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Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive MIMO

Wenqian Shen, Linglong Dai, Jianping An, Pingzhi Fan, Robert W. Heath,

arXiv:1903.09441v1cs.IT

TL;DR

OTFS massive MIMO requires challenging downlink channel estimation because many base-station antennas must be characterized, especially in FDD systems. The paper models the channel's delay-Doppler-angle structure as sparse recovery and solves it with 3D-SOMP. Simulations report accurate CSI with reduced pilot overhead and improved NMSE performance over traditional estimators.

  • Problem

    Downlink channel estimation is challenging in OTFS massive MIMO because FDD lacks channel reciprocity and the base station has many antennas.

  • Method

    The paper exploits delay-Doppler-angle structured sparsity, formulates estimation as sparse signal recovery, and uses 3D-SOMP to estimate path supports.

  • Results

    The proposed technique achieves accurate CSI with low pilot overhead and outperforms traditional impulse-based and OMP-based channel estimation in reported NMSE comparisons.

  • Takeaways & Limitations

    Structured sparsity enables OTFS massive MIMO channel estimation with reduced pilot overhead while maintaining superior reported simulation performance.

Abstract

from arXiv · show

Orthogonal time frequency space (OTFS) modulation outperforms orthogonal frequency division multiplexing (OFDM) in high-mobility scenarios. One challenge for OTFS massive MIMO is downlink channel estimation due to the large number of base station antennas. In this paper, we propose a 3D structured orthogonal matching pursuit algorithm based channel estimation technique to solve this problem. First, we show that the OTFS MIMO channel exhibits 3D structured sparsity: normal sparsity along the delay dimension, block sparsity along the Doppler dimension, and burst sparsity along the angle dimension. Based on the 3D structured channel sparsity, we then formulate the downlink channel estimation problem as a sparse signal recovery problem. Simulation results show that the proposed algorithm can achieve accurate channel state information with low pilot overhead.

I. INTRODUCTION

OTFS addresses time-variant high-mobility channels by multiplexing data in the delay-Doppler domain, while massive MIMO introduces challenging downlink CSI acquisition. The paper exploits delay-Doppler-angle structured sparsity and proposes 3D-SOMP-based sparse recovery with reduced pilot overhead.

  • OFDM can suffer severe inter-carrier interference from Doppler spread in high-mobility, time-variant channels.
  • OTFS converts time-variant channels into roughly constant delay-Doppler channels and multiplexes information-bearing data in that domain.
  • In FDD OTFS massive MIMO, downlink channel estimation is necessary because channel reciprocity is unavailable and the base station has many antennas.
  • Prior OFDM massive MIMO estimation methods are not directly applicable because OTFS multiplexes data in delay-Doppler rather than frequency-time.
  • The OTFS massive MIMO channel is sparse along delay, block-sparse along Doppler, and burst-sparse along angle.
  • The proposed 3D-SOMP technique formulates estimation as sparse signal recovery using overlapping independent complex Gaussian pilots and estimates path supports dimension by dimension.

B. OTFS SISO Demodulation

OTFS demodulation transforms the received signal through conventional frequency-time processing and post-processing into delay-Doppler data. The resulting data block is a phase-compensated two-dimensional periodic convolution with the delay-Doppler channel.

  • The receiver rearranges the received signal into a matrix, removes cyclic prefixes, and applies an M-point DFT to obtain the frequency-time block YFT.
  • A receive window and SFFT transform YFT into the delay-Doppler data block YDD.
  • YDD is a phase-compensated two-dimensional periodic convolution of the transmitted delay-Doppler block XDD with the channel impulse response HDD.
  • OTFS data experiences a roughly constant delay-Doppler channel while exploiting full diversity across frequency-time channels.
  • Equalization requires HDD because each transmitted delay-Doppler symbol experiences inter-symbol interference from other symbols.

C. OTFS Massive MIMO

OTFS massive MIMO uses multiple antennas to serve users simultaneously, requiring downlink CSI for precoding. Conventional impulse-based estimation becomes impractical as antenna count grows because pilot overhead scales with the number of antennas.

  • The base station uses Nt antennas to serve U single-antenna users simultaneously, with downlink precoding based on downlink CSI.
  • The estimation goal is to recover the delay-Doppler channel impulse response HDD from received delay-Doppler data YDD.
  • Impulse-based estimation requires Nt impulses to distinguish the channels associated with Nt base-station antennas.
  • Guard intervals must span the channel support dimensions, making the pilot length proportional to NtNmaxMmax.
  • The proposed 3D-SOMP estimator targets accurate CSI with considerably reduced pilot overhead compared with the impulse-based approach.

