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Interference-Precancelled Pilot Design for LMMSE Channel Estimation of GFDM

Ching-Lun Tai, Borching Su, Cai Jia

TL;DR

A pilot design framework with linear minimum mean square error (LMMSE) channel estimation for GFDM is formulated, and a novel pilot design to achieve interference precancellation during pilot generation with the fixed transmit sample values at selected frequency bins is proposed.

Abstract

Generalized frequency division multiplexing (GFDM) is a promising candidate waveform for next-generation wireless communication systems. However, GFDM channel estimation is still challenging due to the inherent interference. In this paper, we formulate a pilot design framework with linear minimum mean square error (LMMSE) channel estimation for GFDM, and propose a novel pilot design to achieve interference precancellation during pilot generation with the fixed transmit sample values at selected frequency bins. Numerical results demonstrate that the proposed method reduces the channel estimation mean square error and the symbol error rate (SER) in high signal-to-noise ratio (SNR) regions, compared with the conventional methods.

Interference-Precancelled Pilot Design for LMMSE Channel Estimation of GFDM

TL;DR

A pilot design framework with linear minimum mean square error (LMMSE) channel estimation for GFDM is formulated, and a novel pilot design to achieve interference precancellation during pilot generation with the fixed transmit sample values at selected frequency bins is proposed.

Abstract

Generalized frequency division multiplexing (GFDM) is a promising candidate waveform for next-generation wireless communication systems. However, GFDM channel estimation is still challenging due to the inherent interference. In this paper, we formulate a pilot design framework with linear minimum mean square error (LMMSE) channel estimation for GFDM, and propose a novel pilot design to achieve interference precancellation during pilot generation with the fixed transmit sample values at selected frequency bins. Numerical results demonstrate that the proposed method reduces the channel estimation mean square error and the symbol error rate (SER) in high signal-to-noise ratio (SNR) regions, compared with the conventional methods.

Paper Structure

This paper contains 9 sections, 1 theorem, 16 equations, 4 figures.

Table of Contents

  1. Introduction
  2. GFDM System Model
  3. Proposed Method
  4. Pilot Design and LMMSE Channel Estimation
  5. Proposed Choice of Parameters
  6. Simulation
  7. Parameter Settings
  8. Simulation Results
  9. Conclusion

Key Result

Theorem 1

Given the received samples ${\bf y}$ as defined in (eq:y), the LMMSE estimated channel $\hat{{\bf h}}_{\footnotesize{\hbox{LMMSE}}}$ can be derived as with where ${\bf X}_r=\hbox{diag}({\bf W}_D{\bf A}{\bf S}{\bf d}_r)$, $\mathbf{\Sigma}_{hh}=\mathop{\mathrm{E}}\nolimits\{{\bf h}{\bf h}^H\}=\hbox{diag}({\bf p})$, and $\mathbf{\Sigma}_{\Psi \Psi}=({\bf F}_N \mathbf{\Sigma}_{hh} {\bf F}_N^H)({\bf

Figures (4)

  • Figure 1: GFDM system model with channel estimation ("r/m" stands for "remove".)
  • Figure 2: Pilot insertion and frequency bin deployment, with green solid circles denoting the elements in ${\bf d}_p$, yellow solid circles the elements in ${\bf d}_d$, red solid circles and squares the chosen frequency bins of ${\bf x}_f$ and ${\bf y}_f$, orange circles and squares the rest of frequency bins of ${\bf x}_f$ and ${\bf y}_f$, where ${\bf y}_f=\mathop{\mathrm{diag}}\nolimits({\bf F}_N{\bf h}){\bf x}_f+{\bf W}_D{\bf w}$, and the relationship between ${\bf x}_f$ and ${\bf y}_f$ benefiting the frequency-domain channel estimation
  • Figure 3: Performance comparison for $K=8,M=128$
  • Figure 4: Performance comparison for $K=16,M=64$

Theorems & Definitions (2)

  • Theorem 1
  • proof