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Preamble-based Channel Estimation in OFDM/OQAM Systems: A Review
E. Kofidis, D. Katselis, A. Rontogiannis, S. Theodoridis
TL;DR
OFDM/OQAM channel estimation is complicated by intrinsic imaginary interference among neighboring subcarriers and symbols. This paper reviews known-preamble structures and estimation methods for SISO and MIMO systems, comparing their performance in mildly and highly frequency-selective channels, where E-IAM-C outperformed the other methods under the studied conditions.
Problem
Intrinsic imaginary interference complicates estimating the complex channel frequency response in OFDM/OQAM systems.
Method
The paper reviews preamble structures, associated channel-estimation methods, and preamble optimization for SISO and MIMO OFDM/OQAM systems.
Results
E-IAM-C outperformed the other principal methods in simulations for realistic, fair SISO and MIMO scenarios across mildly and highly frequency-selective channels.
Takeaways & Limitations
Known-preamble channel-estimation methods can be compared across SISO and MIMO OFDM/OQAM settings using realistic simulations that include data interference.
Takeaways & Limitations
For MIMO systems, analogous MSE-optimal preamble results had not yet been derived, and more than one guard symbol may require extra training bandwidth.
Abstract
from arXiv · showhide
Filter bank-based multicarrier communications (FBMC) have recently attracted increased interest in both wired (e.g., xDSL, PLC) and wireless (e.g., cognitive radio) applications, due to their enhanced flexibility, higher spectral efficiency, and better spectral containment compared to conventional OFDM. A particular type of FBMC, the so-called FBMC/OQAM or OFDM/OQAM system, consisting of pulse shaped OFDM carrying offset QAM (OQAM) symbols, has received increasing attention due to, among other features, its higher spectral efficiency and implementation simplicity. It suffers, however, from an imaginary inter-carrier/inter-symbol interference that complicates signal processing tasks such as channel estimation. This paper focuses on channel estimation for OFDM/OQAM systems based on a known preamble. A review of the existing preamble structures and associated channel estimation methods is given, for both single- (SISO) and multiple-antenna (MIMO) systems. The various preambles are compared via simulations in both mildly and highly frequency selective channels.
1 Introduction
FBMC, particularly OFDM/OQAM, offers spectral and implementation advantages over CP-OFDM but introduces intrinsic imaginary interference that complicates channel estimation. This paper reviews known-preamble estimation methods for SISO and MIMO systems and compares them through simulations.
- FBMC provides enhanced flexibility, higher spectral efficiency, and better spectral containment than CP-OFDM.
- OFDM/OQAM combines pulse-shaped OFDM with staggered OQAM symbols and offers potential maximum spectral efficiency with implementation simplicity.
- OFDM/OQAM subcarriers are orthogonal only over the real field, creating intrinsic imaginary interference among neighboring subcarriers and symbols.
- The paper reviews known-preamble structures and channel-estimation methods for both SISO and MIMO OFDM/OQAM systems.It also discusses preamble optimization and compares principal methods in mildly and highly frequency-selective channels.
- The paper is organized around the system model, SISO and MIMO preamble methods, comparative simulations, and conclusions.
2 System Model
The OFDM/OQAM system uses real OQAM symbols and a prototype-filter-based synthesis filter bank, whose subcarrier functions are real-field orthogonal. Channel distortion is modeled through a local, approximately frequency-flat channel response plus intrinsic interference and noise, enabling pseudo-pilot-based estimation.
- The prototype filter generates subcarrier functions that are orthogonal in the real field, not fully complex-orthogonal.
- Even without channel distortion or noise, neighboring frequency-time points produce purely imaginary intrinsic interference at the analysis filter bank output.
- With well-localized pulses and an approximately constant CFR over the neighborhood, interference outside the local neighborhood can be neglected.
- The local subchannel model becomes inaccurate when the subcarrier count is too small for the channel frequency selectivity, and also in high-mobility scenarios.
- Known neighboring pilots can approximate the interference term and form a complex pseudo-pilot for CFR estimation.
- A help pilot can force the interference to zero when neighboring points otherwise contain unknown data symbols.
- The model extends to MIMO systems by collecting per-transmit/per-receive channel responses into a frequency-time input-output relation.
3 Preamble-based Channel Estimation Methods: The Single-Antenna Case
This section reviews preamble-based channel estimation for SISO OFDM/OQAM systems, where complex CFR estimation must account for imaginary intrinsic interference. It covers POP, IAM, and related variants under localized-filter and time-invariant-channel assumptions.
- Preamble-based estimation uses known training symbols gathered at a frame beginning or placed at isolated frequency-time points.
