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OTFS-NOMA: An Efficient Approach for Exploiting Heterogenous User Mobility Profiles

Zhiguo Ding, Robert Schober, Pingzhi Fan, H. Vincent Poor

arXiv:1904.02783v1cs.IT

TL;DR

The paper addresses communication with users having heterogeneous mobility profiles by proposing OTFS-NOMA, which combines OTFS and NOMA across delay-Doppler and time-frequency resources. The protocol applies to uplink and downlink transmission, and analytical results show benefits for both mobility groups, including improved detection reliability, spectral efficiency, and latency.

  • Problem

    The paper addresses how to serve users with heterogeneous mobility profiles, including high-mobility and low-mobility users, in one communication system.

  • Method

    OTFS-NOMA groups users with different mobility profiles and uses OTFS for high-mobility signals, time-frequency transmission for low-mobility signals, and NOMA for their joint service.

  • Results

    Both high-mobility and low-mobility users benefit from OTFS-NOMA, which enhances high-mobility detection reliability and improves spectral efficiency and latency.

  • Takeaways & Limitations

    OTFS-NOMA provides a transmission approach that shares time-frequency bandwidth with low-mobility users instead of reserving it solely for high-mobility users.

Abstract

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This paper considers a challenging communication scenario, in which users have heterogenous mobility profiles, e.g., some users are moving at high speeds and some users are static. A new non-orthogonal multiple-access (NOMA) transmission protocol that incorporates orthogonal time frequency space (OTFS) modulation is proposed. Thereby, users with different mobility profiles are grouped together for the implementation of NOMA. The proposed OTFS-NOMA protocol is shown to be applicable to both uplink and downlink transmission, where sophisticated transmit and receive strategies are developed to remove inter-symbol interference and harvest both multi-path and multi-user diversity. Analytical results demonstrate that both the high-mobility and low-mobility users benefit from the application of OTFS-NOMA. In particular, the use of NOMA allows the spreading of the high-mobility users' signals over a large amount of time-frequency resources, which enhances the OTFS resolution and improves the detection reliability. In addition, OTFS-NOMA ensures that low-mobility users have access to bandwidth resources which in conventional OTFS-orthogonal multiple access (OTFS-NOMA) would be solely occupied by the high-mobility users. Thus, OTFS-NOMA improves the spectral efficiency and reduces latency.

I. INTRODUCTION

The paper proposes OTFS-NOMA for users with heterogeneous mobility profiles, combining OTFS and NOMA to serve high- and low-mobility users together. Analytical results indicate benefits in detection reliability, spectral efficiency, latency, and low-mobility reception complexity.

  • I. INTRODUCTION: OTFS uses time-invariant channel gains in the delay-Doppler plane, simplifying channel estimation and signal detection in high-mobility scenarios.This motivates applying OTFS to NOMA in doubly-dispersive channels.
  • I. INTRODUCTION: OTFS-NOMA groups users with different mobility profiles, serving high-mobility signals in the delay-Doppler plane and low-mobility signals in the time-frequency plane.High-mobility signals use OTFS, while low-mobility signals use an OFDM-like modulation.
  • I. INTRODUCTION: The protocol supports both uplink and downlink transmission with rate and power allocation, equalization, and diversity strategies to manage interference and improve outage performance.The proposed equalizers include FD-LE and FD-DFE, while multi-path and multi-user diversity are also exploited.
  • I. INTRODUCTION: NOMA spreads high-mobility users’ signals across more time-frequency resources, enhancing OTFS resolution and improving detection reliability.The improved resolution helps locate channels accurately in the delay-Doppler plane.
  • I. INTRODUCTION: OTFS-NOMA lets low-mobility users access bandwidth otherwise occupied by high-mobility users in OTFS-OMA, improving spectral efficiency and reducing latency.For low-mobility users, OFDM-like modulation also provides the same reception reliability as OTFS while avoiding complicated OTFS transforms.

B. Channel Model

The channel model represents each user’s wireless channel through sparse propagation paths characterized by gain, delay, and Doppler shift. OTFS-NOMA uses both delay-Doppler and time-frequency resources to serve heterogeneous-mobility users and share spectrum.

  • B. Channel Model: Each user’s channel is modeled by a small number of propagation paths, with each path characterized by a complex gain, delay, and Doppler shift.The path gains are assumed independent and identically distributed for analysis.
  • B. Channel Model: The discrete time-frequency and delay-Doppler grids are selected according to channel delay spread and Doppler-shift characteristics.T must not be smaller than the maximal delay spread, and Δf must not be smaller than the largest Doppler shift.
  • B. Channel Model: The numbers of time-frequency samples affect OTFS resolution and must be sufficiently large to locate channel responses accurately in the delay-Doppler plane.Adequate resolution also suppresses interference caused by fractional delay and fractional Doppler shifts.
  • B. Channel Model: The proposed scheme places high-mobility users in the delay-Doppler plane and low-mobility users in the time-frequency plane, managing their interference through NOMA.This enables spectrum sharing while reducing detection complexity for low-mobility users compared with OTFS-OMA.
  • B. Channel Model: In the downlink model, opportunistic NOMA users share time-frequency resource blocks with the high-mobility user’s signals, which are transformed from the delay-Doppler plane.The base station superimposes the signals before transmission.

