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Orthogonal Zadoff-Chu Based Pilot Design For Fractional Channel Estimation in MIMO-OTFS
Omid Aghda, Prabhat Gupta, João Guerreiro, Nuno Souto, Michal Szczachor, Lukasz Krzymien, Rui Dinis
TL;DR
Fractional delay and Doppler complicate OTFS channel estimation, and impulse-based pilots used with A&M estimation have high PAPR. This paper uses orthogonal ZC pilots and correlation-based A&M estimation for MIMO-OTFS. Simulations report lower PAPR than the impulse-based scheme, while estimation performance degrades as transmit antenna count increases.
Problem
OTFS channel estimation must address fractional path delays and Dopplers, which distort CSI and DD-channel sparsity; impulse-based pilots used with A&M estimation also have high PAPR.
Source: §I · p. 1Method
The method assigns orthogonal ZC pilot sequences to transmit antennas and uses correlation-based processing with A&M to estimate fractional delay and Doppler.
Source: §I · pp. 1–2, A. Pilot Design · p. 3Results
The proposed method achieves lower PAPR than the pilot design and channel-estimation scheme in, while increasing transmit-antenna count raises interference power and degrades estimation performance.
Source: §IV · p. 5Takeaways & Limitations
Different-root ZC pilots allow simultaneous transmission on the same resource grid while maintaining receiver-side signal separability and efficient resource use.
Source: §I · p. 2, A. Pilot Design · p. 3
Abstract
from arXiv · showhide
In this paper, we propose a Zadoff-Chu (ZC) sequence-based pilot design for fractional channel estimation in orthogonal time frequency space (OTFS) modulation for point-to-point multi-input multi-output (MIMO) scenarios. Orthogonal pilot sequences are assigned to each transmit antenna using ZF sequences. At the receiver, a correlation-based scheme is used to construct the signal for estimation. The estimation relies on a two-dimensional extension of the Aboutanios and Mulgrew (A&M) frequency estimation method. Simulation results show that the proposed approach achieves low peak-to-average power ratio (PAPR) while maintaining stable performance as the number of transmit antennas increases.
I. Introduction
OTFS channel estimation must handle paths whose delays and Dopplers fall between integer sampling points, while existing fractional-parameter methods can rely on approximations or incur high complexity. The paper proposes ZC pilots with correlation-based A&M estimation to reduce the high PAPR associated with impulse-based pilots.
I. Introduction
- OTFS is presented as a candidate for dynamic 6G use cases, including communications involving terminals moving at up to 1000 km/h.The introduction names further enhanced mobile broadband, ultra-reliable low-latency communications, and high-mobility communications among the use cases.Source: §I · p. 1
- Fractional delay and Doppler misalignments distort CSI and DD-channel sparsity, while virtual-tap approximations can degrade equalization and detection and SBL refinement incurs high complexity.The misalignment arises because digital-domain processing uses integer sampling points, whereas path delays and Dopplers may not align with them.Source: §I · p. 1
- Impulse-based pilots used with 2D A&M estimation have high PAPR, motivating a pilot design that avoids this drawback.The earlier formulation in treats fractional delay and Doppler estimation as frequency estimation.Source: §I · p. 1
- ZC pilots spread across the DD domain enable correlation-based A&M estimation and simultaneous same-grid transmission with lower PAPR than the impulse-based approach in.Assigning different root indices to transmit antennas supports receiver-side signal separability and efficient resource use.Source: §I · pp. 1–2
II. System Model
The system represents transmitted and received signals on an M-by-N delay-Doppler grid and models path-dependent coupling between them. It assumes shared delay and Doppler parameters across antenna pairs, with path gains varying by pair.
II. System Model
- The DD domain has M delay bins and N Doppler bins, and each transmit antenna’s signal is represented by an M-by-N matrix.The model denotes the received DD-domain signal at each receive antenna by a corresponding M-by-N matrix.Source: §II · p. 2
- The model assumes identical path delays and Dopplers across transmit–receive pairs, while the complex path gains vary with antenna indices.Each path’s normalized delay and Doppler are decomposed into integer and fractional parts.Source: §II · p. 2
- Each path contributes a DD-domain response characterized by its normalized delay and Doppler, and the path responses form the matrix Φ_t.The model expresses the path contribution as a vector and uses a periodic function to represent the two-dimensional circular convolution.Source: §II · p. 2
- At the receiver, each signal is correlated with the transmit antenna’s orthogonal pilot matrix before A&M estimates channel parameters; shared delay-Doppler estimates can support gain estimation across antenna pairs.The figure depicts estimates from one antenna pair being used to determine the gains of the others under the common-parameter assumption.Source: §II · p. 2, Figure 1 · p. 3
III. Pilot Design and Channel Estimation
The section states two matrix lemmas that precede the proposed pilot design: a diagonalization result for block-circulant matrices and a condition under which a normal matrix is unitary.
