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A Survey on Multicarrier Communications: Prototype Filters, Lattice Structures, and Implementation Aspects

Alphan Şahin, Ismail Güvenç, Hüseyin Arslan

arXiv:1212.3374v2cs.IT

TL;DR

Multicarrier systems need flexible, efficient designs whose gains justify added complexity over established OFDM approaches. This survey unifies schemes through symbols, filters, and lattices, reviews prototype-filter trade-offs, and examines practical implementation considerations.

  • Problem

    Adopting filter-bank multicarrier techniques requires determining whether their gains over OFDM justify a reasonable increase in complexity.

  • Method

    The survey organizes multicarrier schemes by transmitted symbols, filters, and lattices, then reviews their relationships, prototype filters, and practical trade-offs.

  • Results

    FBMC achieves aggregate uplink spectral efficiencies around 45% higher than CP-OFDM, with reported superior multiuser-uplink BER at lower computational complexity.

  • Takeaways & Limitations

    The survey provides a broader basis than rectangular-lattice OFDM for comparing waveform choices and their practical trade-offs.

Abstract

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Due to their numerous advantages, communications over multicarrier schemes constitute an appealing approach for broadband wireless systems. Especially, the strong penetration of orthogonal frequency division multiplexing (OFDM) into the communications standards has triggered heavy investigation on multicarrier systems, leading to re-consideration of different approaches as an alternative to OFDM. The goal of the present survey is not only to provide a unified review of waveform design options for multicarrier schemes, but also to pave the way for the evolution of the multicarrier schemes from the current state of the art to future technologies. In particular, a generalized framework on multicarrier schemes is presented, based on what to transmit, i.e., symbols, how to transmit, i.e., filters, and where/when to transmit, i.e., lattice. Capitalizing on this framework, different variations of orthogonal, bi-orthogonal, and nonorthogonal multicarrier schemes are discussed. In addition, filter design for various multicarrier systems is reviewed considering four different design perspectives: energy concentration, rapid decay, spectrum nulling, and channel/hardware characteristics. Subsequently, evaluation tools which may be used to compare different filters in multicarrier schemes are studied. Finally, multicarrier schemes are evaluated from the view of the practical implementation issues, such as lattice adaptation, equalization, synchronization, multiple antennas, and hardware impairments.

I. INTRODUCTION · II. PRELIMINARY CONCEPTS: SYMBOLS, LATTICES, AND FILTERS · A. Fundamentals

The survey motivates multicarrier communication as a flexible broadband technology, critiques OFDM limitations, and adopts a generalized framework organized by symbols, filters, and lattices,. It introduces Gabor-system fundamentals to explain how prototype filters, time-frequency lattices, and transmitter–receiver analysis synthesize and recover symbols.

  • I. INTRODUCTION: The survey targets adaptive, flexible, and efficient broadband radio access, emphasizing multicarrier support for multiuser diversity, simpler equalization, and adaptive modulation and coding.
  • I. INTRODUCTION: OFDM dominates current broadband systems but suffers from high spectral leakage, stringent synchronization requirements, and susceptibility to frequency dispersion.
  • I. INTRODUCTION: The survey chooses a generalized multicarrier framework, with OFDM as a special case, to unify schemes through what, how, and where/when to transmit: symbols, filters, and lattices,.
  • I. INTRODUCTION: Its broader goals are to relate existing schemes, review prototype filters, clarify practical trade-offs, and support future multicarrier development.
  • II. PRELIMINARY CONCEPTS: SYMBOLS, LATTICES, AND FILTERS: The preliminary section establishes notation for symbols, lattices, and filters within Gabor systems, linking Gabor theory to communication applications through key studies –.
  • A. Fundamentals: In the communication model, transmitted symbols are mapped into signal space by synthesis functions, while received symbols are recovered by projection onto analysis functions.
  • A. Fundamentals: A Gabor system derives time- and frequency-shifted pulses from one prototype filter, whose coordinates form a two-dimensional time-frequency lattice; the receiver constructs an analogous translated analysis-filter system.
  • A. Fundamentals: The basic multicarrier model therefore consists of transmitter synthesis and receiver analysis equations organized in the time-frequency plane.

B. Symbols … 2) Orthogonality of Scheme:

The framework distinguishes transmitted symbol sets, pulse shapes, and lattice orthogonality, showing how these choices determine reconstruction, SNR, channel behavior, and noise correlation.

