Multicarrier and Spread-Spectrum Communications

Introduction

Wireless systems must convey information over channels affected by thermal noise, interference, multipath propagation, fading, limited spectrum, and hardware constraints. Two influential families of waveform techniques address these problems from different perspectives. Spread-spectrum systems deliberately occupy a bandwidth substantially larger than the minimum information bandwidth, thereby improving resistance to interference, fading, and interception. Multicarrier systems divide a high-rate data stream among many orthogonal lower-rate subcarriers, making frequency-selective channels easier to equalize.

Direct-sequence spread spectrum (DSSS), frequency-hopping spread spectrum (FHSS), and code-division multiple access (CDMA) are based primarily on spreading and correlation. Orthogonal frequency-division multiplexing (OFDM), single-carrier frequency-division multiple access (SC-FDMA), and filter-bank multicarrier (FBMC) systems are based on structured spectral decomposition and pulse shaping. Modern broadband systems frequently combine these ideas with adaptive modulation, channel coding, multiple antennas, beamforming, and resource scheduling.

This chapter develops the operating principles, mathematical models, design trade-offs, and practical selection criteria for these waveforms.

Learning Objectives

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

1. Explain the principles of DSSS, FHSS, and CDMA.

2. Derive the principal processing-gain and spreading relationships.

3. Describe OFDM signal generation, orthogonality, cyclic-prefix design, and receiver processing.

4. Analyze intercarrier interference (ICI), intersymbol interference (ISI), and peak-to-average power ratio (PAPR).

5. Explain SC-FDMA and filter-bank multicarrier waveforms.

6. Compare waveform choices for broadband wireless systems.

7. Evaluate implementation, regulatory, energy, and security considerations.

1. Spread-Spectrum Foundations

A spread-spectrum signal intentionally occupies a bandwidth greater than the minimum required for its information rate. The spreading operation is controlled by a pseudo-random, or pseudo-noise (PN), sequence known to the receiver. Despreading concentrates the desired signal while interference that is uncorrelated with the sequence remains distributed over the detection bandwidth.

The principal benefits are interference suppression, frequency-selective-fading mitigation, low probability of detection in some operating conditions, and support for multiple users through distinct codes or hopping patterns. These benefits require synchronization, additional signal-processing complexity, and often reduced spectral efficiency when spreading is used without aggressive multiuser reuse.

1.1 Direct-Sequence Spread Spectrum

In binary DSSS, a data symbol is multiplied by a sequence of chips. If the symbol duration is $T_b$ and the chip duration is $T_c$, the spreading factor or processing gain is

$$G_p = \frac{T_b}{T_c} = \frac{R_c}{R_b},$$

where $R_b$ is the information bit rate and $R_c$ is the chip rate. This relationship assumes one bit per binary symbol and rectangular chip timing. For a modulation with $k$ bits per symbol, the corresponding symbol-domain spreading factor is $T_s/T_c$.

Using a bipolar representation, a transmitted DSSS waveform may be written as

$$s(t)=\sqrt{P}\,d(t)c(t),$$

where $P$ is average transmit power, $d(t)$ is the data waveform taking values in $\{+1,-1\}$, and $c(t)$ is the spreading waveform, also taking values in $\{+1,-1\}$. The receiver multiplies the received signal by a synchronized replica of $c(t)$ and integrates over a bit interval. Since $c^2(t)=1$, the desired data term is recovered, whereas sufficiently uncorrelated interference is reduced after integration.

For additive white Gaussian noise and ideal synchronization, the processing gain is approximately the ratio of spread bandwidth to despread information bandwidth. In decibels,

$$G_{p,\mathrm{dB}}=10\log_{10}G_p.$$

This is not an unconditional signal-to-noise-ratio improvement: it applies to interference or noise that is effectively wideband relative to the information signal and is not correlated with the spreading code. A narrowband interferer can be strongly attenuated after despreading, but a jammer that knows the code or transmits across the full spread bandwidth may not be suppressed in the same way.

DSSS receivers require code-phase acquisition, tracking, carrier recovery, and often accurate power control in multiuser systems. Correlation properties of the codes are important. A preferred code family has low cross-correlation between different users and a sharp autocorrelation peak for synchronization.

1.2 Frequency-Hopping Spread Spectrum

In FHSS, the carrier frequency changes according to a pseudo-random hopping sequence. A slow-hopping system may retain one frequency for several transmitted symbols, whereas a fast-hopping system may hop several times during one symbol. The hop pattern is shared by transmitter and receiver.