IV. PROPOSED 3D-SOMP BASED CHANNEL ESTIMATION IN OTFS MASSIVE MIMO SYSTEMS

The channel-estimation section presents the channel's 3D structured sparsity, casts downlink estimation as sparse signal recovery, and introduces 3D-SOMP while analyzing its pilot overhead.

  • The section demonstrates 3D structured sparsity in OTFS massive MIMO channels.
  • It formulates downlink channel estimation as a sparse signal recovery problem.
  • It proposes 3D-SOMP and analyzes the pilot overhead required by the resulting channel-estimation technique.

A. 3D Structured Sparsity of Delay-Doppler-angle Channel

The OTFS massive MIMO channel has structured sparsity across delay, Doppler, and angle dimensions: sparse, block-sparse, and burst-sparse, respectively. This structure reflects dominant-path and subpath behavior and supports low-overhead CSI estimation.

  • Delay dimension: Dominant paths share approximately the same delay across their subpaths, producing sparse support along the delay dimension.The channel has finite delay support determined by the largest path delay.
  • Doppler dimension: Doppler support forms one non-zero block centered near zero, with block length determined by the maximum Doppler spread.For 180 km/h at 2.15 GHz and 15 kHz subcarrier spacing, about 5% of Doppler elements are dominant.
  • Angle dimension: Small angle spread creates non-zero angle bursts whose start positions vary with the paths' arrival directions.Unlike traditional block sparsity, the burst start position is unknown.
  • 3D channel structure: The delay-Doppler-angle channel is sparse along delay, block-sparse along Doppler, and burst-sparse along angle.These three structures are summarized in the channel tensor representation.
  • Implication: The identified 3D structured sparsity can be exploited to estimate channel state information with low pilot overhead.The structure follows from decomposing the multipaths of time-variant channels.

B. Formulation of Downlink Channel Estimation

The paper uses overlapping, independent random pilots in the delay-Doppler domain with guard intervals to formulate OTFS downlink estimation as sparse recovery. The resulting linear model estimates a truncated delay-Doppler-angle channel using a sensing matrix built from periodic convolution and windowing operations.

  • Pilot observation: The received delay-Doppler pilots are represented through a phase-compensated two-dimensional periodic convolution with the channel.The frame contains pilot regions and guard intervals along both delay and Doppler dimensions.
  • Pilot design: Pilots at different antennas overlap in the delay-Doppler domain while using independent complex Gaussian sequences to reduce pilot overhead.Guard intervals prevent pilot-data interference caused by two-dimensional periodic convolution.
  • Sparse recovery formulation: Vectorizing the received pilots and channel produces the linear sparse-recovery model y = Ψh + v.The channel vector can be inversely vectorized into a truncated delay-Doppler-angle tensor.
  • Sparse recovery formulation: The sensing matrix Ψ is formed from the periodic-convolution and windowing matrices, while h contains the truncated channel coefficients.The truncation covers finite delay and Doppler supports and all antenna-angle indices.
  • Estimator choice: Traditional OMP can solve the sparse-recovery problem, motivating 3D-SOMP to exploit the channel's structured sparsity.The proposed algorithm targets improved performance over traditional OMP.

C. 3D-SOMP Algorithm

3D-SOMP identifies each dominant path's delay, Doppler, and angle support from a tensorized correlation vector, then updates the channel estimate and residual iteratively. Its support search is tailored to normal, block, and burst sparsity.

  • Correlation tensor: 3D-SOMP reshapes the OMP correlation vector into a tensor to exploit three-dimensional channel structure.The tensor dimensions correspond to delay, Doppler, and angle.
  • Iterative update: After adding the selected support, the algorithm obtains a partial least-squares estimate, zeros its complement, updates residual measurements, and outputs h(Np).The support is identified one dominant path at a time.
  • Delay support: For each dominant path, the algorithm selects the delay index from the largest row-norm correlation in the mode-1 unfolding.This produces the delay support associated with the path.
  • Doppler support: It estimates the Doppler support as the smallest block whose norm exceeds a threshold fraction of the Doppler correlation norm.The procedure assumes one non-zero Doppler block centered around zero.
  • Angle support: To locate the angle burst, 3D-SOMP lifts burst sparsity into block sparsity, then selects the start position from the largest transformed row-norm correlation.The resulting support is {ps, ps + 1, · · ·, ps + D − 1}.