  • B. Symbols: Transmitted symbols may be complex or real, represent full modulation symbols or components, and affect one-to-one message-to-signal mapping and perfect reconstruction,,,,.This includes signaling over Weyl–Heisenberg frames, faster-than-Nyquist signaling, and partial-response signaling.
  • C. Filters: Pulse shapes distribute symbol energy across time, frequency, or other domains, thereby determining signal dispersion that receiver filters coherently recombine.
  • 1) Matched Filtering:: Matched filtering uses identical transmit and receive prototype filters and maximizes signal-to-noise ratio, whereas bi-filtering permits different transmit and receive prototypes.
  • 2) Orthogonality of Scheme:: Orthogonality or bi-orthogonality requires zero cross-correlation between distinct lattice points, while nonorthogonality permits correlation; orthogonal schemes use identical prototype filters.
  • 2) Orthogonality of Scheme:: The weighting parameter ρ selects the scheme: ρ = 1/2 yields orthogonality, ρ → 0 or ρ → 1 yields bi-orthogonality, and ρ = 1 gives the minimum-norm dual pulse.
  • 2) Orthogonality of Scheme:: Orthogonal schemes maximize AWGN-channel SNR through matched filtering, whereas bi-orthogonal schemes may perform better on dispersive channels; nonorthogonal receive filters correlate noise samples,.
  • 2) Orthogonality of Scheme:: Prototype-filter localization measures time and frequency energy variances using ||tp(t)||2 and ||fP(f)||2, distinguishing localized from non-localized filters.

3) Localization: … 2) Lattice Density/Volume:

The paper frames lattices as time-frequency sampling structures that determine multicarrier bandwidth efficiency, reconstruction, and filter-placement geometry. It distinguishes undersampled, critically sampled, and oversampled regimes, each trading off basis properties, localization, efficiency, and representation uniqueness.

  • D. Lattices: Lattices algebraically sample the time-frequency plane, locating filters and determining multicarrier bandwidth efficiency and symbol reconstruction properties,,,,.
  • D. Lattices: The generator matrix L specifies lattice geometry by generating all indexed points from its identifying vectors and integer coordinates.
  • 1) Lattice Geometry:: With F = 1/T and unit minimum spacing for the rectangular lattice, the quincunx lattice has minimum spacing 1.25.
  • 2) Lattice Density/Volume:: Lattice density, computed from the lattice volume via a determinant, quantifies bandwidth efficiency and relates to perfect symbol reconstruction through β, the bits per volume.
  • 2) Lattice Density/Volume:: Undersampling, δ(Λ) < 1, provides linearly independent basis functions and permits well-localized filters, but prevents completeness and reduces bandwidth efficiency.
  • 2) Lattice Density/Volume:: Critical sampling, δ(Λ) = 1, yields a complete Gabor basis but, by the Balian-Low theorem [12], precludes functions well localized in both time and frequency.Using a well-localized Gaussian makes the Gram matrix ill-conditioned, with its condition number approaching infinity as δ(Λ) →1.
  • 2) Lattice Density/Volume:: Oversampling, δ(Λ) > 1, creates an overcomplete Gabor frame that can use well-localized pulses, although signal representations may be non-unique.Non-unique representations do not necessarily eliminate one-to-one mapping between modulation symbols and the constructed signal.

E. A Combined Approach: Lattice Staggering … A. Orthogonal Schemes

The survey frames multicarrier design through symbols, filters, and lattice placement, showing how lattice staggering uses symmetry to relax filter constraints and connects to orthogonal scheme variants. It then organizes orthogonal schemes by lattice geometry, filtering, and modulation, without asserting superiority among schemes.

