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Jutted BMOCZ for Non-Coherent OFDM

Parker Huggins, Alphan Sahin

Abstract

In this work, we propose a zero constellation for binary modulation on conjugate-reciprocal zeros (BMOCZ), called jutted BMOCZ (J-BMOCZ), and study its application to non-coherent orthogonal frequency division multiplexing (OFDM). With J-BMOCZ, we introduce asymmetry to the zero constellation for Huffman BMOCZ, which removes ambiguity at the receiver under a uniform rotation of the zeros. The asymmetry is controlled by the magnitude of "jutted" zeros and enables the receiver to estimate zero rotation using a simple cross-correlation. The proposed method, however, leads to a natural trade-off between asymmetry and zero stability. Accordingly, we introduce a reliability metric to measure the stability of a polynomial's zeros under an additive perturbation of the coefficients, and we apply the metric to optimize the J-BMOCZ zero constellation parameters. We then combine the advantages of J-BMOCZ and Huffman BMOCZ to design a hybrid waveform for OFDM with BMOCZ (OFDM-BMOCZ). The pilot-free waveform enables blind synchronization/detection and has a fixed peak-to-average power ratio that is independent of the message. Finally, we assess the proposed scheme through simulation and demonstrate non-coherent OFDM-BMOCZ using low-cost software-defined radios.

Jutted BMOCZ for Non-Coherent OFDM

Abstract

In this work, we propose a zero constellation for binary modulation on conjugate-reciprocal zeros (BMOCZ), called jutted BMOCZ (J-BMOCZ), and study its application to non-coherent orthogonal frequency division multiplexing (OFDM). With J-BMOCZ, we introduce asymmetry to the zero constellation for Huffman BMOCZ, which removes ambiguity at the receiver under a uniform rotation of the zeros. The asymmetry is controlled by the magnitude of "jutted" zeros and enables the receiver to estimate zero rotation using a simple cross-correlation. The proposed method, however, leads to a natural trade-off between asymmetry and zero stability. Accordingly, we introduce a reliability metric to measure the stability of a polynomial's zeros under an additive perturbation of the coefficients, and we apply the metric to optimize the J-BMOCZ zero constellation parameters. We then combine the advantages of J-BMOCZ and Huffman BMOCZ to design a hybrid waveform for OFDM with BMOCZ (OFDM-BMOCZ). The pilot-free waveform enables blind synchronization/detection and has a fixed peak-to-average power ratio that is independent of the message. Finally, we assess the proposed scheme through simulation and demonstrate non-coherent OFDM-BMOCZ using low-cost software-defined radios.

Paper Structure

This paper contains 26 sections, 1 theorem, 53 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contributions
  3. System Model
  4. Preliminaries on Binary MOCZ
  5. Subcarrier Mappings for OFDM-BMOCZ
  6. Problem Statement: Zero Rotation under Timing Offset
  7. Jutted BMOCZ
  8. Template-based Estimation of Zero Rotation
  9. Reliability Metric for Measuring Zero Stability
  10. Optimization of Zero Constellation Parameters
  11. Pilot-free OFDM Framework
  12. Hybrid Packet Structure
  13. Coarse Synchronization and CFO Estimation
  14. Implementation of Residual TO Estimation
  15. PAPR Analysis with FM
  16. ...and 11 more sections

Key Result

Proposition 1

Let $K\geq2$ and $R,\zeta>1$. A sufficient condition for $\mathop{\mathrm{arg\,max}}\limits_{\omega\in[0,2\pi)}A_{\mathrm{J}}(\mathrm e^{j\omega})=0$ is where $a\triangleq\zeta R+\zeta^{-1}R^{-1}$ and $b\triangleq R+R^{-1}$.

Figures (11)

  • Figure 1: Proposed JBMOCZ zero pattern for $K=8$, $R=1.176$, and $\zeta=1.15$. (a) Full zero constellation with $2K$ zero positions. (b) Transmitted zeros corresponding to the message $\boldsymbol{\rm{b}}=(1,0,1,1,1,0,0,1)$. (c) Received zeros rotated by $\phi=(12/7)\theta_K$ radians. (d) Received zeros after correcting $\phi$ via \ref{['eq:template_corr']}, which exactly correspond to the transmitted message.
  • Figure 2: Example JBMOCZ template transforms for $K=16$ and $R=1.093$.
  • Figure 3: JBMOCZ zero perturbation at $E_\mathrm{b}/N_0=10$ dB with $K=8$, $R=1.176$, and $\zeta=1.15$. The zeros are shaded according to their stability estimated via \ref{['eq:zero_capacity']} as $\hat{C}_k=C_k/N$, where $N=1024$.
  • Figure 4: Design curves for JBMOCZ parameter selection showing the minimum zero stability identified via \ref{['eq:seq_capacity']} as a function of the radius and asymmetry factor.
  • Figure 5: Proposed hybrid OFDM-BMOCZ waveform with repeated Huffman BMOCZ preamble for coarse time synchronization and CFO estimation, JBMOCZ symbol for residual TO estimation, and Huffman BMOCZ payload. Observe that, without correction, the residual TO (and hence the DFT window) evolves with the OFDM symbol index.
  • ...and 6 more figures

Theorems & Definitions (8)

  • Definition 1
  • Example 1
  • Example 2
  • Example 3
  • Remark 1
  • Proposition 1
  • Remark 2
  • proof