FHSS can be represented by

$$s(t)=\sqrt{2P}\,m(t)\cos\left[2\pi(f_c+f_h(t))t+\phi\right],$$

where $f_c$ is a nominal carrier, $f_h(t)$ is the time-varying hop offset, $m(t)$ is the modulation waveform, and $\phi$ is carrier phase. The hop set is divided into channels or frequency bins. Interference affecting one bin is avoided when the system hops to another bin, provided the receiver can reacquire the hop timing.

FHSS is attractive where narrowband interference, coexistence, and frequency-selective fading are major concerns. Its disadvantages include synthesizer and hopping-control complexity, acquisition delay, spectral splatter caused by abrupt transitions, and lower instantaneous spectral efficiency than a continuously occupied broadband waveform.

1.3 DSSS and FHSS Comparison

DSSS spreads each transmitted symbol across a broad frequency range at the same time. FHSS occupies a narrower range at any instant but changes the occupied range over time. DSSS generally provides straightforward correlation-based despreading and can support code-based multiple access. FHSS can be robust against localized interference and may simplify coexistence with systems using other frequency channels. Neither method is universally superior; the appropriate choice depends on interference statistics, mobility, synchronization capability, spectrum regulation, and terminal cost.

2. CDMA and Multiuser Detection

Code-division multiple access allows multiple users to occupy the same time and frequency resources while being separated by spreading codes. In a synchronous binary CDMA model, the received baseband signal is

$$r(t)=\sum_{k=1}^{K}\sqrt{P_k}b_k(t)c_k(t)+n(t),$$

where $K$ users transmit data waveforms $b_k(t)$, spreading waveforms $c_k(t)$, powers are $P_k$, and $n(t)$ is noise. A correlator matched to user $i$ produces a desired term plus cross-correlation terms from other users.

If the codes are orthogonal over the symbol interval, then

$$\int_0^{T_b}c_i(t)c_j(t)\,dt=0 \quad (i\ne j),$$

under the assumed timing and channel conditions. Multipath propagation, asynchronous arrivals, and filtering distort this orthogonality. Consequently, practical CDMA systems experience multiple-access interference (MAI).

A simplified interference-limited expression for a user’s signal-to-interference-plus-noise ratio is

$$\mathrm{SINR}_i=\frac{P_i}{N_0B+\sum_{j\ne i}P_j\rho_{ij}},$$

where $N_0B$ is the in-band noise power and $\rho_{ij}$ represents effective code cross-correlation and channel-induced interference. This expression is a model rather than a universal CDMA capacity formula.

The near–far problem occurs when a nearby user arrives with much greater power than a distant user. Even codes with good correlation properties may not adequately suppress the strong user’s leakage. Fast and accurate power control is therefore central to cellular CDMA. RAKE receivers exploit resolvable multipath components by correlating with delayed versions of the spreading sequence and combining their outputs. Advanced receivers may use successive-interference cancellation, linear minimum-mean-square-error detection, or joint multiuser detection.

CDMA illustrates a general principle: spreading alone does not eliminate interference. Performance depends on code correlation, power balance, channel estimation, synchronization, receiver architecture, and the number of active users.

3. OFDM Principles

Orthogonal frequency-division multiplexing divides a broadband channel into $N$ closely spaced subcarriers. Each subcarrier carries a lower-rate complex symbol during an OFDM symbol interval. The subcarriers overlap in frequency, but their spectra are orthogonal at the sampling instants used for detection.

Let $X[k]$ denote the complex data symbol on subcarrier $k$, for $k=0,1,\ldots,N-1$. The discrete-time OFDM symbol generated by an inverse discrete Fourier transform (IDFT) is

$$x[n]=\frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}X[k]e^{j2\pi kn/N},\quad n=0,1,\ldots,N-1.$$

The $1/\sqrt{N}$ normalization preserves energy under the corresponding unitary DFT convention. Other engineering conventions use $1/N$ in the IDFT and no factor in the DFT; the system must use consistent scaling.

The receiver removes any cyclic prefix, applies an $N$-point DFT, and obtains approximately

$$Y[k]=H[k]X[k]+W[k],$$

when the channel is sufficiently represented as circular convolution over the useful symbol interval. Here $H[k]$ is the channel frequency response at subcarrier $k$ and $W[k]$ is transformed noise. Equalization can then be performed independently on each subcarrier, for example by zero forcing or minimum mean-square-error equalization.

