PaperlayerView exact revision on arXiv

Source-linked AI summary

A New Path Division Multiple Access for the Massive MIMO-OTFS Networks

Muye Li, Shun Zhang, Feifei Gao, Pingzhi Fan, Octavia A. Dobre

arXiv:2003.08228v1eess.SP

TL;DR

High mobility shortens channel coherence time, challenging acquisition of many unknown channels. The paper proposes unified uplink and downlink PDMA for massive MIMO-OTFS using 3D channel modeling, channel-parameter extraction, and path scheduling. Simulations are reported to demonstrate the validity of the scheme.

  • Problem

    High mobility shortens channel coherence time, making it more challenging to acquire many unknown channels within that time.

    Source: §I · p. 2

  • Method

    The paper proposes unified uplink and downlink PDMA for massive MIMO-OTFS, using 3D-NOMP channel extraction and uplink path scheduling to avoid overlapping user observation regions.

    Source: §VI · pp. 27–28

  • Results

    Simulations are reported to demonstrate the validity of the proposed unified uplink/downlink PDMA scheme.

    Source: §VI · p. 28

  • Takeaways & Limitations

    The proposed scheme schedules users’ angle-domain resources to keep their observation regions non-overlapping in the angle-delay-Doppler domain.

    Source: §VI · p. 28

Abstract

from arXiv · show

This paper focuses on a new path division multiple access (PDMA) for both uplink (UL) and downlink (DL) massive multiple-input multiple-output network over a high mobility scenario, where the orthogonal time frequency space (OTFS) is adopted. First, the 3D UL channel model and the received signal model in the angle-delay-Doppler domain are studied. Secondly, the 3D-Newtonized orthogonal matching pursuit algorithm is utilized for the extraction of the UL channel parameters, including channel gains, directions of arrival, delays, and Doppler frequencies, over the antenna-time-frequency domain. Thirdly, we carefully analyze energy dispersion and power leakage of the 3D angle-delay-Doppler channels. Then, along UL, we design a path scheduling algorithm to properly assign angle-domain resources at user sides and to assure that the observation regions for different users do not overlap over the 3D cubic area, i.e., angle-delay-Doppler domain. After scheduling, different users can map their respective data to the scheduled delay-Doppler domain grids, and simultaneously send the data to base station (BS) without inter-user interference in the same OTFS block. Correspondingly, the signals at desired grids within the 3D resource space of BS are separately collected to implement the 3D channel estimation and maximal ratio combining-based data detection over the angle-delay-Doppler domain. Then, we construct a low complexity beamforming scheme over the angle-delay-Domain domain to achieve inter-user interference free DL communication. Simulation results are provided to demonstrate the validity of our proposed unified UL/DL PDMA scheme.

I. INTRODUCTION

High mobility shortens channel coherence time, making acquisition of massive MIMO channels more challenging; existing time-varying channel models also have limitations. The paper proposes unified uplink and downlink path division multiple access (PDMA) for massive MIMO-OTFS in the angle-delay-Doppler domain.

I. INTRODUCTION

  • High mobility shortens channel coherence time, making acquisition of many unknown channels within that time more challenging.The introduction says AR- and BEM-based approaches have limitations: block-fading assumptions can lose within-block variation, BEM parameters are mobility-sensitive, and both models have approximation errors, especially at high speeds.Source: §I · pp. 2–3
  • OTFS represents data in the delay-Doppler domain, where time-varying channels can be described by constant variables determined by scattering-path parameters such as delay and Doppler frequency.The introduction notes that OTFS multi-user signals can have different double circular shifts, complicating low-complexity data detection.Source: §I · p. 3
  • The proposed unified PDMA combines uplink path scheduling with low-complexity downlink beamforming for massive MIMO-OTFS.The scheme also develops a 3D channel model and uses 3D-NOMP to extract uplink channel parameters.Source: §I · p. 4
  • The paper analyzes energy dispersion and power leakage in 3D angle-delay-Doppler channels and uses the resulting resource assignments to support its uplink and downlink scheme.It also describes the downlink beamforming strategy as targeting inter-user-interference-free communication.Source: §I · p. 4
  • Uplink scheduling assigns angle-domain resources so users’ observation regions do not overlap, supporting simultaneous transmission without inter-user interference in one OTFS block.The base station collects signals at desired grids for 3D channel estimation and MRC-based data detection.Source: §I · p. 4

II. SYSTEM MODEL

The system models a high-mobility massive-MIMO channel as multiple paths with angle, delay, Doppler, and gain parameters. OTFS and spatial DFT express received signals and sparse channels in the angle-delay-Doppler domain.