D. Performance Comparison

The proposed 3D-SOMP estimator is reported to require substantially less pilot overhead than impulse-based channel estimation by exploiting structured sparsity and compressed sensing scaling.

  • Pilot overhead comparison: The proposed pilot overhead scales as ∝NmaxNpD log(NgMgNt), versus ∝NtNmaxMmax for extended impulse-based estimation.The proposed scaling uses sparsity level S = NmaxNpD and vector length L = NgMgNt.

V. SIMULATION RESULTS

Simulations evaluate NMSE against pilot overhead, BS antenna count, and SNR, comparing 3D-SOMP with impulse-based and traditional OMP estimators. The proposed method achieves lower NMSE with reduced pilot overhead and remains effective as antenna count increases.

  • Simulation setup: The simulations compare NMSE for 3D-SOMP, impulse-based, and traditional OMP channel estimation under varying pilot overhead, antenna count, and SNR.Pilot overhead ratio is defined as the fraction of delay-Doppler resource units used for pilots.
  • Pilot overhead: At 32% pilot overhead, 3D-SOMP achieves an NMSE of 0.03 under the Fig. 5 conditions.The comparison uses 16 BS antennas and 5 dB SNR; the required 3D-SOMP overhead scales as ∝NmaxNpD log(NgMgNt).
  • Pilot overhead: The impulse-based estimator degrades when pilot overhead is small because adjacent impulses interfere when their delay or Doppler intervals are insufficient.The stated thresholds are Nmax along Doppler and Mmax along delay.
  • BS antenna count: When the pilot overhead ratio is fixed at 50%, impulse-based NMSE exceeds 10^-1 for more than 8 BS antennas, whereas 3D-SOMP works well with many antennas.The antenna-count comparison uses 5 dB SNR.
  • Estimator comparisons: 3D-SOMP outperforms traditional OMP across the considered antenna counts and by about 6 dB in the SNR comparison.The SNR comparison uses 32 BS antennas and 50% pilot overhead; proposed NMSE improves as SNR increases.
  • SNR: In the SNR comparison, 3D-SOMP outperforms the traditional impulse-based estimator, whose NMSE exhibits a floor caused by insufficient pilot overhead and inter-antenna interference.The comparison uses 32 BS antennas and 50% pilot overhead.

VI. CONCLUSIONS

The paper formulates OTFS massive-MIMO downlink channel estimation using the channel’s delay-Doppler-angle structured sparsity and solves it with 3D-SOMP. Simulations verify superior performance, while several system-level problems remain open.

  • VI. CONCLUSIONS: The OTFS massive-MIMO channel is sparse along delay, block-sparse along Doppler, and burst-sparse along angle.This structured sparsity is represented in a delay-Doppler-angle 3D channel.
  • VI. CONCLUSIONS: The paper formulates downlink channel estimation as sparse signal recovery and solves it with a proposed 3D-SOMP algorithm.The method is based on the identified three-dimensional channel structure.
  • VI. CONCLUSIONS: Simulation results verify the superior performance of the proposed channel-estimation technique.
  • VI. CONCLUSIONS: Future work includes low-complexity equalization, downlink precoding, and efficient channel feedback in OTFS massive-MIMO systems.

APPENDIX I

The appendix derives the OTFS input-output representation through OFDM symbols, transforms received symbols into the delay-Doppler domain, and analyzes dominant channel terms using Fourier expansions.

  • System model: Each column vector s_i of S represents an OFDM symbol without a cyclic prefix before transmission.The base station adds a cyclic prefix to each OFDM symbol before transmitting them through the channel.
  • Delay-Doppler transformation: After cyclic-prefix removal, the received symbols are arranged in Z and transformed as YDD = ZFN into the delay-Doppler data block.The appendix then expands the resulting delay-Doppler input-output relation.
  • System model: The cyclic-prefix length NCP is chosen larger than the channel length L to avoid inter-symbol interference.Under this condition, each received OFDM symbol is modeled through circular convolution with the time-variant channel and additive noise.
  • Channel expansion: The time-variant channel is expanded using a Fourier series with P frequency components and coefficients associated with each channel tap.The resulting expression for Λ depends on these frequency components and coefficients.
  • Channel representation: The delay-Doppler channel impulse response HDD is defined over delay and Doppler indices, and substituting the asymptotic expression completes the derivation.The appendix defines HDD and uses equation (52) in equation (44) to obtain the final result.
  • Dominant terms: Because |ΥN(x)| approaches zero for |x| much greater than one, the appendix identifies P dominant items in the channel expression.These dominant terms arise under the conditions specified immediately after equation (50).
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