3.1 Orthogonality

For subcarrier spacing

$$\Delta f=\frac{1}{T_u},$$

where $T_u$ is the useful OFDM symbol duration, adjacent subcarriers satisfy

$$\int_0^{T_u}e^{j2\pi(k-l)t/T_u}\,dt=0 \quad \text{for } k\ne l.$$

Thus, although subcarrier spectra overlap, the integral of one subcarrier against another over the useful interval is zero. Orthogonality is maintained only when frequency offsets, timing errors, phase noise, and channel variation do not significantly disturb the assumed signal model.

The gross subcarrier symbol rate is $1/T_u=\Delta f$. If a cyclic prefix of duration $T_{cp}$ is added, the efficiency associated with the prefix is

$$\eta_{cp}=\frac{T_u}{T_u+T_{cp}},$$

excluding other overhead such as pilots, guard subcarriers, synchronization signals, and coding. Increasing $T_u$ by using smaller subcarrier spacing improves prefix efficiency for a fixed delay spread, but it makes the system more sensitive to oscillator offsets and rapid channel variation.

3.2 Cyclic Prefix Design

A cyclic prefix is formed by copying the last $N_{cp}$ samples of the useful OFDM symbol and placing them before the symbol. If the discrete-time channel has maximum significant delay $L_h-1$ samples, a sufficient ideal condition is

$$N_{cp}\ge L_h-1,$$

assuming timing is selected so that the complete channel response lies within the prefix protection interval. In continuous time, the corresponding design condition is commonly stated as

$$T_{cp}\ge \tau_{\max},$$

where $\tau_{\max}$ is the maximum excess delay relative to the chosen channel reference.

The cyclic prefix performs two functions. First, it absorbs delayed replicas from the previous symbol, preventing ISI within the useful interval. Second, it converts linear convolution into circular convolution, enabling one-tap frequency-domain equalization. The prefix carries no new information and therefore reduces spectral efficiency and energy efficiency.

A practical design uses measured or modeled delay statistics, not merely a nominal average delay. Excessive prefix length wastes resources; insufficient length produces ISI and ICI that cannot be removed by ordinary one-tap equalization. In standards, multiple numerologies or prefix options may be selected for different propagation environments and operating frequencies.

3.3 OFDM Transmitter and Receiver

A typical transmitter performs channel coding, interleaving, bit-to-symbol mapping, resource-element mapping, pilot insertion, IDFT processing, cyclic-prefix insertion, digital-to-analog conversion, filtering, frequency conversion, and power amplification. The receiver reverses these operations and adds synchronization, channel estimation, equalization, demapping, deinterleaving, and decoding.

Guard subcarriers may be left unused near band edges to satisfy spectral masks. A DC subcarrier may be nulled in direct-conversion architectures. Pilot patterns support channel estimation and tracking of common phase error. Windowing or filtering can reduce spectral leakage caused by finite symbol transitions, although excessive windowing may affect orthogonality and useful energy.

4. OFDM Impairments

4.1 Intercarrier Interference

ICI occurs when energy from one subcarrier appears in another subcarrier’s decision variable. Major causes include carrier-frequency offset (CFO), sampling-frequency offset, Doppler variation, phase noise, and insufficient timing alignment. If the received signal is multiplied by a frequency offset $\epsilon\Delta f$, where $\epsilon$ is normalized CFO, the orthogonality integrals no longer vanish for different subcarriers.

CFO has two common components: an integer-subcarrier offset, which shifts the subcarrier allocation, and a fractional offset, which creates ICI. Synchronization algorithms estimate and correct CFO before demodulation. Residual CFO and phase noise remain and may be tracked using pilots. High subcarrier spacing reduces the normalized impact of a given absolute frequency error, but increases the number of subcarriers or reduces symbol duration for a fixed bandwidth.

Doppler spread produces time variation during the useful symbol interval. If the channel is approximately constant over that interval, each subcarrier experiences a scalar channel gain. If it varies substantially, orthogonality is lost and ICI appears. A useful design criterion is that the coherence time should be appreciably longer than the useful symbol duration, although exact margins depend on the acceptable ICI level and channel model.