  • E. A Combined Approach: Lattice Staggering: Lattice staggering circumvents Balian–Low filter-design restrictions by creating real-domain orthogonality through prototype-filter symmetry, thereby relaxing filter constraints.The approach is also known as offset quadrature amplitude modulation or staggered modulation,,,,.
  • E. A Combined Approach: Lattice Staggering: For orthogonal or biorthogonal lattice-staggered schemes, transmit–receive filter correlation must vanish at time-frequency multiples of 2τ0 and 2ν0, giving null-cell area 2τ0 × 2ν0 = 2.With even-symmetric filters and τ0 = 1/2ν0, cosine-plane cross-correlations vanish, while each lattice location carries one real symbol.
  • F. Summary: The survey relates symbols, lattice geometry, and filters through Gabor theory, allowing these elements to be selected according to communication-system requirements.Figure 3 summarizes these relationships across multicarrier schemes.
  • III. MULTICARRIER SCHEMES: The multicarrier taxonomy emphasizes relationships among orthogonal, biorthogonal, and nonorthogonal schemes within Gabor theory rather than claiming that one scheme is superior.The framework also interprets spreading operations in multicarrier systems, including SC-FDMA.
  • A. Orthogonal Schemes: Orthogonal schemes use orthogonal basis functions at transmitter and receiver with matched filtering, while OFDM specifically denotes the rectangular-filter case.The survey first considers orthogonal schemes without lattice staggering, then introduces staggered variants.
  • A. Orthogonal Schemes: Plain OFDM uses rectangular filters with δ(Λ) = 1, ZP-OFDM adds a guard interval by stretching the time lattice, and FMT uses frequency guard bands with δ(Λ) ≤ 1.FMT does not prescribe a specific filter and avoids frequency overlap among filters.
  • A. Orthogonal Schemes: Lattice-OFDM adapts lattice geometry and orthogonalized Gaussian pulses to time- and frequency-dispersive channels, whereas SMT and CMT use lattice staggering to increase filter-design flexibility.SMT and CMT use real symbols when ϵ = β; SMT uses QAM-type signals, while CMT uses VSB, although their structures are identical and can be transformed by frequency shifting and symbol placement,.

B. Bi-orthogonal Schemes · C. Non-orthogonal Schemes · D. Multicarrier Schemes with Spreading Approaches

The survey distinguishes bi-orthogonal schemes with mutually orthogonal transmit and receive filters, non-orthogonal schemes without orthogonality relations, and spreading approaches that distribute symbol energy across multiple subcarriers to reduce PAPR.

  • B. Bi-orthogonal Schemes: Bi-orthogonal schemes use mutually orthogonal transmit and receive filters without requiring matched filtering or orthogonal basis functions individually.This category includes schemes where the transmitter and receiver filters are orthogonal to each other, while their individual bases need not be orthogonal.
  • B. Bi-orthogonal Schemes: CP-OFDM forms a bi-orthogonal scheme because its longer transmit filter does not match the receiver filter, while retaining single-tap equalization and simple synchronization,,.The cyclic prefix combats multipath channels and induces a lattice with δ(Λ) > 1.
  • B. Bi-orthogonal Schemes: Windowed-OFDM reduces out-of-band radiation by smoothing rectangular-filter edges; adding a guard period yields a bi-orthogonal scheme with δ(Λ) > 1.The rectangular filter causes high out-of-band radiation, motivating the windowing operation.
  • B. Bi-orthogonal Schemes: BFDM uses different transmitter and receiver filters to reduce interference from other symbols in doubly dispersive channels, addressing CP-OFDM’s unequal treatment of time and frequency dispersion.The passage presents properly designed filters as an alternative to extending the rectangular filter as in CP-OFDM.
  • C. Non-orthogonal Schemes: Non-orthogonal schemes lack orthogonal basis functions and any bi-orthogonal relation between transmitter and receiver filters.GFDM permits lattice-point correlation while using well-localized filters at δ(Λ) = 1, with successive interference cancellation at the receiver,.
  • C. Non-orthogonal Schemes: Faster-than-Nyquist signaling can reduce symbol spacing to 0.802T without loss in minimum Euclidean distance under certain reconstruction conditions.The approach studies packing symbols beyond the Nyquist rate while preserving reconstruction properties.
  • D. Multicarrier Schemes with Spreading Approaches: Spreading reduces PAPR by mapping modulation symbols onto multiple lattice points or subcarriers, as in SC-FDMA and FB-S-FBMC; OFDM uses a Dirac prototype because it spreads no frequency-domain symbols,.The spreading interpretation introduces another Gabor system that distributes symbol energy across multiple subcarriers.

E. Milestones for Orthogonal Schemes … 6) Extended Gaussian Function:

The paper traces orthogonal multicarrier development and organizes prototype-filter design around energy concentration, emphasizing trade-offs among localization, sidelobes, Nyquist interference, orthogonalization, and latency. Gaussian-derived designs culminate in EGF, which preserves isotropic concentration and can be truncated with optimized localization.

