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On the BER vs. Bandwidth-Efficiency Trade-offs in Windowed OTSM Dispensing with Zero-Padding

Zeping Sui, Hongming Zhang, Hien Quoc Ngo, Michail Matthaiou, Lajos Hanzo

TL;DR

This paper addresses the BER–bandwidth-efficiency trade-off in windowed OTSM systems operating under strong phase noise by discarding zero-padding and employing practical smooth windows. It derives the DS-domain input-output relation using transform connections among DS, TF, and TD domains, and develops a closed-form BER upper bound based on CPEP/UPEP analyses in the presence of PHN. By evaluating several window functions (Rectangular, Hamming, Hanning, Blackman, Bartlett-Hann), it shows that smoother windows reduce out-of-band emission (OOBE) at the cost of some BER performance, enabling a tunable BER–OOBE trade-off; the BER upper bound is tight at moderate-to-high $SNR$. The results demonstrate that windowed OTSM can achieve spectral efficiency gains without padding, while maintaining PHN resilience, with practical implications for 6G waveform design and spectrum sharing.

Abstract

An orthogonal time sequency multiplexing (OTSM) scheme using practical signaling functions is proposed under strong phase noise (PHN) scenarios. By utilizing the transform relationships between the delay-sequency (DS), time-frequency (TF) and time-domains, we first conceive the DS-domain input-output relationship of our OTSM system, where the conventional zero-padding is discarded to increase the spectral efficiency. Then, the unconditional pairwise error probability is derived, followed by deriving the bit error ratio (BER) upper bound in closed-form. Moreover, we compare the BER performance of our OTSM system based on several practical signaling functions. Our simulation results demonstrate that the upper bound derived accurately predicts the BER performance in the case of moderate to high signal-to-noise ratios (SNRs), while harnessing practical window functions is capable of attaining an attractive out-of-band emission (OOBE) vs. BER trade-off.

On the BER vs. Bandwidth-Efficiency Trade-offs in Windowed OTSM Dispensing with Zero-Padding

TL;DR

This paper addresses the BER–bandwidth-efficiency trade-off in windowed OTSM systems operating under strong phase noise by discarding zero-padding and employing practical smooth windows. It derives the DS-domain input-output relation using transform connections among DS, TF, and TD domains, and develops a closed-form BER upper bound based on CPEP/UPEP analyses in the presence of PHN. By evaluating several window functions (Rectangular, Hamming, Hanning, Blackman, Bartlett-Hann), it shows that smoother windows reduce out-of-band emission (OOBE) at the cost of some BER performance, enabling a tunable BER–OOBE trade-off; the BER upper bound is tight at moderate-to-high . The results demonstrate that windowed OTSM can achieve spectral efficiency gains without padding, while maintaining PHN resilience, with practical implications for 6G waveform design and spectrum sharing.

Abstract

An orthogonal time sequency multiplexing (OTSM) scheme using practical signaling functions is proposed under strong phase noise (PHN) scenarios. By utilizing the transform relationships between the delay-sequency (DS), time-frequency (TF) and time-domains, we first conceive the DS-domain input-output relationship of our OTSM system, where the conventional zero-padding is discarded to increase the spectral efficiency. Then, the unconditional pairwise error probability is derived, followed by deriving the bit error ratio (BER) upper bound in closed-form. Moreover, we compare the BER performance of our OTSM system based on several practical signaling functions. Our simulation results demonstrate that the upper bound derived accurately predicts the BER performance in the case of moderate to high signal-to-noise ratios (SNRs), while harnessing practical window functions is capable of attaining an attractive out-of-band emission (OOBE) vs. BER trade-off.
Paper Structure (14 sections, 28 equations, 4 figures)

This paper contains 14 sections, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmitter Description of Non-ZP OTSM Relying on Smooth Windowing
  4. PHN-contaminated Received Signals
  5. Performance Analysis and Smooth Windows
  6. Analysis of Error Performance
  7. Smooth Windows
  8. Rectangular Window
  9. Hamming Window
  10. Hanning Window
  11. Blackman Window
  12. Bartlett-Hann Window
  13. Simulation Results
  14. Conclusions

Figures (4)

  • Figure 1: Illustration of the LDPC-coded OTSM system with practical windows and PHN, where $\Pi$ and $\Pi^{-1}$ respresent the interleaver and deinterleaver, respectively.
  • Figure 2: BER performance and the upper bound of OTSM systems using different windows.
  • Figure 3: OOBE performance of different window functions based OTSM systems.
  • Figure 4: BER performance of different windows for OTSM systems invoking an LMMSE detector in the face of white phase noise.