A. High Mobility Massive MIMO Channel Model

  • High user mobility makes channels vary rapidly and experience both frequency- and time-selective fading across multiple scattering paths.The model includes a line-of-sight path or reflections from scatterers.Source: A. High Mobility Massive MIMO Channel… · p. 5
  • Each path is parameterized by its direction of arrival, channel gain, delay, and Doppler shift; fractional delays are excluded and delays are integer multiples of the sampling period.The model also treats each path's direction as constant over a long time interval.Source: A. High Mobility Massive MIMO Channel… · p. 6

B. Massive MIMO-OTFS Scheme

  • Users arrange data on delay-Doppler grids and apply OTFS transforms and OFDM processing to form transmitted blocks and recover received delay-Doppler data.The received processing removes the cyclic prefix, applies a DFT, and then an SFFT.Source: B. Massive MIMO-OTFS Scheme · pp. 6–7
  • A spatial DFT maps the received signal into the angle-delay-Doppler domain, where channel energy is sparse and dominant values correspond to path parameters.The dominant values occur near coordinates set by each path's delay, Doppler frequency, and direction.Source: B. Massive MIMO-OTFS Scheme · pp. 7–8

III. UPLINK CHANNEL PARAMETER CAPTURE WITH 3D-NOMP

The section frames uplink channel estimation as the next task after constructing the received-signal model. It adopts 3D-NOMP to estimate the uplink channel parameter sets.

III. UPLINK CHANNEL PARAMETER CAPTURE WITH 3D-NOMP

  • The channel-estimation goal follows construction of the received-signal model.The supplied passage does not specify the estimation objective beyond this transition.Source: §III · p. 9
  • The method uses an uplink training model and 3D-NOMP to estimate channel parameter sets.Source: §III · p. 9

A. UL Training Model

The uplink training model collects users' training signals under a TDD setup and forms a received-signal model for channel estimation. 3D-NOMP searches angle, delay, and Doppler, first coarsely and then precisely.

A. UL Training Model

  • Users perform channel-parameter estimation within a TDD model, using the same training sequence.The BS collects received samples after discarding cyclic-prefix samples.Source: A. UL Training Model · pp. 9–10
  • The training sequence has power P_t, and each user's training duration is (L_cp + N_t)T_s.Users start training sequentially at offsets determined by that duration.Source: A. UL Training Model · p. 9

1) 3D-coarse searching:

  • 3D coarse searching uses an under-sampled angle-delay-Doppler map to reduce search complexity, followed by precise searching near the coarse estimates.The map covers angle, delay, and Doppler domains.Source: 1) 3D-coarse searching · pp. 10–11

3) Single refinement:

3D-NOMP refines path parameters and gains through iterative searches and updates, then stops when the residual approaches the noise power. The resulting channel estimates support the paper's uplink path scheduling and low-complexity downlink beamforming schemes.

3) Single refinement:

  • Single refinement uses an extended Newton method to refine angle and Doppler estimates and update gain while minimizing the new residual power.The objective is evaluated over repeated refinement iterations.Source: 3) Single refinement · pp. 11–12

4) Cyclic refinement:

  • Cyclic refinement revisits estimates from earlier iterations, producing estimates of path gains, angles, delays, and Doppler shifts.The text describes the resulting estimates as accurate.Source: 4) Cyclic refinement · p. 12

5) Gain updating:

6) Stopping criterion:

IV. PDMA OVER THE ANGLE-DELAY-DOPPLER DOMAIN

  • The model treats angles and path distances as nearly constant over several OTFS blocks; in the stated example, angle change over five blocks is 0.2° at 360 km/h and 500 m.Source: §IV · p. 13
  • The uplink PDMA schedules paths to separate users' observation regions, then estimates channel gains and detects data; a low-complexity downlink beamforming strategy follows.Source: §IV · p. 13

A. Analysis of 3D Channel over the Angle-Delay-Doppler Domain

The section characterizes how OTFS channel energy spreads and leaks across the angle-delay-Doppler domain. It motivates path scheduling to keep users’ observation regions separate while allowing parallel transmission.

