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Sensing Integrated DFT-Spread OFDM Waveform and Deep Learning-powered Receiver Design for Terahertz Integrated Sensing and Communication Systems

Yongzhi Wu, Filip Lemic, Chong Han, Zhi Chen

arXiv:2109.14918v3eess.SP

TL;DR

THz ISAC must address channel and transceiver challenges to combine high-rate communication with accurate sensing. This paper proposes an SI-DFT-s-OFDM waveform and deep-learning receiver for sensing and data recovery. Simulations report lower PAPR, improved BER, accurate range and velocity estimation, and receiver robustness to impairments.

  • Problem

    THz ISAC waveform and receiver design must address varying channel delay spread, Doppler, phase noise, and THz transceiver impairments.

    Source: §I · pp. 1–2

  • Method

    The paper combines CP- and FGI-based SI-DFT-s-OFDM waveforms with deep-learning networks for sensing parameter estimation and data recovery.

    Source: B. Contributions · p. 3, §VI · p. 14

  • Results

    5 dB gain at the 10^-3 BER level versus OFDM; the FGI waveform also reports 174 Gbps mean achievable rate and 10^-5 BER at 20 dB SNR, with millimeter-level range and decimeter-per-second-level velocity accuracy.

    Source: §VI · p. 14

  • Takeaways & Limitations

    The proposed receiver is reported as more robust to Doppler effects, phase noise, and multi-path propagation than conventional ISAC systems and other DL methods.

    Source: §VI · p. 14

Abstract

from arXiv · show

Terahertz (THz) communications are envisioned as a key technology of next-generation wireless systems due to its ultra-broad bandwidth. One step forward, THz integrated sensing and communication (ISAC) system can realize both unprecedented data rates and millimeter-level accurate sensing. However, THz ISAC meets stringent challenges on waveform and receiver design to fully exploit the peculiarities of THz channel and transceivers. In this work, a sensing integrated discrete Fourier transform spread orthogonal frequency division multiplexing (SI-DFT-s-OFDM) system is proposed for THz ISAC, which can provide lower peak-to-average power ratio than OFDM and is adaptive to flexible delay spread of the THz channel. Without compromising communication capabilities, the proposed SI-DFT-s-OFDM realizes millimeter-level range estimation and decimeter-per-second-level velocity estimation accuracy. In addition, the bit error rate (BER) performance is improved by 5 dB gain at the $10^{-3}$ BER level compared with OFDM. At the receiver, a deep learning based ISAC receiver with two neural networks is developed to recover transmitted data and estimate target range and velocity, while mitigating the imperfections and non-linearities of THz systems. Extensive simulation results demonstrate that the proposed deep learning methods can realize mutually enhanced performance for communication and sensing, and is robust against Doppler effects, phase noise, and multi-target estimation.

I. INTRODUCTION

THz ISAC promises high data rates and accurate sensing, but its channels and transceivers pose distinctive waveform and receiver-design challenges. The paper proposes an SI-DFT-s-OFDM waveform and deep-learning receivers for joint sensing and communication.

I. INTRODUCTION

  • THz ISAC can combine communication and sensing to support high data rates and millimeter-level sensing, but propagation and transceiver impairments complicate system design.Challenges include varying delay spread, strong Doppler and phase noise, and the need for low-PAPR signals.Source: §I · pp. 1–2

A. Related Work

  • Prior work includes shared-waveform ISAC, but few attempts address higher integration levels in THz systems, while joint sensing and communication parameter estimation remains challenging.The paper targets a common waveform and a deep-learning receiver for THz ISAC.Source: A. Related Work · pp. 2–3

B. Contributions

  • The proposed SI-DFT-s-OFDM integrates sensing through data and reference blocks and uses a flexible guard interval to reduce CP overhead for varying THz delay spreads.The contribution passage reports tens of Gbps higher data rate and 3 dB lower PAPR than CP OFDM, and a 5 dB gain at the 10^-3 BER level versus OFDM.Source: B. Contributions · p. 3
  • SensingNet estimates range and velocity, with higher accuracy than other DL methods and lower computational complexity and improved sensing resolution than MUSIC.The network processes received reference signals and averages per-input predictions into a final estimate.Source: B. Contributions · p. 3
  • ComNet uses a two-level network to extract channel information from reference blocks and recover data symbols, achieving better BER under Doppler and phase noise than existing DL and conventional detectors.The received data symbols are combined with the first-level network output for recovery.Source: B. Contributions · p. 3
  • A joint SensingNet–ComNet receiver estimates sensing parameters and recovers data symbols in passive sensing, improving passive sensing accuracy over the single-task model.The paper presents this as joint parameter estimation and data detection.Source: B. Contributions · p. 3

II. THZ ISAC SYSTEM MODEL

The system uses a shared DFT-s-OFDM waveform for communication and sensing, with deep-learning receivers for the two tasks. It describes active and passive sensing modes and separate communication and sensing channel models.