4.2 Peak-to-Average Power Ratio

The OFDM time-domain waveform is the sum of many independently modulated subcarriers. Constructive addition can generate large peaks. PAPR is defined as

$$\mathrm{PAPR}=\frac{\max_{0\le t<T}|x(t)|^2}{\mathbb{E}[|x(t)|^2]},$$

where $T$ is the observation interval and the expectation denotes average signal power. In sampled implementations, oversampling is needed to estimate peaks that occur between ordinary sample instants.

High PAPR requires a power amplifier to operate with substantial input back-off, reducing power efficiency and potentially reducing coverage or battery life. Nonlinear amplification causes in-band distortion, which raises error-vector magnitude, and out-of-band spectral regrowth, which can violate emission limits.

PAPR-reduction methods include clipping and filtering, tone reservation, tone injection, selected mapping, partial-transmit sequences, active constellation extension, and coding. Each method introduces trade-offs involving distortion, side information, computational complexity, lost data tones, or increased signal-processing burden. PAPR is a distributional property; reducing a few extreme peaks does not necessarily guarantee improved link performance if distortion or side-information errors are introduced.

5. SC-FDMA

SC-FDMA, also called discrete Fourier transform spread OFDM, applies an $M$-point DFT to the $M$ modulation symbols before mapping them onto selected OFDM subcarriers. An $N$-point IDFT then generates the transmit waveform, where typically $M\le N$.

For input symbols $d[m]$, the DFT-spread symbols are

$$D[r]=\frac{1}{\sqrt{M}}\sum_{m=0}^{M-1}d[m]e^{-j2\pi rm/M}.$$

These values are mapped to subcarriers, followed by an $N$-point IDFT. Localized mapping assigns contiguous subcarriers; interleaved mapping distributes them across the band. After cyclic-prefix removal and frequency-domain equalization, the receiver applies the inverse operations.

The DFT-spreading operation creates a waveform with lower PAPR than conventional OFDM for many modulation and allocation conditions. This benefit is especially valuable for battery-powered uplink terminals. SC-FDMA retains frequency-domain equalization and flexible scheduling, but its frequency-domain resource allocation and equalization are more coupled than in OFDM. Frequency-selective allocation and multiuser scheduling must preserve the required mapping structure.

SC-FDMA is not completely constant-envelope, and its PAPR depends on modulation, mapping, pulse shaping, number of allocated subcarriers, and implementation details. It should therefore be evaluated using measured complementary cumulative distribution functions (CCDFs), amplifier efficiency, and error performance rather than by a simple categorical label.

6. Filter-Bank Multicarrier Waveforms

OFDM uses a rectangular time-domain pulse over each useful symbol interval. Its discontinuities produce sidelobes, and the cyclic prefix is required to protect against multipath. Filter-bank multicarrier (FBMC) systems instead apply carefully designed prototype filters to individual subcarriers or subbands. The filters provide better spectral localization and can reduce adjacent-channel leakage.

In a filter-bank implementation, a synthesis filter bank generates the transmit signal and an analysis filter bank separates received subchannels. The prototype filter is selected to satisfy time-frequency localization and perfect-reconstruction or near-perfect-reconstruction conditions under the chosen modulation structure. Polyphase networks make practical implementations efficient.

Offset-QAM FBMC, commonly called FBMC/OQAM, offsets the real and imaginary components in time. It can achieve real-field orthogonality with overlapping subcarrier pulses, but it does not provide ordinary complex orthogonality at arbitrary instants. This creates challenges for pilots, MIMO channel estimation, and interference handling. Other filtered multicarrier approaches include filtered-OFDM, universal filtered multicarrier, and generalized frequency-division multiplexing.

FBMC can reduce out-of-band emissions and may be useful for fragmented spectrum, asynchronous access, and dynamic spectrum sharing. However, longer filter transients, higher implementation complexity, intrinsic interference in OQAM systems, and difficult integration with certain MIMO and coding structures have limited universal adoption. Waveform selection must therefore consider the complete transceiver and network, not only the spectral shape.

7. Comparative Waveform Selection

Waveform selection is a multi-criteria engineering decision. Important criteria include:

• Spectral efficiency and occupied-bandwidth compliance.
• Robustness to multipath delay spread and Doppler spread.
• PAPR and power-amplifier efficiency.
• Synchronization and channel-estimation complexity.
• Latency, burst length, and transient behavior.
• Support for MIMO, beamforming, and multiuser scheduling.
• Adjacent-channel leakage and coexistence requirements.
• Computational complexity and memory.
• Compatibility with existing standards and hardware.
• Security, privacy, and resilience to intentional interference.