  • E. Milestones for Orthogonal Schemes: Orthogonal multicarrier research dates to the 1960s, including filter-bank parallel transmission and Chang’s band-limited-filter orthogonality condition,.
  • IV. FILTER DESIGN: Prototype filters determine symbol correlation and robustness against dispersive channels, motivating designs for time-selective and frequency-selective channels classified by design criteria.
  • A. Design Criterion: Energy Concentration: Shorter or truncated pulses reduce computational complexity and latency but can increase frequency-domain sidelobes, creating a time-frequency concentration trade-off.
  • A. Design Criterion: Energy Concentration: PSWFs provide optimally concentrated pulses by minimizing out-of-band leakage for time-limited signals or maximizing in-band concentration for band-limited signals.
  • 1) Prolate Window:: The prolate window minimizes sidelobe energy for given length and bandwidth, whereas the Kaiser filter approximates it with controllable sidelobes and stop-band attenuation through β.
  • 2) Kaiser Function:: Because the prolate window violates the Nyquist criterion, OFDP generalizes the optimization procedure to obtain a finite-duration Nyquist pulse.
  • 3) Optimal Finite Duration Pulses:: Gaussian filters have Gaussian Fourier responses and optimal time-frequency concentration at ρ = 1, but their lack of zero-crossings prevents Nyquist orthogonality.
  • 4) Gaussian Function:: IOTA orthogonalizes the Gaussian pulse to prevent neighboring-lattice interference, while EGF gives its analytical form; EGF can be truncated to one symbol duration while retaining optimized localization.Hermite-Gaussian combinations similarly introduce zero-crossings for Nyquist operation and can incorporate channel-dispersion characteristics.

7) Hermite Filter: … 3) Root-Raised-Cosine Function:

The rapid-decay discussion links sidelobe decay to filter smoothness and presents cosine-based and Mirabbasi–Martin designs with tunable or derivative-continuity-controlled decay. These filters trade time–frequency localization, transition-band width, stop-band attenuation, and sidelobe-decay rates.

  • B. Design Criterion: Rapid-Decay: PSWFs optimize energy concentration but do not ensure rapid sidelobe decay, as illustrated in Fig. 5.This distinguishes energy concentration from rapid-decay filter design.
  • B. Design Criterion: Rapid-Decay: Sidelobe decay depends on filter smoothness: an impulsive mth derivative yields frequency sidelobes decaying as |ω|−m, or 6m dB/octave.Smoothness is measured by the number of continuous derivatives,,.
  • 1) Raised-Cosine Function (Hanning Filter):: The Hanning filter has continuous zeroth- and first-order derivatives, producing sidelobe decay of 1/|ω|3, equivalent to 18 dB/octave.Its shape is captured through a period of a cosine function.
  • 2) Tapered-Cosine Function (Tukey Filter):: The tapered-cosine family controls time–frequency localization through roll-off factor α, spanning rectangular filtering at α = 0 to Hanning filtering at α = 1.Its sidelobe-decay range is 6 dB/octave to 18 dB/octave.
  • 3) Root-Raised-Cosine Function:: RRC filters satisfy the Nyquist criterion after matched filtering and derive from the raised-cosine filter.At α = 1, RRC becomes the half-cosine function used in,,,,.
  • 3) Root-Raised-Cosine Function:: The half-cosine function offers a time/frequency compromise: relaxed transition bands enable short time-domain approximations while retaining high stop-band attenuation.This property is reported for the α = 1 RRC case.
  • 3) Root-Raised-Cosine Function:: Mirabbasi–Martin coefficients enforce derivative continuity and achieve decay rates of 1/|ω|5 for K = 6 and 1/|ω|7 for K = 8.The coefficients are specified for different K in Table II, and the decay efficacy is shown in Fig. 6,.

4) Mirabbasi-Martin Filter: … 1) Rectangular Function:

The surveyed designs pursue faster decay, deliberate spectral nulling, and robustness to channel dispersion by adapting prototype-filter shapes and exploiting structured cancellation. The section contrasts these approaches with rectangular filtering for CP-OFDM and channel-aware pulse designs.

