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Embedded Pilot-Aided Channel Estimation for OTFS in Delay-Doppler Channels
P. Raviteja, Khoa T. Phan, Yi Hong
TL;DR
OTFS detection requires the receiver to know the delay–Doppler channel response, motivating embedded pilot-aided estimation. The paper arranges pilot, guard, and data symbols for integer and fractional Doppler channels, then uses threshold estimation with message-passing detection. Simulations show marginal loss versus ideal channel knowledge and significant outperformance of OFDM with known channel information.
Problem
OTFS detection requires channel impulse-response information at the receiver, while high-Doppler conditions degrade OFDM performance.
Method
The paper embeds pilot, guard, and data symbols in the delay–Doppler grid and applies threshold-based channel estimation followed by message-passing data detection.
Results
The proposed OTFS schemes show only marginal performance degradation relative to perfectly known channel information and significantly outperform OFDM with known channel information.
Takeaways & Limitations
Channel estimation and data detection can be performed within the same OTFS frame with minimum overhead, including extensions to MIMO and multi-user uplink/downlink.
Abstract
from arXiv · showhide
Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay--Doppler channels. In order to detect OTFS modulated data, the channel impulse response needs to be known at the receiver. In this paper, we propose embedded pilot-aided channel estimation schemes for OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the delay--Doppler plane to suitably avoid interference between pilot and data symbols at the receiver. We develop such symbol arrangements for OTFS over multipath channels with integer and fractional Doppler shifts, respectively. At the receiver, channel estimation is performed based on a threshold method and the estimated channel information is used for data detection via a message passing (MP) algorithm. Thanks to our specific embedded symbol arrangements, both channel estimation and data detection are performed within the same OTFS frame with a minimum overhead. We compare by simulations the error performance of OTFS using the proposed channel estimation and OTFS with ideally known channel information and observe only a marginal performance loss. We also demonstrate that the proposed channel estimation in OTFS significantly outperforms OFDM with known channel information. Finally, we present extensions of the proposed schemes to MIMO and multi-user uplink/downlink.
I. INTRODUCTION
OTFS addresses OFDM’s degradation in high-Doppler channels by representing time-varying multipath channels in the delay–Doppler domain. This paper develops embedded pilot-aided estimation that supports same-frame detection with low overhead and extends the schemes to broader OTFS systems.
- OFDM suffers heavy performance degradation under high Doppler, motivating modulation schemes robust to channel time variations.
- OTFS represents time-varying multipath channels through delay–Doppler coordinates and multiplexes information symbols over a two-dimensional orthogonal basis.
- Receiver-side delay–Doppler channel estimation is necessary for OTFS detection, while prior approaches used full-frame pilots or higher-complexity time–frequency processing.
- The proposed scheme embeds a pilot, guard symbols, and data in each delay–Doppler grid for channels with integer or fractional Doppler shifts.
- Threshold-based estimation and message-passing detection operate within the same OTFS frame, with overhead of 1% for integer Doppler and 8% for fractional Doppler.
- Simulations show marginal degradation relative to perfectly known channel information, and the proposed OTFS estimation significantly outperforms OFDM with known channel information.
- The paper also presents extensions to MIMO and multi-user uplink/downlink systems.
B. OTFS mod/demod
OTFS maps delay–Doppler information symbols into time–frequency samples, transmits the resulting waveform through a sparse delay–Doppler channel, and transforms received samples back for detection. The input–output relation captures path-dependent circular shifts and noise, with ideal pulses providing the baseline model.
- The OTFS modulator maps delay–Doppler information symbols to time–frequency samples using the inverse symplectic finite Fourier transform and then applies the Heisenberg transform.
- The transmitted time-domain signal passes through a channel impulse response h(τ, ν), after which Wigner processing, sampling, and SFFT produce received delay–Doppler symbols.
- The channel is modeled as sparse in delay–Doppler space because a small number of reflectors determine path gains, delays, and Doppler shifts.
- Ideal transmit and receive pulses satisfy a bi-orthogonal cross-ambiguity condition, while rectangular pulses are treated separately.
- The OTFS input–output relation sums path gains and shifted transmitted symbols, with modulo operations implementing circular delay and Doppler shifts.