OFDM is attractive for broadband downlink systems because it supports simple per-subcarrier equalization, adaptive modulation, frequency-selective scheduling, and MIMO integration. Its principal weaknesses are PAPR, sensitivity to synchronization errors, and cyclic-prefix overhead. SC-FDMA is attractive for uplinks where terminal power efficiency is important. FBMC is attractive when spectral containment and asynchronous operation outweigh implementation complexity. DSSS or CDMA remains useful where code-based access, processing gain, and interference tolerance are central. FHSS remains relevant for robust short-range links, industrial systems, and environments with localized interference.

No waveform eliminates the channel’s limitations. Coding, antenna configuration, link adaptation, interference coordination, synchronization, and power-amplifier design often affect system performance as strongly as the nominal waveform.

8. Worked Example: OFDM Prefix and Efficiency

Consider an OFDM system with sampling rate $15.36$ MHz, $N=1024$ useful samples, and a channel whose significant maximum excess delay is $4.69$ microseconds. The subcarrier spacing is

$$\Delta f=\frac{15.36\times10^6}{1024}=15\text{ kHz}.$$

The useful symbol duration is therefore

$$T_u=\frac{1}{15\text{ kHz}}=66.67\ \mu\text{s}.$$

The sampling period is

$$T_s=\frac{1}{15.36\times10^6}=65.10\text{ ns}.$$

The number of prefix samples required is at least

$$N_{cp}\ge \frac{4.69\ \mu\text{s}}{65.10\text{ ns}}\approx72.0.$$

Thus, an implementation should select at least 72 samples, usually with a standardized margin or a convenient supported prefix length. If $N_{cp}=80$, the prefix duration is

$$T_{cp}=80(65.10\text{ ns})=5.208\ \mu\text{s}.$$

The useful-time efficiency is

$$\eta_{cp}=\frac{66.67}{66.67+5.208}=0.9275,$$

or approximately $92.75\%$, before accounting for pilots, guard tones, coding, and other overhead. The example demonstrates why a prefix must exceed the delay spread while remaining as short as practical.

9. Applied Case: Broadband Uplink Waveform Selection

Background

Consider an illustrative cellular system operating in a frequency-selective urban environment. The base station has a stable power supply and many antennas, while user equipment is battery powered and must transmit over a variable distance. The system supports adaptive modulation, MIMO reception, and scheduling across a licensed broadband channel.

Problem

A conventional OFDM uplink provides flexible frequency-domain scheduling but produces high envelope variation. The resulting power amplifier must operate with back-off, reducing handset efficiency. At the same time, the channel has multipath delay spread that makes single-carrier time-domain equalization expensive.

Analysis

A waveform is required that retains frequency-domain equalization while reducing PAPR. The design team compares OFDM, SC-FDMA, and a filtered multicarrier option. OFDM has the simplest integration with existing pilot and MIMO processing but imposes the greatest amplifier back-off. FBMC provides excellent spectral localization but creates additional pilot and MIMO complications. SC-FDMA offers a compromise: a DFT-spread signal can be equalized in the frequency domain and generally has lower PAPR.

The team also examines localized versus interleaved subcarrier mapping. Localized mapping supports contiguous scheduling and frequency-selective resource assignment. Interleaved mapping can produce different time-domain properties but restricts scheduling flexibility. Channel estimation, control signaling, amplifier efficiency, and spectral-mask compliance are evaluated jointly.

Approach and Solution

SC-FDMA with localized mapping is selected for the uplink. The cyclic prefix is designed from the upper-percentile channel delay spread rather than the mean delay. Pilot symbols are inserted using a pattern that supports interpolation across frequency and time. The receiver uses frequency-domain minimum-mean-square-error equalization, followed by inverse DFT processing and symbol demapping. The power amplifier is characterized using error-vector magnitude, adjacent-channel leakage ratio, and efficiency at the required output power.

Outcome

The selected waveform preserves low-complexity frequency-domain equalization and improves terminal power efficiency relative to conventional OFDM. The trade-off is reduced flexibility in arbitrary subcarrier allocation and additional DFT processing. The system also retains cyclic-prefix overhead and remains sensitive to synchronization errors.