IV. DOWNLINK OTFS-NOMA - DETECTING THE HIGH-MOBILITY USER’S SIGNALS

The downlink OTFS-NOMA receiver detects the high-mobility user in the delay-Doppler plane, where block-circulant channel structure motivates specialized transforms and equalization. Large OTFS grids become feasible through spectrum sharing, improving resolution without the spectral-efficiency penalty of OTFS-OMA.

  • The high-mobility user’s downlink signal is detected directly in the delay-Doppler plane after applying the SFFT to the received observations.
  • Sufficiently large N and M eliminate interference caused by fractional delay and fractional Doppler shifts under the stated assumption.
  • Large N and M can significantly reduce OTFS-OMA spectral efficiency, whereas spectrum sharing makes large grids possible for OTFS-NOMA.
  • The received system is represented with a block-circulant channel matrix whose M × M submatrices are circulant.
  • Inter-symbol interference remains in the OTFS-NOMA system, so FD-LE and FD-DFE equalization are considered for detection.

A. Design and Performance of FD-LE

FD-LE provides an efficient frequency-domain linear equalizer for the high-mobility user, while the analysis characterizes its SINR and outage behavior. The resulting diversity order is one, and OTFS-NOMA preserves the high-mobility user’s diversity while improving spectral efficiency over OTFS-OMA.

  • A. Design and Performance of FD-LE: FD-LE yields identical SINRs for all x0[k, l] when the NOMA users use the same power-allocation coefficient.
  • A. Design and Performance of FD-LE: The proposed FD-LE implementation avoids inversion of a full NM × NM matrix by exploiting FFT structure and diagonalization.
  • A. Design and Performance of FD-LE: The FD-LE outage analysis is difficult because the relevant channel terms are dependent and inverse-exponential sums are difficult to characterize.
  • A. Design and Performance of FD-LE: The FD-LE diversity order is one when the stated power condition holds; otherwise, the outage probability is always one.
  • A. Design and Performance of FD-LE: OTFS-NOMA preserves the high-mobility user’s diversity order while improving spectral efficiency relative to OTFS-OMA.

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FD-DFE gives different data streams different effective fading gains, enabling unequal error protection and multi-path diversity. Its strongest diversity results rely on perfect decision-making, while error propagation limits the resulting reliability guarantees.

  • Error propagation means the stated FD-DFE reception-reliability result is an upper bound when propagation cannot be completely avoided.
  • FD-DFE can realize unequal error protection because different symbols experience different effective fading gains, unlike FD-LE.
  • FD-DFE’s unequal error protection and diversity benefits come at the price of higher computational complexity.
  • FD-DFE can realize the maximal multi-path diversity, including full multi-path diversity order P0 + 1 for the analyzed symbol.
  • The FD-DFE diversity conclusions assume no error propagation, and not all NM data streams achieve the full diversity gain.

A. Stage I of SIC

In Stage I of SIC, each low-mobility NOMA user first decodes the high-mobility signal using reduced-size observations, then prepares its own time-frequency detection. The block-diagonal channel structure enables lower-complexity processing and one-tap equalization for the low-mobility signals.

  • A. Stage I of SIC: Assuming no Doppler shift for low-mobility users makes each channel matrix block diagonal, with one nonzero circulant block.
  • A. Stage I of SIC: The low-mobility users can detect signals from reduced-size observation vectors, reducing computational complexity.
  • A. Stage I of SIC: After the high-mobility signal is removed, each low-mobility user detects its information-bearing signal with a one-tap equalizer in the time-frequency plane.
  • A. Stage I of SIC: Because the low-mobility channel is time invariant, the SNRs across the corresponding time-frequency observations are equal.

1) Random User Scheduling:

Random user scheduling analyzes diversity and detection in OTFS-NOMA, including downlink and uplink processing strategies. The analysis establishes diversity gains and describes SIC-based detection of NOMA and high-mobility signals.

  • A diversity order of 1 is achievable for NOMA users under FD-LE, while the corresponding FD-DFE conclusion is supported only by simulations.The paper explicitly notes that no formal proof is available for the FD-DFE conclusion.
  • Greedy scheduling selects one NOMA user to transmit across all resource blocks, exploiting the channel quantity identified as critical to outage performance.
  • The proposed scheduling strategy realizes the maximal multi-user diversity gain K for FD-LE and also improves FD-DFE performance.
  • The uplink formulation uses a time-frequency observation with Gaussian noise, common transmit pulses and powers, and ISFFT-derived high-mobility signals.
  • In uplink detection, the base station first applies SIC in the time-frequency plane and then detects the high-mobility user in the delay-Doppler plane.

