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ISAC Super-Resolution Receivers: The Effect of Different Dictionary Matrices

Iman Valiulahi, Christos Masouros, Athina P. Petropulu

Abstract

This paper presents an off-the-grid estimator for ISAC systems using lifted atomic norm minimization (LANM). The main challenge in the ISAC systems is the unknown nature of both transmitted signals and radar-communication channels. We use a known dictionary to encode transmit signals and show that LANM can localize radar targets and decode communication symbols when the number of observations is proportional to the system's degrees of freedom and the coherence of the dictionary matrix. We reformulate LANM using a dual method and solve it with semidefinite relaxation (SDR) for different dictionary matrices to reduce the number of observations required at the receiver. Simulations demonstrate that the proposed LANM accurately estimates communication data and target parameters under varying complexity by selecting different dictionary matrices.

ISAC Super-Resolution Receivers: The Effect of Different Dictionary Matrices

Abstract

This paper presents an off-the-grid estimator for ISAC systems using lifted atomic norm minimization (LANM). The main challenge in the ISAC systems is the unknown nature of both transmitted signals and radar-communication channels. We use a known dictionary to encode transmit signals and show that LANM can localize radar targets and decode communication symbols when the number of observations is proportional to the system's degrees of freedom and the coherence of the dictionary matrix. We reformulate LANM using a dual method and solve it with semidefinite relaxation (SDR) for different dictionary matrices to reduce the number of observations required at the receiver. Simulations demonstrate that the proposed LANM accurately estimates communication data and target parameters under varying complexity by selecting different dictionary matrices.

Paper Structure

This paper contains 7 sections, 1 theorem, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Sensing Vectors with Independent Components.
  4. Subsampled Orthogonal Transforms:
  5. Subsampled Tight or Continuous Frames:
  6. NUMERICAL Results
  7. Conclusion

Key Result

Theorem 1

Theorem maintheorem states that for the linear system in (1) and its sampled version in (2), if the unknown waveforms can be expressed as $\bm{x}_{k} = \bm{D}\bm{h}_{k}$, where $\bm{D}$ satisfies Assumption assum1 and $\bm{h}_{k}$ follows Assumption assumption2, and if the shifts meet the minimum se

Figures (4)

  • Figure 1: System model.
  • Figure 2: The absolute value of the dual polynomial is shown in the $(\phi, \rho)$ and $(\tau, v)$ domains in Figs. \ref{['fig.bound45']} and \ref{['fig.bound5']}, respectively. Blue stars indicate the estimated radar parameters.
  • Figure 3: The NMSE and SER of the proposed estimator, using different compression matrices, are compared with ANM as a benchmark in Figs. \ref{['fig.bound451']} and \ref{['fig.bound52']}, respectively.
  • Figure 4: The success rate of LANM versus the number of targets and the subspace dimension $T$ when the number of measurements changes in Figs. \ref{['fig.bound412']}, \ref{['fig.bound412']}, and \ref{['fig.bound124']} for Hadamard, Fourier transform, and Gaussian matrices, respectively, for $k=2$.

Theorems & Definitions (1)

  • Theorem 1