Learning Points

1. A waveform should be selected using end-to-end metrics, not PAPR alone.

2. Uplink and downlink requirements may differ substantially.

3. Channel delay spread determines prefix design, while mobility and oscillator quality influence subcarrier spacing.

4. Hardware efficiency, scheduling, pilots, and regulatory emissions must be evaluated together.

10. Challenges, Governance, and Contemporary Developments

Waveform design has regulatory and governance implications. Spectral masks, adjacent-channel leakage, permitted emissions, and coexistence rules constrain filter design and amplifier operation. Interference management must consider neighboring operators, unlicensed users, critical infrastructure, and emergency communications. Deliberate spreading or hopping may improve resilience but does not by itself provide confidentiality; strong cryptographic protection remains necessary.

Security threats include pilot contamination, synchronization attacks, jamming, spoofed timing references, and malicious interference with spreading-code acquisition. Systems should authenticate control information, monitor anomalous interference, and avoid treating waveform obscurity as encryption.

Contemporary broadband systems use flexible numerologies, bandwidth parts, dynamic scheduling, advanced channel coding, massive MIMO, and beam management. Research continues on subband filtering, low-PAPR waveforms, integrated sensing and communications, reconfigurable intelligent surfaces, and machine-learning-assisted waveform adaptation. Artificial intelligence can assist in waveform selection, channel prediction, interference classification, and resource allocation, but training-data bias, adversarial inputs, explainability, computational cost, and regulatory validation must be addressed. AI should augment, not replace, analytical link budgets, conformance testing, and safety-critical engineering review.

Best practice is to establish requirements first, derive the channel and hardware constraints, select candidate waveforms, simulate standardized channel models, implement a fixed-point or RF-aware prototype, and validate performance using measured impairments. Evaluation should include throughput, block-error rate, latency, energy per bit, PAPR CCDF, amplifier efficiency, spectral emissions, synchronization margin, and robustness to interference.

Chapter Summary

Spread-spectrum systems increase occupied bandwidth deliberately to obtain processing gain, interference tolerance, and code- or hop-based separation. DSSS multiplies data by a chip sequence, while FHSS changes carrier frequency according to a synchronized hop pattern. CDMA extends spreading to multiuser access but is limited by code correlation, multipath, multiple-access interference, and the near–far problem.

OFDM divides a high-rate stream among orthogonal subcarriers and uses IDFT/DFT processing to simplify equalization in frequency-selective channels. A cyclic prefix prevents ISI and converts linear convolution into circular convolution, but it consumes time and energy. Frequency offsets, phase noise, Doppler, and timing errors cause ICI. OFDM’s high PAPR challenges power-amplifier efficiency and spectral compliance.

SC-FDMA applies DFT spreading before subcarrier mapping, reducing envelope variation while retaining frequency-domain equalization. FBMC and related filtered waveforms improve spectral localization but introduce filter transients, implementation complexity, and challenges in pilots and MIMO. Waveform selection is therefore a system-level decision involving channel conditions, mobility, spectrum, hardware, scheduling, energy, regulation, and security.

Key Terms

Processing gain: Ratio of spread bandwidth or chip rate to information bandwidth or bit rate under the stated spreading model.

Chip: A short-duration element of a spreading sequence.

DSSS: Spread-spectrum technique that multiplies data by a high-rate pseudo-noise sequence.

FHSS: Spread-spectrum technique that changes carrier frequency according to a hopping pattern.

CDMA: Multiple-access method in which users share time and frequency resources and are separated by codes.

Multiple-access interference: Interference caused by simultaneous transmissions from other users.

Near–far problem: Difficulty detecting a weak user in the presence of a much stronger user.

OFDM: Multicarrier modulation using orthogonal closely spaced subcarriers.

Subcarrier spacing: Frequency separation between adjacent OFDM subcarriers.

Cyclic prefix: Repeated end portion of an OFDM symbol inserted at its beginning.

Intercarrier interference: Leakage between subcarriers caused by loss of orthogonality.

PAPR: Ratio of the maximum instantaneous signal power to average signal power.

SC-FDMA: DFT-spread OFDM waveform commonly used to reduce uplink envelope variation.

FBMC: Multicarrier technique using subcarrier filter banks for improved spectral localization.

Localized mapping: Assignment of DFT-spread symbols to contiguous subcarriers.

Interleaved mapping: Assignment of DFT-spread symbols across regularly separated subcarriers.

Spectral regrowth: Out-of-band emissions generated by nonlinear amplification.

Coherence time: Approximate time over which a wireless channel remains correlated.

Multiple-input multiple-output: Use of multiple transmit and receive antennas to improve capacity, reliability, or coverage.