A. System Framework

  • The transmitter uses DFT-s-OFDM with CP or FGI and inserts reference blocks for sensing parameter estimation and communication channel estimation.The shared waveform is intended to use time resources more efficiently than time division, where communication channel capacity is sacrificed.Source: A. System Framework · p. 3

B. Active and Passive Sensing

  • Active sensing estimates target locations from back-reflected signals, whereas passive sensing uses the received communication signal for joint sensing estimation and data detection.The system uses SensingNet for sensing and ComNet for communication, and can combine them for passive sensing.Source: B. Active and Passive Sensing · p. 4

C. Channel Models

  • The communication channel model accounts for LoS and NLoS paths, with path delays and time-varying responses influenced by Doppler shifts.The described channel has one LoS and Nr NLoS rays.Source: C. Channel Models · p. 4
  • The sensing channel models P targets as back-reflected paths, with delay and Doppler related to each target’s range and relative speed.The stated two-way propagation relations are τp = 2rp/c0 and νp = 2fcvp/c0.Source: C. Channel Models · pp. 4–5

III. SENSING INTEGRATED DFT-S-OFDM

The SI-DFT-s-OFDM waveform integrates sensing references into data frames and provides lower PAPR than OFDM. Its CP framing uses DFT-spread data blocks and reference blocks to support sensing and signal recovery.

III. SENSING INTEGRATED DFT-S-OFDM

A. SI-DFT-s-OFDM with Cyclic Prefix

  • Each data block is DFT-spread, mapped to consecutive subcarriers, and transformed into a time-domain block before a guard interval is added.A frame contains data and reference blocks, with reference blocks inserted at equidistant intervals.Source: A. SI-DFT-s-OFDM with Cyclic Prefix · p. 5
  • The CP is formed by copying the last samples of each block to its front to guard against multipath-induced inter-block interference.Reference blocks use constant-envelope Zadoff–Chu sequences as sensing and demodulation references.Source: A. SI-DFT-s-OFDM with Cyclic Prefix · pp. 5–6

B. SI-DFT-s-OFDM with Flexible Guard Interval

The flexible guard interval (FGI) adapts to varying THz channel delay spread without changing the data-block size. It replaces copied CP samples with a fixed sequence embedded in each block.

B. SI-DFT-s-OFDM with Flexible Guard Interval

  • FGI is formed from a fixed sequence inserted into each data block, whose tail becomes an approximate cyclic prefix within the IDFT output.The fixed sequence is generated from the tail of the reference block.Source: B. SI-DFT-s-OFDM with Flexible Guard… · p. 6
  • At fixed block size, adjusting the data-symbol count and fixed-sequence length accommodates different guard-interval requirements without adding a separate CP operation.This design addresses fluctuating delay spread while avoiding CP-length changes that alter symbol duration and make frame settings incompatible.Source: B. SI-DFT-s-OFDM with Flexible Guard… · p. 6

IV. DEEP LEARNING BASED RECEIVER FOR THZ ISAC

The receiver preprocessing models each received block using a channel with path gains, delays, and Doppler shifts, while accounting for phase noise and AWGN. With FGI, the receiver derives frequency-domain signals for sensing and data detection, although long-delay paths may cause weak inter-block interference.

A. Signal Pre-processing

  • The unified channel model represents each propagation path by its complex gain, delay, and Doppler shift.The model covers active and passive sensing received blocks.Source: A. Signal Pre-processing · p. 6
  • The noisy received block includes phase noise modeled as a diagonal matrix and an additive white Gaussian noise vector.The phase-noise process is modeled as a Wiener process.Source: A. Signal Pre-processing · p. 7
  • Under FGI, the received samples may retain weak inter-block interference from propagation paths with long delay.The receiver applies an N-point DFT and subcarrier demapping to obtain frequency-domain signals for sensing and data detection.Source: A. Signal Pre-processing · p. 7

B. Analysis of Sensing and Communication Tasks

The receiver uses reference blocks for sensing and communication processing. Sensing estimates delay and Doppler from the estimated channel response, while communication uses reference blocks for channel estimation and frequency-domain equalization.