A. Analysis of 3D Channel over the Angle-Delay-Doppler Domain

  • A path’s angle, delay, and Doppler identify its dispersed OTFS grids, which can be collected to decode the transmitted symbol.The path corresponds to a delay-Doppler-angle signature, and the received symbol information appears at the associated grids.Source: A. Analysis of 3D Channel over the… · pp. 14, 16
  • Under high mobility, secondary-channel power cannot be ignored: sin(πνk,pℓTs) is 8×10−3 at 36 km/h and 7.85×10−2 at 360 km/h.The scenarios have maximum Doppler frequencies of 1 kHz and 10 kHz, respectively.Source: A. Analysis of 3D Channel over the… · p. 14
  • At geometric grid distance dνθ = dν + dθ = 1, ηk,p(dν, dθ) is only −20 dB; when dνθ > 1, it becomes small and power leakage almost has no influence.Source: A. Analysis of 3D Channel over the… · p. 15
  • Users with orthogonal angle-delay-Doppler channels can transmit on the same delay-Doppler grid without inter-user interference, motivating path scheduling when dense data placements cause overlap.Scheduling every symbol over delay-Doppler could create interference-free subchannels, but the system spectrum efficiency would be very low; the paper instead proposes exploiting massive-antenna spatial super resolution.Source: A. Analysis of 3D Channel over the… · p. 16

B. Path Scheduling Algorithm

The algorithm schedules users’ effective data regions so their received angle-delay-Doppler regions do not overlap. It groups users by angle signatures, then separates groups in delay-Doppler while accounting for channel dispersion.

B. Path Scheduling Algorithm

  • Equal placement of nonzero effective symbols along Doppler can further optimize the data pattern to eliminate interference power.The paper contrasts compact effective-data blocks with optimized sparse blocks in Fig. 5.Source: B. Path Scheduling Algorithm · p. 18, Figure 5 · p. 18
  • Each user’s rectangular effective-data region maps to received locations on P angle-delay-Doppler layers, one for each path.The region’s delay and Doppler bounds determine the span of the received regions.Source: B. Path Scheduling Algorithm · pp. 18–19
  • Scheduling first separates users by angle signatures, then separates users with overlapping angle signatures in delay-Doppler.The goal is to prevent different users’ received effective-data regions from overlapping in the 3D cubic area.Source: B. Path Scheduling Algorithm · p. 19
  • Users with non-overlapping angle-signature sets share a delay-Doppler resource while occupying distinct angle grids.Within a group, users are assigned the same delay-Doppler region and their resulting 3D regions are disjoint.Source: B. Path Scheduling Algorithm · p. 19
  • Different user groups receive distinct delay-Doppler resources with guard gaps to mitigate channel dispersion along delay and Doppler.The guard gaps are Dτ and Dν.Source: B. Path Scheduling Algorithm · p. 20
  • Each user can send one pilot to estimate main and secondary channel gains, after which the 3D channels can be reconstructed across the cubic area.The reconstruction uses the recovered path parameters.Source: C. 3D Channel Reconstruction along UL · pp. 20–21

D. UL Data Detection over the Angle-Delay-Doppler Domain

UL detection collects the observations associated with each data symbol’s P scattering paths. It combines those signals using maximal-ratio combining and applies a classical detector to recover the data.

D. UL Data Detection over the Angle-Delay-Doppler Domain

  • The BS collects the P received-grid observations associated with a data symbol and combines them using maximal-ratio combining.Each path’s signal is weighted according to the MRC principle.Source: D. UL Data Detection over the… · p. 21
  • MRC uses a weighting factor for each scattering path and combines the P received signals into one received signal.The paper defines a SINR vector over the P paths and derives the combined signal’s optimized SINR.Source: D. UL Data Detection over the… · p. 22
  • After acquiring the optimal SINR, the transmitted data can be recovered with classical estimation algorithms such as the LS detector.Source: D. UL Data Detection over the… · p. 22

E. DL Data Detection within the Delay-Doppler Domain

The DL reuses the UL path schedule under channel reciprocity, assigning disjoint transmission regions to users. At each user’s effective-data grid, the BS applies beamforming to transmit the desired data.