Review Questions

Short Answer Questions

1. Define processing gain and state the assumptions behind $G_p=R_c/R_b$.

2. Why does a cyclic prefix enable one-tap OFDM equalization?

3. Identify two causes of intercarrier interference.

4. Explain the near–far problem in CDMA.

5. Why is PAPR important in a battery-powered transmitter?

Long Answer Questions

1. Compare DSSS and FHSS in terms of bandwidth occupation, interference resistance, synchronization, and implementation complexity.

2. Derive the OFDM subcarrier orthogonality condition for subcarrier spacing $1/T_u$.

3. Explain cyclic-prefix design, including its benefits, overhead, and failure when the delay spread exceeds the prefix duration.

4. Describe SC-FDMA transmitter and receiver processing and compare it with conventional OFDM.

5. Critically evaluate FBMC as an alternative to CP-OFDM for asynchronous broadband systems.

Analytical / Application Questions

1. An OFDM system has a useful symbol duration of $50\ \mu$s and a maximum excess delay of $3\ \mu$s. Determine the minimum ideal cyclic-prefix fraction and explain practical design margins.

2. A wireless terminal must operate in a frequency-selective channel while minimizing power-amplifier back-off. Compare OFDM and SC-FDMA and recommend a waveform with justification.

3. A system experiences strong narrowband interference occupying only one of many hop frequencies. Analyze how FHSS and DSSS would respond and identify the synchronization or implementation costs of each approach.

Multiple Choice Questions with Answers

Question 1

In a binary DSSS system, the chip rate is 10 times the information bit rate. What is the ideal processing gain in decibels?

A. 3 dB

B. 10 dB

C. 20 dB

D. 100 dB

Correct Answer: B. 10 dB

Question 2

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

A. To increase the data rate above the Nyquist rate

B. To convert linear convolution into circular convolution over the useful interval

C. To eliminate transmitter power-amplifier nonlinearity

D. To provide encryption for the transmitted data

Correct Answer: B. To convert linear convolution into circular convolution over the useful interval

Question 3

For useful OFDM symbol duration Tu, which subcarrier spacing preserves ideal orthogonality?

A. Tu

B. 1/Tu

C. 2Tu

D. Tu squared

Correct Answer: B. 1/Tu

Question 4

Which impairment directly causes energy from one OFDM subcarrier to leak into another?

A. Perfect channel estimation

B. Carrier-frequency offset

C. A sufficiently long cyclic prefix

D. Orthogonal code correlation

Correct Answer: B. Carrier-frequency offset

Question 5

Why is high PAPR undesirable in an OFDM transmitter?

A. It prevents any frequency-domain equalization

B. It requires greater amplifier back-off and can cause nonlinear distortion

C. It removes the need for synchronization

D. It makes all subcarriers nonorthogonal even in an ideal channel

Correct Answer: B. It requires greater amplifier back-off and can cause nonlinear distortion

Question 6

What operation distinguishes SC-FDMA from conventional OFDM?

A. A DFT is applied to the modulation symbols before subcarrier mapping

B. The cyclic prefix is always removed

C. All subcarriers are replaced by a single unmodulated carrier

D. No frequency-domain equalization is used

Correct Answer: A. A DFT is applied to the modulation symbols before subcarrier mapping

Question 7

In CDMA, the near–far problem occurs when:

A. All users have identical received powers

B. A strong user interferes with detection of a much weaker user

C. The spreading code has zero autocorrelation at zero delay

D. The carrier frequency is exactly synchronized

Correct Answer: B. A strong user interferes with detection of a much weaker user

Question 8

A channel has a maximum significant excess delay of 5 microseconds. Which cyclic-prefix duration is sufficient under the ideal delay-spread criterion?

A. 1 microsecond

B. 3 microseconds

C. 5 microseconds

D. 0 microseconds

Correct Answer: C. 5 microseconds

Question 9

What is a principal advantage of FBMC over rectangular-pulse OFDM?

A. Improved spectral localization through subcarrier filtering

B. Guaranteed zero PAPR

C. No need for channel estimation

D. Elimination of all synchronization requirements

Correct Answer: A. Improved spectral localization through subcarrier filtering

Question 10

Which waveform is generally especially attractive for a power-limited uplink terminal?

A. SC-FDMA

B. Uncoded high-PAPR OFDM only

C. An unspread impulse train

D. A waveform with deliberately uncontrolled spectral regrowth

Correct Answer: A. SC-FDMA