1) Integer Doppler shifts:
The integer-Doppler channel model represents received symbols as shifted transmitted symbols weighted by sparse path coefficients and affected by additive noise. Fractional Doppler spreads each received symbol across more transmitted symbols than the integer-Doppler case.
- The path indicator b[k′, l′] identifies whether a Doppler–delay tap contains a path, while ĥ[k′, l′] gives its corresponding path magnitude.
- The received-symbol model includes additive white noise v[k, l] with variance σ^2.
- Each channel path circularly shifts transmitted symbols according to its delay and Doppler taps.
- With fractional Doppler shifts, each received symbol is affected by more transmitted symbols than under integer Doppler.
D. OTFS data detection via message passing (MP)
OTFS data detection uses an MP algorithm after embedded pilot-based channel estimation separates channel-estimation symbols from data-detection symbols. The arrangement reserves pilot and guard symbols while keeping both operations within one frame.
- Known OTFS channel parameters enable data-symbol detection with the MP algorithm using MN linear equations.
- Each frame places one pilot, guard symbols, and data symbols in the delay–Doppler grid to separate channel estimation from data detection.
- The pilot and guard arrangement uses Nn = (2lτ + 1)(4kν + 1) − 1 guard symbols, with less than 1% overhead in LTE channels.
- The receiver uses pilot-region symbols for channel estimation and the remaining grid symbols for data detection.
- A threshold T identifies paths from received pilot-region magnitudes, estimates their gains by dividing by xp, and sets non-detected paths to zero.
- Changing T trades off miss detection and false alarms, thereby affecting data-detection error performance.
B. The fractional Doppler case
For fractional Doppler channels, the symbol arrangement is considered in full-guard and reduced-guard forms. Full guards improve channel estimation but reduce spectral efficiency relative to reduced guards.
- Fractional-Doppler OTFS is evaluated using full-guard and reduced-guard symbol arrangements.
- Full guard symbols favor channel-estimation accuracy, whereas reduced guards favor spectral efficiency by using more data symbols.
1) The case with full guard symbols:
With full guard symbols, fractional-Doppler OTFS estimates whether each delay tap contains at least one path and then applies MP detection to the remaining received symbols. The design requires about 8% pilot-and-guard overhead in LTE channels.
- The full-guard arrangement uses a pilot at [kp, lp] and guard symbols across the delay region while placing data elsewhere.
- About 8% of LTE-frame resources are allocated to pilot and guard symbols in the full-guard fractional-Doppler case.
- Full-guard channel estimation uses received symbols with lp ≤ l ≤ lp + lτ, leaving the remaining symbols for data detection.
- Unlike integer-Doppler estimation, the fractional-Doppler scheme detects whether at least one path exists for each delay tap rather than for each delay–Doppler tap.
- The MP algorithm is adapted for data detection from the received symbols outside the channel-estimation region.
- Wider guard coverage over the Doppler axis is required to prevent interference between channel-estimation and data-detection symbols.
2) The case of reduced guard symbols:
Reduced guards improve spectral efficiency by increasing data symbols, but neighboring data symbols introduce interference into channel estimation. Simulations report only a marginal performance gap versus full guards despite about 2% overhead.
- The reduced-guard arrangement expands the guarded Doppler interval according to the integer parameter ˆk.
- Reducing the guard region increases the number of data symbols and improves spectral efficiency.
- Channel estimation uses the expanded pilot-region symbols, while the remaining received symbols are assigned to data detection.
- Interference I[k, l] in the channel-estimation region comes from neighboring data symbols.
- The interference increases as ˆk becomes smaller, constraining how far the guard region can be reduced.
- Treating interference as additive noise yields a reduced-guard performance gap that is marginal relative to the full-guard case, with 2% versus 8% overhead.
C. OTFS with rectangular waveforms
The proposed embedded channel-estimation schemes also apply to practical rectangular transmit and receive pulses, despite their lack of bi-orthogonality. Rectangular waveforms modify the input-output relation through a phase, allowing threshold-based estimation to remain applicable.
- Rectangular transmit and receive pulses are considered because ideal pulses cannot be realized in practice.These pulses do not satisfy the bi-orthogonality conditions.