E. DL Data Detection within the Delay-Doppler Domain

  • Under TDD reciprocity, the UL path schedule can be applied to DL so different users’ transmission resources are orthogonal over angle-delay-Doppler.The passage states that the UL scheduling results ensure the DL regions are disjoint.Source: E. DL Data Detection within the… · pp. 22–23
  • The user’s effective observation region along DL can be set to its UL transmission region, Dk.The DL transmitting data area is defined over the BS’s 3D transmission-resource space.Source: E. DL Data Detection within the… · pp. 22–23
  • The BS designs a beamforming vector for each user’s observation grid to transmit that user’s effective data.The beamformer can be designed under a minimum-MSE framework.Source: E. DL Data Detection within the… · p. 23

V. SIMULATION RESULTS

The simulations evaluate channel-parameter recovery and UL/DL data detection in high-mobility massive MIMO-OTFS settings. They report parameter-estimation behavior across mobility, observation count, and refinement, alongside detection limits associated with channel mismatch and interference.

Channel-parameter recovery

  • In Fig. 7, 3D-NOMP at 360 km/h performs only 1–2 dB lower than at 240 km/h; across velocities, higher speed corresponds to lower MSE curves for θk, νk, and hk.Source: §V · pp. 24–25, Figure 7 · p. 25
  • As Nt increases, MSEs for all estimated channel parameters decrease and converge, as more observations help distinguish Doppler effects.The evaluation fixes SNR at 20 dB.Source: §V · p. 25, Figure 8 · p. 26

Channel recovery with secondary channels

  • Ignoring secondary channels produces much higher main-channel recovery MSE, especially at high mobility, where secondary-channel influence increases with Doppler shift.The secondary-channel MSE is always higher than the main-channel MSE, which the authors attribute to the estimating-equation approximation.Source: §V · p. 26, Figure 10 · p. 27

Data detection

  • UL data-detection MSE decreases with SNR and then converges as interference within the data block becomes dominant at high SNR.Sparse scheduling has a lower MSE than dense data placement; greater separation between dominant received grids reduces power-leakage interference.Source: §V · p. 26, Figure 11 · p. 27
  • DL detection MSE is much lower with perfect channel knowledge than with mismatched channel gain, and it converges at very high SNR.The authors attribute the mismatch gap to inaccurate estimated 3D channels and the high-SNR convergence to interference.Source: Figure 12 · p. 27, §V · p. 27

VI. CONCLUSIONS

The conclusion presents a unified UL/DL PDMA scheme for massive MIMO-OTFS and describes its channel-estimation, scheduling, and communication stages. Its simulations are reported as demonstrating the scheme’s validity.

VI. CONCLUSIONS

  • The paper proposes a PDMA scheme for both UL and DL in massive MIMO-OTFS.The work studies a 3D UL channel and received-signal model in the angle-delay-Doppler domain.Source: §VI · p. 27
  • 3D-NOMP extracts UL channel parameters, followed by path scheduling that assigns angle-domain resources and keeps users’ observation regions non-overlapping.The scheduling design follows analysis of energy dispersion and power leakage in the 3D channels.Source: §VI · pp. 27–28
  • With scheduling, users map data to scheduled delay-Doppler grids and transmit simultaneously in one OTFS block without inter-user interference.Source: §VI · p. 28
  • At the BS, signals from desired 3D resource-space grids are collected separately for 3D channel recovery and MRC-based data detection.Source: §VI · p. 28
  • The paper constructs a low-complexity beamforming scheme for inter-user-interference-free DL communication and reports simulations demonstrating the unified scheme’s validity.Source: §VI · p. 28

APPENDIX

The appendix derives a received-signal expression from the time-varying channel model and discusses how the channel associated with a path relates to the received grid.

APPENDIX

  • The appendix derives the received-signal expression using the time-varying channel model.Source: APPENDIX · p. 28
  • The original channel associated with each path depends on the received-grid position, which the text identifies as difficult for further path scheduling.Source: APPENDIX · p. 28
  • The appendix then defines ΥN(x) and uses it to express the preceding relation in another form.Source: APPENDIX · p. 28
Loading 2003.08228v1…