- Unlike OFDM/QAM, OFDM/OQAM must estimate a complex CFR in the presence of imaginary interference from neighboring frequency-time points.
- The section reviews three SISO preamble approaches, including POP, IAM, and their variants.POP uses algebraic relations across time instants, while IAM approximates neighboring-pilot interference to construct complex pseudo-pilots.
- The reviewed methods assume a prototype filter sufficiently localized in time and frequency, enough subcarriers for the system model, and a channel invariant during the preamble.
- The same principles apply when pilot blocks are placed in the middle of a frame as midambles.
3.1 Pairs of Pilots (POP) Method
The POP method estimates the CFR from observations at two time instants using algebraic relations or equivalent zero-forcing equalizer expressions. Its simplicity and filter-independence come with potentially unpredictable noise performance.
- POP constructs equations at two time instants to estimate the real and imaginary parts of the CFR.
- In the noise-free formulation, POP defines zero-forcing equalizer coefficients as the reciprocal of the CFR.
- The practical POP preamble uses two consecutive OFDM/OQAM symbols, with an alternating first symbol and an all-zero second symbol.
- The CFR is recovered from the reciprocal of the estimated zero-forcing coefficient.
- POP does not explicitly depend on the prototype filter, but its derivation assumes negligible noise.
- With noise, POP can show unpredictable performance because noise enhancement depends on unknown data.
3.2 Interference Approximation Method (IAM)
The IAM family constructs pseudo-pilots by using known neighboring symbols to approximate intrinsic interference, with designs optimized for magnitude, energy efficiency, or stronger pilots. Extended IAM-C further strengthens pseudo-pilots by using side symbols, but requires more transmit power.
- Interference Approximation Method: IAM estimates the interference from known immediate neighbors, forming complex pseudo-pilots for channel estimation.The method requires known training symbols throughout each pilot’s immediate neighborhood.
- Interference Approximation Method: Maximum-magnitude pseudo-pilots are obtained when surrounding training terms have matching signs and add constructively across frequencies.The interference weights are determined by the prototype filter and follow a regular pattern.
- IAM variants: IAM2 uses nulls in the first and third symbols and oppositely signed neighboring middle pilots, achieving pseudo-pilot magnitude √(1 + 4β^2).IAM3 randomizes the middle symbols to reduce possible peak-to-average power ratio increases, while IAM2 is emphasized for maximizing pseudo-pilot magnitude.
- IAM variants: IAM-I permits maximum-modulus imaginary pilots, producing larger imaginary pseudo-pilots when pilot and neighbor signs align appropriately.IAM-C modifies the middle vector so pseudo-pilots are purely real or imaginary at all subcarriers.
- Optimal Preambles: Optimal sparse preambles use equidistant pilot-carrying subcarriers with equipowered pilots, while optimal full preambles use equal phase-adjusted pilots with alternating signs.These optimality results concern minimizing MSE under a fixed transmit-energy budget.
- Extended IAM-C: E-IAM-C uses side symbols to produce stronger pseudo-pilots than IAM-C; for M = 512 and K = 3, magnitudes are 2.6076d versus 1.5d.For prototype filters with ǫ < 0, the E-IAM-C preamble can be modified, including for EGF-based filter banks.
3.3 Interference Cancellation/Avoidance Methods
Interference-cancellation and avoidance methods design preambles to suppress intrinsic interference rather than exploit it. They range from nulling neighboring data to structured signaling and iterative estimation with unknown surrounding data.
- Direct cancellation: One cancellation approach nulls data around pilot FT points and may also null the middle symbol on alternating subcarriers.This permits CFR estimation on the complementary even- or odd-indexed subcarriers.
- Structured cancellation: A spectrally efficient design cancels first-order-neighbor interference in pairs while transmitting structured data at neighboring FT positions.It uses symmetry in neighboring times instead of relying entirely on guard symbols or nulls.
- Structured cancellation: Applying the structured pattern every third subcarrier yields about 4M/3 data symbols, improving spectral efficiency relative to earlier methods.Applying it every second subcarrier can improve intermediate-frequency estimates but constrains transmitted data to 3 + M/2 symbols.
- Iterative estimation: Higher-efficiency preambles can use one reference symbol surrounded by unknown data, but then interference elimination requires an iterative procedure.Without guard symbols or specially structured data, surrounding-symbol interference is completely unknown.
4 Preamble-based Channel Estimation Methods: The Multiple-Antenna Case
The MIMO methods extend preamble-based OFDM/OQAM channel estimation by designing training across transmit antennas and exploiting orthogonal or sparse structures. Training duration, pseudo-pilot magnitude, matrix orthogonality, and prototype-filter localization govern estimation accuracy and complexity.
