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Sparse Zero Correlation Zone Arrays for Training Design in Spatial Modulation Systems

Cheng-Yu Pai, Zilong Liu, Chao-Yu Chen

Abstract

This paper presents a novel training matrix design for spatial modulation (SM) systems, by introducing a new class of two-dimensional (2D) arrays called sparse zero correlation zone (SZCZ) arrays. An SZCZ array is characterized by a majority of zero entries and exhibits the zero periodic auto- and cross-correlation zone properties across any two rows. With these unique properties, we show that SZCZ arrays can be effectively used as training matrices for SM systems. Additionally, direct constructions of SZCZ arrays with large ZCZ widths and controllable sparsity levels based on 2D restricted generalized Boolean functions (RGBFs) are proposed. Compared with existing training schemes, the proposed SZCZ-based training matrices have larger ZCZ widths, thereby offering greater tolerance for delay spread in multipath channels. Simulation results demonstrate that the proposed SZCZ-based training design exhibits superior channel estimation performance over frequency-selective fading channels compared to existing alternatives.

Sparse Zero Correlation Zone Arrays for Training Design in Spatial Modulation Systems

Abstract

This paper presents a novel training matrix design for spatial modulation (SM) systems, by introducing a new class of two-dimensional (2D) arrays called sparse zero correlation zone (SZCZ) arrays. An SZCZ array is characterized by a majority of zero entries and exhibits the zero periodic auto- and cross-correlation zone properties across any two rows. With these unique properties, we show that SZCZ arrays can be effectively used as training matrices for SM systems. Additionally, direct constructions of SZCZ arrays with large ZCZ widths and controllable sparsity levels based on 2D restricted generalized Boolean functions (RGBFs) are proposed. Compared with existing training schemes, the proposed SZCZ-based training matrices have larger ZCZ widths, thereby offering greater tolerance for delay spread in multipath channels. Simulation results demonstrate that the proposed SZCZ-based training design exhibits superior channel estimation performance over frequency-selective fading channels compared to existing alternatives.

Paper Structure

This paper contains 12 sections, 5 theorems, 55 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries and Definitions
  3. 2D Restricted Generalized Boolean Functions
  4. Spatial Modulation
  5. Training Framework for SM Systems
  6. Training Matrix Design
  7. Proposed SZCZ Training Matrix for SM System
  8. Simulation Results
  9. Conclusion
  10. Proof of Theorem \ref{['thm:SZCZ_1']}
  11. Proof of Corollary \ref{['crly:SZCZ_CZCP']}
  12. Proof of Theorem \ref{['thm:SZCZ']}

Key Result

Lemma 1

According to (eq:C2), one can attain the minimum NMSE for the channel estimation if and only if the SM training matrix is an $(N,L,Z,\mathcal{S})$-SZCZ array with $Z\geq \lambda$ and $\mathcal{S}=(L-M)/L$.

Figures (6)

  • Figure 1: Generic transmitter structure of SC-SM systems.
  • Figure 2: A training-based multiple-antenna transmission structure.
  • Figure 3: PACFs of ${\bm C}_0$ and PCCFs of ${\bm C}_0$ and ${\bm C}_3$ in Example \ref{['eg:SZCZ_CZCP']}.
  • Figure 4: PACFs of ${\bm C}_0$ and PCCFs of ${\bm C}_0$ and ${\bm C}_3$ in Example \ref{['eg:SZCZ']}.
  • Figure 5: Comparison of NMSE performance for different training matrices with $N_t=4$ and $N_r=4$.
  • ...and 1 more figures

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Example 1
  • Remark 1
  • Example 2
  • Lemma 1
  • Definition 3
  • Remark 2
  • Theorem 1
  • Remark 3
  • ...and 7 more