  • 4) Mirabbasi-Martin Filter:: Kaiser windows are modified into Mirabbasi-Martin filters to achieve faster decay than the 1/|ω| rate of the discontinuous Kaiser window.
  • 5) Modified Kaiser Function:: The modified Kaiser-function design is evaluated through time- and frequency-domain characteristics and has zeros at |t| = 1/2.
  • C. Design Criterion: Spectrum-nulling: The generalized spectrum-nulling form uses K frequency bins and coefficients a_l, and supports OFDM applications such as cancellation carriers.
  • C. Design Criterion: Spectrum-nulling: Spectrum-nulling filters sum sinc functions whose tails coherently cancel, allowing systematic placement of spectral zeros, although equal-ripple behavior may limit prototype-filter quality.
  • 1) Hamming Filter:: The Exact Hamming filter places a null at the first sidelobe, whereas the Exact Blackman filter places nulls at the third and fourth sidelobes.
  • D. Design Criterion: Channel Characteristics and Hardware: Radio-channel dispersion can destroy multicarrier orthogonality and cause ISI and ICI, motivating pulses optimized to minimize interference between lattice points.
  • 1) Rectangular Function:: The rectangular function uniformly distributes symbol energy in time and serves as the CP-OFDM prototype, combating ISI and ICI in time-invariant multipath channels by extending its duration.
  • D. Design Criterion: Channel Characteristics and Hardware: Channel-aware prototypes can use optimally weighted Hermite-Gaussian functions to widen ambiguity-surface zero-interference regions and improve robustness in doubly dispersive channels.

2) Channel-based Pulses: … C. Ambiguity Function

The survey covers channel- and hardware-aware prototype-pulse design, then evaluates filters and multicarrier schemes using time-frequency metrics and ambiguity functions. These tools characterize localization, pulse orientation, and robustness against interference from channel impairments while relating ambiguity behavior to Nyquist criteria.

  • 2) Channel-based Pulses:: Prototype pulses can be optimized for SINR or minimum ISI/ICI, while relaxing orthogonality enables alternative designs for preamble transmission,,,.
  • 2) Channel-based Pulses:: Hardware-aware prototype design can reduce PAPR and timing-jitter problems by minimizing the filter tails.
  • V. EVALUATION METRICS AND TOOLS FOR MULTICARRIER SCHEMES: The evaluation framework introduces Heisenberg uncertainty, direction, and ambiguity-function tools for comparing prototype filters and multicarrier schemes.
  • A. Heisenberg Uncertainty Parameter: Filters with Heisenberg parameter closer to 1 have better time-frequency localization, with the Gaussian filter attaining exactly 1 when ρ = 1,,.The parameter uses time and frequency energy dispersions around their mean support locations.
  • B. Direction Parameter: The direction parameter κ describes pulse orientation in the time-frequency plane: rectangular filters have κ = 0, Gaussian filters with ρ = 1 have κ = 1, and larger κ indicates greater time-axis stretching.
  • C. Ambiguity Function: The ambiguity function generalizes transmitter-receiver lattice correlations across fractional time-frequency offsets and visualizes robustness to ICI/ISI from time- and frequency-selective channels,,,.It is a two-dimensional correlation function in the time-frequency plane.
  • C. Ambiguity Function: Gaussian filters yield circular, rapidly decaying ambiguity surfaces without nulls, whereas Hermite-Gaussian combinations and IOTA filters provide localized ambiguity functions while satisfying the Nyquist criterion at integer lattice points.The survey illustrates ambiguity surfaces for rectangular, half-cosine, Gaussian, IOTA, and Hermite-Gaussian filter pairs in Fig. 9.

D. Signal-to-Interference Ratio in Dispersive Channels

This section formulates average SIR from desired-signal and interference powers, then explains how filter representation and dispersive channels spoil ideal orthogonality. Under stated statistical assumptions, time-varying multipath produces ISI and ICI from neighboring lattice points, unlike the interference-free time-invariant single-path case.

  • D. Signal-to-Interference Ratio in Dispersive Channels: Average SIR is defined from the powers of the desired signal and interference leaking from other symbols.
  • D. Signal-to-Interference Ratio in Dispersive Channels: For orthogonal and biorthogonal schemes, SIR should ideally be infinite when no other interference sources are considered.
  • D. Signal-to-Interference Ratio in Dispersive Channels: Orthogonality can be spoiled by digital filter truncation and by dispersive-channel effects.
  • D. Signal-to-Interference Ratio in Dispersive Channels: In a time-invariant single-path channel, ambiguity-function values at lattice grid points vanish, whereas time-varying multipath creates ISI and ICI from neighboring points.