- The embedded channel-estimation schemes can also be employed with rectangular waveforms.
- A known phase α[k, l] is introduced during detection so threshold-based channel estimation remains applicable.The thresholds remain the same as for ideal waveforms because the channel differs only by a phase.
A. The integer Doppler case
The proposed embedded channel estimation maintains BER close to ideal OTFS detection while using pilot and guard symbols within the same frame. Performance depends on pilot power, threshold selection, guard overhead, and modulation order.
- Integer Doppler: With approximately 1% frame overhead, integer-Doppler estimation approaches ideal OTFS performance when SNRp = 40 dB.The comparison uses lτ = 20, kν = 4, and T = 3σ.
- Integer Doppler: BER remains highly similar across maximum Doppler taps kν = 1, 4, and 16, with slight improvement at kν = 16.The improvement is attributed to more guard symbols and fewer transmitted data symbols at higher Doppler frequencies.
- Threshold selection: The optimal threshold is approximately 3σ because lower thresholds increase false detections, whereas higher thresholds can miss weak paths.Threshold selection balances false detection and miss detection probabilities.
- Fractional Doppler: For fractional Doppler, SNRp = 50 dB yields performance similar to OTFS with known channel information, but requires approximately 8% pilot-and-guard overhead.Fractional-Doppler channels require larger pilot power than integer-Doppler channels.
- Comparison: The proposed OTFS channel estimation significantly outperforms OFDM with known channel information in delay–Doppler channels.The comparison is based on BER.
- Reduced guards: Reducing guard symbols lowers overhead to roughly 1.5% or 2.3%, while ˆk = 5 produces performance close to the full-guard case.Larger ˆk reduces neighboring-data interference but creates a spectral-efficiency versus error-performance tradeoff.
- Reduced guards: With 16-QAM, ˆk = 10 and about 3.6% guard overhead are needed for performance close to the full-guard case.The 16-QAM detector is more sensitive to channel-estimation errors than the 4-QAM case.
V. EXTENSIONS TO MIMO AND MULTIUSER UPLINK/DOWNLINK
The paper extends embedded pilot-aided estimation from SISO OTFS to MIMO systems by separating transmit-antenna pilots and assigning received regions for channel estimation and joint data detection.
- MIMO: Each transmit antenna places its own pilot, guard, and information symbols on the delay–Doppler grid.The pilot from each transmit antenna estimates its channels to every receive antenna.
- MIMO: The proposed MIMO arrangement applies to arbitrary Nt ≥1 and Nr ≥1, with fractional-Doppler channels described as a straightforward extension.The presentation explicitly develops the integer-Doppler case.
- MIMO: Transmit-antenna pilots are separated by the maximum delay tap so they do not interfere at receive antennas.This separation enables independent channel-estimation regions for the different transmit antennas.
- MIMO: At each receive antenna, designated received-symbol groups estimate individual transmit channels, while the remaining symbols support joint data detection.The data symbols depend on all transmit antennas and are jointly decoded using message passing.
B. Multiuser
The paper extends embedded channel estimation to multiuser uplink and downlink OTFS by separating pilots, guards, and users’ data regions. These arrangements support channel estimation and user-specific detection while controlling interuser interference.
- Multiuser setup: Multiuser schemes use transmit-symbol arrangements for users and the base station in uplink or downlink systems.The base station may have single or multiple antennas.
- Uplink: In the uplink, users place sufficiently separated pilots and occupy nonoverlapping portions of the remaining grid for data transmission.The described single-antenna-base-station case assumes orthogonal resource allocation.
- Uplink: With multiple base-station antennas, pilot and guard locations remain unchanged, while each user can exploit a larger or full portion of the remaining grid.This extends the available data region similarly to the MIMO case.
- Downlink: In the downlink, a base-station pilot is enclosed by guards for channel estimation, while users’ data symbols are separated by guard symbols.Each user uses appropriate received-symbol groups to estimate its channel and detect its own data.
- Summary: The paper presents embedded pilot-and-guard arrangements as extensions of the proposed OTFS channel-estimation schemes to multiuser uplink and downlink.The conclusion also places these extensions alongside the core integer- and fractional-Doppler schemes.