

C. Quantization problem

D. Thermal runaway

Correct Answer: A. Near–far problem

Question 6

The Shannon capacity formula C = B log₂(1 + S/N) assumes, among other conditions,

A. zero bandwidth

B. ideal coding over an AWGN channel

C. no received signal

D. mandatory uncoded transmission

Correct Answer: B. ideal coding over an AWGN channel

Question 7

Compared with ordinary OFDM, SC-FDMA is commonly valued in uplinks because it generally

A. has lower PAPR

B. requires no synchronization

C. uses no frequency-domain processing

D. eliminates fading

Correct Answer: A. has lower PAPR

Question 8

If the cyclic prefix is made longer while all other parameters remain fixed, CP efficiency

A. increases

B. decreases

C. becomes exactly 100%

D. is unaffected by symbol duration

Correct Answer: B. decreases

Question 9

In WDM, independent optical channels are distinguished primarily by their

A. antenna height

B. wavelengths

C. coding rates only

D. time-domain sample labels

Correct Answer: B. wavelengths

Question 10

A high PAPR signal can reduce transmitter energy efficiency because the power amplifier must generally

A. operate with back-off to limit nonlinear distortion

B. remove all guard bands

C. increase channel delay spread

D. use a lower sampling theorem limit

Correct Answer: A. operate with back-off to limit nonlinear distortion