VI. PRACTICAL IMPLEMENTATION ASPECTS · A. Lattice and Filter Adaptations · B. Equalization

The practical implementation discussion focuses on adapting lattices and prototype filters to doubly dispersive channels and managing self-interference through progressively more complex equalization strategies. It also highlights the difficulty of supporting multiple users or intentionally overlapping symbol structures with one design.

  • A. Lattice and Filter Adaptations: Lattice and filter adaptations match channel dispersion in time and frequency, aligning rectangular-grid spacings with RMS delay spread and maximum Doppler frequency or dilating pulses accordingly.These adaptations aim to match the proportion of channel dispersion to pulse dispersion.
  • A. Lattice and Filter Adaptations: Lattice-OFDM argues that rectangular OFDM is suboptimal in doubly dispersive channels, while hexagonal symbol placement can provide better ISI protection,.The framework adapts both pulse shape and lattice geometry to channel conditions.
  • A. Lattice and Filter Adaptations: A single lattice and prototype filter is difficult for multiple users with different channels, motivating worst-case designs or multiple lattice and filter structures within a frame.The design tradeoff arises because users may experience different channel characteristics.
  • B. Equalization: Time-varying multipath channels disperse signals in time and frequency, producing self-interference whose structure depends on the transmit filter and channel dispersion.The discussion frames equalization around controlling or exploiting this interference.
  • B. Equalization: Well-localized filters limit the number of interfering symbols, enabling manageable ICI and ISI and supporting simpler equalization in doubly dispersive channels,.The first strategy assumes neighboring-symbol interference is negligible and uses single-tap per-subcarrier equalization,,,, –.
  • B. Equalization: Receiver equalization can operate per subcarrier at the symbol rate to address aliasing from lattice staggering, or at fractional symbol rate to reduce aliasing with more samples,, –.Fractional-rate equalization supports MMSE and other equalizer types but increases processing requirements.
  • B. Equalization: Prototype-filter shape determines equalization complexity through the composite transmit-channel-receive response and the effective number of interfering symbols estimated using AIC.The analysis explicitly relates pulse shape, receiver SNR, and model order rather than studying only the equalizer itself.

C. Time-Frequency Synchronization · D. Spatial Domain Approaches · E. Channel Estimation

The survey links synchronization robustness to ambiguity-surface null regions and shows how filters and lattice staggering affect CFO/TO immunity. It then details spatial-domain complications and channel-estimation methods for lattice-staggered schemes.

  • C. Time-Frequency Synchronization: Prototype filters provide different immunity to CFO and TO, while suitable filters with lattice staggering can improve synchronization robustness.This conclusion is supported by simulations and theoretical analyses, –.
  • C. Time-Frequency Synchronization: Hermite, IOTA, and Gaussian filters have identical TO and CFO immunity when ρ = 1 because their time- and frequency-domain responses match.
  • C. Time-Frequency Synchronization: Lattice staggering improves filters that violate the Nyquist criterion, with Gaussian functions gaining significant performance from inherent real-domain orthogonality.Conventional OFDM’s cyclic prefix widens the time null region for timing errors but does not protect against CFO.
  • D. Spatial Domain Approaches: Lattice staggering complicates multiple-antenna implementation because real-domain orthogonality can make imaginary components interfere with spatial processing.Complex-domain schemes such as FMT and CP-OFDM do not face this same implementation difficulty.
  • D. Spatial Domain Approaches: Spatial multiplexing can use zero-forcing, MMSE, or MLSE after equalization removes channel-induced ISI and ICI; lattice staggering benefits MLSE through real-domain symbols.The described formulation considers two transmit and two receive antennas with single-tap channels.
  • D. Spatial Domain Approaches: Receiver diversity introduces no lattice-staggering complication, but transmit diversity mixes real and imaginary parts and requires additional receiver processing.Spreading approaches with lattice staggering were used for spatial diversity in and, including Alamouti STBC with CDMA-based spreading.
  • E. Channel Estimation: Complex-domain schemes have extensive channel-estimation literature, whereas lattice-staggered schemes have fewer studies and need more effective algorithms.Pilot-based estimation uses auxiliary symbols to cancel imaginary interference, but this can increase PAPR,.
  • E. Channel Estimation: Preamble-based estimation for lattice-staggered schemes includes pilot pairs using consecutive real symbols and simple matrix operations, but the approach suffers from noise enhancement.These preambles can also serve synchronization purposes, and the methods are proposed in.