- MIMO IAM: IAM preambles can be extended from SISO designs using independent, scattered, or orthogonal antenna-training patterns.Orthogonal IAM constructions use matrix patterns analogous to MIMO-OFDM training designs.
- MIMO IAM: MIMO channel estimation requires at least Nt nonzero OFDM/OQAM symbols and assumes channel invariance across the training period.The described IAM constructions use durations proportional to Nt, while shorter sparse alternatives use three symbols per antenna.
- MIMO IAM: Orthogonal IAM matrices control noise enhancement through the pseudo-pilot magnitude, yielding covariance σ2/|cp|2 INr and the associated MSE expression.Hadamard matrices generalize the construction to more than two transmit antennas when Nt is a power of 2.
- MIMO IAM: For Nt transmit antennas, guard-symbol IAM preambles require 2Nt + 1 OFDM/OQAM symbols, though a leading null can sometimes be removed.E-IAM-C uses Nt/2 more complex OFDM symbols than MIMO-OFDM, and the added duration can improve estimation accuracy.
- MIMO IAM: IAM pseudo-pilot matrices become nearly row-orthogonal rather than unitary for Nt > 2, unless additional guard symbols are inserted.The correct, nonideal matrix must therefore be used in simulations; extra guards can overcome the difficulty at increased training-bandwidth cost.
- Optimal sparse preamble: Sparse MIMO preambles use three OFDM/OQAM symbols per antenna with nulled pilot subcarriers, and equispaced, equipowered pilot sets support LS estimation.A unitary training matrix makes the LS solution optimal in the MSE sense under white noise.
5 Simulation Results
Simulations compare OFDM/OQAM preamble methods under realistic power normalization, data interference, and frequency-selective channels. E-IAM-C performs best among the tested schemes, while high-SNR error floors arise from residual intrinsic interference and become more severe with greater frequency selectivity.
- SISO Systems: The experiments account for interference from the front tail of following pseudo-random data when estimating required transmit power.This reflects that the middle preamble symbol can receive nonnegligible interference from subsequent data even with well-localized prototype filters.
- SISO Systems: E-IAM-C outperforms the other tested OFDM/OQAM schemes across the considered SNR range in both SISO and 2 × 2 MIMO simulations.The comparisons use Veh-A and Veh-B channels, with Veh-B representing the more frequency-selective case.
- SISO Systems: At low to moderate SNR, all tested OFDM/OQAM methods outperform CP-OFDM, whereas CP-OFDM becomes better at higher SNR.At high SNR, OFDM/OQAM NMSE curves reach an error floor.
- SISO Systems: Residual intrinsic interference causes the OFDM/OQAM high-SNR error floor because the channel-model approximation is not exact for channels with significant time dispersion.The residual interference is masked by noise at low SNR and becomes visible in the weak-noise regime.
- SISO Systems: Equalizing preamble power at the SFB input improves all methods and reduces their performance differences compared with transmitted-signal power normalization.This normalization also significantly remedies the error-floor effect.
6 Conclusions
The paper reviews preamble-based OFDM/OQAM channel estimation for SISO and MIMO systems, compares principal methods through fair simulations, and identifies E-IAM-C as the strongest performer under the tested conditions.
- The paper reviews preamble structures and associated channel-estimation methods for both SISO and MIMO OFDM/OQAM systems.
- It also reviews MSE-optimal zero-guard preamble designs for SISO systems, while analogous MIMO optimality results remain unavailable.
- Simulation results evaluate principal methods in realistic, fair conditions with data interference across mildly and highly frequency-selective channels.
- E-IAM-C outperforms the other evaluated methods at every considered SNR under those simulation conditions.
- Further work is needed on IAM tail-truncation loss, high PAPR from periodic structures, improved IAM designs, and MIMO-OFDM/OQAM optimality.
A Time-Frequency Neighborhood
The appendix derives closed-form interference contributions around an FT point from the prototype filter and uses their symmetries to characterize the relevant time-frequency neighborhood.
- Interference terms from neighboring FT points are computed in closed form using the prototype filter.
- The relevant quantities are evaluated for p ∈ {−2, −1, 0, 1, 2} and q ∈ {−1, 0, 1}, excluding the central point.
- The appendix simplifies the interference expression and observes that the resulting form is independent of n.
- For q = 0, the derivation considers p ∈ {±1, ±2}; conjugacy and prototype-filter properties further simplify the terms.
- The resulting neighborhood around the FT point is organized as a 5×3 time-frequency region.