1) Adaptive-Rate Transmission:

Adaptive-rate transmission evaluates OTFS-NOMA through ergodic rate because adaptive data rates avoid outage when decoding NOMA-user signals. The analysis also identifies high-SNR error floors and their dependence on opportunistic user scheduling.

  • The first SIC stage can be guaranteed successful, minimizing NOMA users’ impact on the high-mobility user and making NOMA transparent to that user.
  • Adaptive-rate NOMA users are evaluated by ergodic rate because outage events do not occur when decoding their signals.
  • A single user may be scheduled on multiple frequency channels, which reduces user fairness.
  • At high SNR, the outage probability has an error floor because the scheduled NOMA user experiences strong interference from the high-mobility user.
  • Increasing the number K of opportunistic users reduces the scheduled NOMA user’s error floor under the stated asymptotic condition.

B. Stage II of SIC

OTFS-NOMA is evaluated for downlink and uplink using equalization, scheduling, adaptive or fixed transmission, and outage or rate criteria. Results show gains from multi-path and multi-user diversity, while low-SNR interference, complexity, and uplink error floors constrain performance.

  • Downlink performance: OTFS-NOMA significantly improves downlink sum rate at high SNR, reaching up to R0 + Ri compared with OTFS-OMA’s cap at R0.Reducing target rates mitigates the low-SNR performance loss by improving successful SIC probability.
  • Equalization: FD-DFE outperforms FD-LE across the considered SNR range, but its gain requires increased computational complexity.FD-DFE also enables multi-path diversity, whereas FD-LE is limited to diversity order one.
  • Equalization: FD-DFE produces unequal reliability across symbols: x0[N −1, M −1] has the lowest outage, while x0[0, 0] has the largest.Different symbols experience different effective channel gains λ0,kl.
  • User scheduling: Scheduling exploits multi-user diversity: FD-DFE gains 0.5 BPCU at moderate SNR, while FD-LE approaches OTFS-OMA at low SNR.Increasing the participating-user pool particularly improves OTFS-NOMA at low and moderate SNR.
  • Uplink performance: With adaptive-rate uplink transmission, OTFS-NOMA is transparent to U0 and provides the same performance as OTFS-OMA for U0.This preserves U0’s QoS requirements while allowing NOMA users to adapt their rates.
  • Uplink performance: Fixed-rate uplink transmission exhibits an error floor for NOMA-user outage, preventing the maximal sum rate R0 + Ri even at high SNR.Increasing K reduces this error floor, while scheduling improves SIC by creating more distinct channel conditions.

VIII. CONCLUSIONS

The paper proposes OTFS-NOMA for uplink and downlink, grouping users with heterogeneous mobility profiles. Analytical results show benefits for both mobility classes, including improved spectral efficiency and reduced latency.

  • OTFS-NOMA provides uplink and downlink transmission schemes for users with different mobility profiles.
  • Both high-mobility and low-mobility users benefit from applying OTFS-NOMA.
  • Spreading high-mobility signals across time-frequency resources enhances OTFS resolution and improves detection reliability.
  • Low-mobility users gain access to bandwidth resources otherwise occupied solely by high-mobility users in OTFS-OMA.
  • OTFS-NOMA improves spectral efficiency and reduces latency.
  • Data-rate allocation policies and the effects of non-zero fractional delays and Doppler shifts remain topics for future research.

APPENDIX A

The appendix develops transform-based representations of the received signals and analyzes their interference-plus-noise covariance and SINR. These steps support diagonalized channel processing and subsequent detection analysis.

  • Transforming the delay-Doppler representation to the time-frequency plane diagonalizes the channel matrix and removes inter-symbol interference.
  • Applying Kronecker-product Fourier transformations produces simplified received-signal representations involving block-diagonal structures.
  • The interference-plus-noise covariance matrix is derived under normalized noise power, enabling SINR analysis.
  • The appendix rewrites the mapped NOMA signals and received-signal model in vectorized form.
  • Unitary transformations preserve the complex Gaussian noise distribution used in the derivation.

APPENDIX C

The appendix derives outage-probability bounds by characterizing effective channel gains and their correlation. It shows that the upper and lower bounds have the same diversity order.

  • The upper and lower outage-probability bounds have the same diversity order.
  • The derivation assumes an outage condition involving γ1 and ε0; otherwise, the outage probability is one.
  • Each effective channel-gain diagonal element is a superposition of P0+1 identically distributed complex Gaussian terms.
  • The appendix derives lower and upper outage-probability bounds from the distributions and extrema of the effective channel gains.
  • The effective channel gains are identically distributed but correlated rather than independent.
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