F. Hardware Impairments · G. Cognitive Radio and Resource Sharing · H. Poly-Phase Network

The survey examines how hardware impairments affect multicarrier waveforms, how filter design supports cognitive-radio resource sharing, and how polyphase networks reduce implementation complexity. It highlights power-amplifier distortion and phase noise, FBMC’s spectral-efficiency and sensing benefits, and FFT-based transmitter–receiver realizations.

  • F. Hardware Impairments: Power-amplifier nonlinearity distorts multicarrier spectra, diminishing band-limited filters’ sidelobe advantage, although filters still determine decay sharpness at band edges.Filter characteristics dominate PSDs before amplification, whereas amplifier distortion heavily affects them afterward; the comparison is shown in Fig. 12.
  • F. Hardware Impairments: FMT with an RRC prototype filter is reported to be more robust to high-frequency phase noise than OFDM, addressing impairments that are especially relevant near 60 GHz.CP-OFDM handles frequency selectivity well but is susceptible to frequency dispersion such as phase noise.
  • G. Cognitive Radio and Resource Sharing: FBMC-based cognitive-radio resource allocation exploits low spectral leakage to improve aggregate bandwidth efficiency while limiting interference to primary users under power and interference constraints.Downlink studies target total network capacity using band-limited filters and report significant gains in certain scenarios.
  • G. Cognitive Radio and Resource Sharing: Around 45% higher aggregate uplink spectral efficiency is reported for FBMC than CP-OFDM, alongside superior multiuser-uplink BER at lower computational complexity.The cited results concern uplink resource allocation and multiuser uplink comparisons.
  • H. Poly-Phase Network: Polyphase representations combined with FFT operations reduce the extra filtering complexity introduced by generic prototype filters in multicarrier transmitters and receivers.The illustrative transmitter uses IDFT-based synthesis and the receiver shifts, filters, and samples the desired subcarrier; polyphase decomposition removes unnecessary intermediate samples.
  • H. Poly-Phase Network: Prototype-filter implementations add filtering before or after IDFT and DFT operations, whereas these filters equal one for OFDM without cyclic prefix.For lattice-staggered schemes, the structure must be replicated and combined with appropriate time shifts to form transmission frames.

I. Complexity Analysis · J. Testbeds and Extensions to Standards · VII. CONCLUDING REMARKS

The survey frames FBMC’s adoption around complexity versus gains over OFDM, reports mixed implementation costs and benefits, and concludes that waveform requirements can be addressed through coordinated choices of lattices, filters, and symbols.

  • I. Complexity Analysis: FBMC adoption depends on achieving gains over existing techniques such as OFDM while maintaining a reasonable complexity increase.Complexity has been studied from multiple perspectives in the literature,,,,, –.
  • I. Complexity Analysis: For N = 512 and K = 3, OFDM requires 6 real multiplications per complex symbol, versus 17 for FBMC synthesis and 24 for analysis, indicating slightly higher FBMC complexity.
  • I. Complexity Analysis: With N = 128, OFDM one-tap equalization uses one complex multiplication per subchannel, whereas FMT equalization requires 46–108, depending on the technique.
  • I. Complexity Analysis: Despite filter-bank and equalization overheads, FBMC can reduce uplink inter-carrier-interference handling complexity by at least an order of magnitude in typical scenarios.OFDM requires additional transmitter complexity to suppress out-of-band leakage, whereas FBMC handles it naturally.
  • J. Testbeds and Extensions to Standards: Testbed implementations are less common than theoretical comparisons, but the PHYDYAS project developed an FBMC platform supporting real-time transmission and reception,,,.Its FPGA-based physical layer can operate in OFDM or FBMC modes, with a receiver using an RF front-end and USRP hardware.
  • VII. CONCLUDING REMARKS: The survey’s generalized Gabor-system framework categorizes multicarrier schemes by lattices, filters, and symbols, enabling analysis of CP-OFDM and alternative waveforms.It is intended to support the development and analysis of new waveform types [s57.p1#4afa83].
  • VII. CONCLUDING REMARKS: Because filters, lattices, and symbols jointly determine system characteristics, requirements can be addressed through their proper selection for a given scenario.CP-OFDM effectively supports low-complexity receivers and multiple antennas, but may face co-channel-interference and frequency-dispersive-channel challenges.
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