B. Analysis of Sensing and Communication Tasks

  • Constant-envelope reference blocks support channel-estimation-based sensing, and the LS estimator does not increase noise variance.The estimated sensing channel response is used as the sensing processing matrix.Source: B. Analysis of Sensing and… · p. 7
  • The sensing task estimates target delay and Doppler from the estimated sensing channel response using spectral-estimation methods such as MUSIC or a DFT-based method.These estimates are used to calculate range and velocity.Source: B. Analysis of Sensing and… · p. 7
  • At the communication receiver, reference blocks support frequency-domain equalization using zero-forcing or minimum mean square error methods.The receiver also implements IDFT/DFT operations, channel estimation, and channel equalization.Source: B. Analysis of Sensing and… · p. 7
  • The deep-learning receiver is designed to estimate sensing parameters and recover communication data while addressing limitations of conventional signal processing under nonlinear distortions such as Doppler and phase noise.Source: B. Analysis of Sensing and… · p. 7

C. Sensing Neural Network for Sensing Parameter Estimation

SensingNet estimates range and velocity from received reference signals using separate block-wise and subcarrier-wise input processing. For range estimation, it predicts a range vector from each reference-signal block and averages the predictions.

C. Sensing Neural Network for Sensing Parameter Estimation

  • SensingNet uses MRB block-wise inputs for range estimation and L subcarrier-wise inputs for velocity estimation, with shared dense layers and an average output.The final estimate is formed by averaging the predictions from the inputs.Source: C. Sensing Neural Network for Sensing… · pp. 7–8

1) Range Estimation:

  • Each range input contains the real and imaginary parts of one received reference-signal block, flattened before five dense layers extract delay information and predict P ranges.The dense layers have 500, 250, 120, 60, and P neurons; batch normalization is applied at each layer.Source: 1) Range Estimation · p. 8
  • The range network uses ReLU in its first four dense layers, sigmoid in the last layer, and supervised MSE training against the true range vector.The sigmoid maps the last-layer output to [0, 1].Source: 1) Range Estimation · p. 8

2) Velocity Estimation:

SensingNet estimates velocity through subcarrier-wise processing, while the first level of ComNet derives data-block channel information from reference blocks. The sensing models are trained on a parameter range and require retraining when channel parameters fall outside it.

2) Velocity Estimation:

  • The SensingNet velocity model processes received reference signals subcarrier-wise, predicts a velocity vector for each input, and averages those vectors.Its final dense layer uses tanh, and training minimizes MSE against the true velocity vector.Source: 2) Velocity Estimation · p. 8
  • SensingNet must be retrained when channel parameters fall outside the randomly generated training range, although training can be performed offline.Range labels are mapped to [0, 1] and velocity labels to [-1, 1].Source: 2) Velocity Estimation · pp. 8–9

1) Network Structure of the First Level:

  • ComNet’s first level processes each received reference-signal subcarrier and uses five dense layers to extract Doppler features and estimate channel frequency response at data blocks.Its final dense layer outputs real and imaginary channel-response values for the data signals.Source: 1) Network Structure of the First Level · p. 9
  • The first-level ComNet outputs are reshaped and concatenated into two matrices, with each output split into real and imaginary parts.The final dense layer uses tanh, while the other dense layers use ReLU.Source: 1) Network Structure of the First Level · p. 9

2) Network Structure of the Second Level:

ComNet combines its first-level output with received data symbols before the second-level network estimates transmitted data. The paper also describes a shared-layer joint network and weighted training across data detection, range estimation, and velocity estimation.

2) Network Structure of the Second Level:

  • The second ComNet level concatenates the first-level output with received data symbols, then processes the combined inputs block-wise.The inputs include the received data symbols and the first-level output for the corresponding block.Source: 2) Network Structure of the Second Level · p. 9
  • The second-level network uses dense layers to recover data vectors, and ComNet can also be applied to OFDM because DFT-s-OFDM is compatible with OFDM.The final ComNet output contains MDB recovered data vectors.Source: 2) Network Structure of the Second Level · p. 9
  • ComNet training divides each frame’s L × MDB symbols into 1/8L groups, predicting every 8MDB symbols with an independently trained model before concatenating the outputs.The receiver regresses QAM data symbols rather than classifying transmitted bits.Source: 2) Network Structure of the Second Level · pp. 9–10
  • Sensing loss falls by three orders of magnitude after 40 epochs, while communication loss falls by two orders after 80 epochs.These convergence results are reported for the proposed deep learning methods.Source: 2) Network Structure of the Second Level · p. 10
  • The joint ISACNet option shares layers to capture channel knowledge and reduce parameters and overfitting risk, while task-specific layers optimize sensing and communication separately.Its weighted loss assigns separate weights to data detection, range estimation, and velocity estimation.Source: 2) Network Structure of the Second Level · p. 10
  • The task-relatedness measure uses task accuracy and weight-space distance, with a small constant preventing division by zero and a parameter controlling tanh decay.The tanh function bounds the measure to (0, 1).Source: 2) Network Structure of the Second Level · p. 10

V. SIMULATION RESULTS

The simulations evaluate the proposed waveform against OFDM and report lower PAPR for SI-DFT-s-OFDM. They also describe the dataset generation and simulation-parameter sources.

V. SIMULATION RESULTS

  • The simulations compare SI-DFT-s-OFDM and OFDM against conventional signal processing methods, with parameters listed in Table I and link-budget inputs referenced to.Subcarrier spacing is set to 15 × 2^n kHz for compatibility with 4G and 5G numerology.Source: §V · p. 10, Table I · p. 10

A. Generation of the Dataset

  • The 50k-sample training and 5k-sample test datasets use random data, channel paths and speeds, with AWGN and phase noise included.Training SNR is fixed at 25 dB; channel speeds are sampled from [-100, 100] km/h.Source: A. Generation of the Dataset · p. 10

B. PAPR

  • At a 1% CCDF, SI-DFT-s-OFDM PAPR is approximately 2.6 dB lower than OFDM with 64 subcarriers and 3.2 dB lower with 1024.SI-DFT-s-OFDM with FGI has slightly lower PAPR than with CP.Source: B. PAPR · p. 11, Figure 6 · p. 11

C. Waveform Comparison

The waveform comparison reports improved high-SNR BER with SI-DFT-s-OFDM and higher achievable rates with FGI in the tested delay-spread setting. The sensing evaluations report millimeter-level range and decimeter-per-second-level velocity accuracy, with method-specific strengths and limits.

C. Waveform Comparison

  • With MMSE equalization, SI-DFT-s-OFDM improves BER by more than 5 dB at the 10^-3 BER level versus OFDM.With ZF equalization, SI-DFT-s-OFDM has higher BER below 15 dB SNR but performs better at high SNR.Source: C. Waveform Comparison · p. 11
  • At 5% symbol-duration delay spread, FGI supports 30 Gbps higher achievable rate than CP; its mean rate is 174 Gbps, approximately 14 Gbps above CP.The CP duration is fixed while FGI duration adjusts to channel delay spread.Source: C. Waveform Comparison · p. 11, Figure 8 · p. 11

D. DL-based Sensing Parameter Estimation

E. DL-based Data Detection

The results report waveform and receiver gains across communication and sensing evaluations, including under Doppler and phase noise. The shared ISACNet model reduces parameter count while improving range estimation, and the conclusion identifies higher-THz operation as a boundary requiring further waveform improvement.

E. DL-based Data Detection

  • With FGI, ComNet gains 2 dB at 10^-3 BER over MMSE under Doppler and outperforms MMSE under tested phase noise, at greater runtime.The conclusion also reports ComNet performs better than MMSE under Doppler and phase-noise effects.Source: E. DL-based Data Detection · pp. 12–13, §VI · p. 14
  • Parameter or channel-statistics variation is reported as tolerable without retraining, but a changed channel-model type requires a different offline-trained DL model.The paper describes channel-model type changes as rare in practice.Source: E. DL-based Data Detection · p. 13

F. Two-Task DL-based Receiver for Passive Sensing

VI. CONCLUSION

  • The conclusion reports 3.2 dB lower PAPR and 5 dB gain at 10^-3 BER versus OFDM, alongside a 174 Gbps mean FGI rate and millimeter-level range and decimeter-per-second-level velocity accuracy.The conclusion also reports 10^-5 BER at 20 dB SNR for SI-DFT-s-OFDM with FGI.Source: §VI · p. 14
  • At higher THz frequencies, lower PA saturation output, stronger Doppler shifts and atmospheric attenuation remain challenges, so the waveform needs further improvement and robustness.Source: §VI · p. 14

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