III. Pilot Design and Channel Estimation
- The two lemmas are presented as preliminary results before the pilot design is introduced.The section explicitly positions them as preceding the proposed design.Source: §III · p. 3
- A square MN-by-MN block-circulant matrix with N circulant M-by-M blocks can be diagonalized via eigendecomposition.The stated decomposition uses a vector containing the matrix’s eigenvalues.Source: §III · p. 3
- A normal matrix whose eigenvalues all have unit magnitude satisfies A^H A = I.This is stated as Lemma 2 for a matrix A in C^(M×M).Source: §III · p. 3
A. Pilot Design
The pilot design uses ZC sequences to construct orthogonal block-circulant pilot matrices for the transmit antennas. Under the stated practical condition, distinct roots can be assigned across antennas.
A. Pilot Design
- ZC sequences serve as the eigenvalue vectors used to construct the block-circulant pilot matrices.The construction draws on the stated lemmas and the sequences’ correlation properties.Source: A. Pilot Design · p. 3
- The resulting pilot matrices are orthogonal, and the construction includes a √MN normalization to ensure unit transmitted-signal power.The passage identifies p_t as the ZC sequence associated with transmit antenna t.Source: A. Pilot Design · p. 3
- When N_t < MN, distinct ZC sequences with different root indices can be assigned to the transmit antennas.The paper describes this antenna-count condition as a practical assumption.Source: A. Pilot Design · p. 3
B. Pilot Correlation
The receiver projects the signal onto an orthogonal pilot basis to estimate each antenna-pair channel, while treating inter-antenna interference as part of the effective noise.
B. Pilot Correlation
- Projecting the received signal onto the orthogonal pilot basis isolates the channel estimate for the selected transmit antenna.Source: B. Pilot Correlation · p. 3
- The block-circulant cross-antenna matrix has eigenvalues given by the Hadamard product of the corresponding pilot eigenvalue vectors.Source: B. Pilot Correlation · p. 3
- The projected signal includes an inter-antenna interference term, which is absorbed into the noise term for estimation.Source: B. Pilot Correlation · p. 3
C. Channel Estimation
The method iteratively estimates integer and fractional delay-Doppler parameters for each channel tap, then projects the received signal onto the estimated basis to recover channel gains.
C. Channel Estimation
- The 2D A&M algorithm estimates delay and Doppler parameters, after which the received signal is projected onto their estimated basis to estimate channel gains.Source: C. Channel Estimation · pp. 3–4
- With known tap count P, the algorithm runs P outer iterations, reshaping the residual and locating the peak to initialize each tap's integer delay and Doppler estimates.Source: C. Channel Estimation · p. 4
- Peak-based integer delay-Doppler detection is reliable only above the maximum-likelihood SNR threshold; fractional delay estimation uses the dual of the Doppler procedure.Source: C. Channel Estimation · p. 4
- The algorithm uses J internal iterations for fractional Doppler estimation, updates the estimate, and applies the dual procedure to estimate fractional delay.Source: C. Channel Estimation · p. 4
- Assuming a known tap count simplifies estimation; one antenna pair saves complexity when delays and Dopplers are shared, while combining pairs may improve accuracy.Source: C. Channel Estimation · p. 4
- After estimating a path, the method cancels its contribution from the received signal and projects onto the estimated delay-Doppler basis for gain estimation.Source: C. Channel Estimation · p. 4
IV. Simulation Results
Simulations compare estimation error across SNR and antenna counts and evaluate transmitted-signal PAPR; the proposed design has lower PAPR than the scheme in.
IV. Simulation Results
- The simulations use a four-path channel, 3,000 Monte Carlo iterations, M = 29, N = 23, and J = 2 internal A&M iterations.Delays and Dopplers are uniformly distributed; carrier frequency is 4 GHz and subcarrier spacing is 15 kHz.Source: §IV · p. 4
- Increasing the number of transmit antennas raises interference power and degrades channel-estimation performance, as shown by NMSE versus SNR.Source: §IV · pp. 4–5, Figure 2 · p. 5
- The proposed method achieves lower PAPR than the pilot design and channel estimation scheme in.For comparison, data is included in both methods; the proposed design superimposes data on the pilot with pilot power ratio 0.17, while uses guard regions for pilot support.Source: Figure 3 · p. 5, §IV · p. 5
V. conclusion
The paper concludes that its ZC-based pilot design supports channel estimation in MIMO-OTFS and achieves lower PAPR than an embedded-pilot scheme.
V. conclusion
- The proposed ZC-based pilot design is formulated for channel estimation in MIMO-OTFS and achieves lower PAPR than the embedded-pilot-based scheme.Source: §V · p. 5
- Future work will integrate the pilot with data transmission and combine received-antenna signals to improve delay-Doppler estimation accuracy.Source: §V · p. 5