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On the Suboptimality of Rate--Distortion-Optimal Compression: Fundamental Accuracy Limits for Distributed Localization

Amir Weiss

Abstract

We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate-distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation model with a Gaussian wideband waveform. Using the Gaussian RD test-channel model together with a Whittle spectral Fisher-information characterization, we obtain an explicit frequency-domain Cramér-Rao lower bound. A two-band, two-level specialization yields closed-form expressions and reveals a rate-induced regime change: RD-optimal compression under a squared-error distortion measure can eliminate localization-informative spectral content. A simple band-selective scheme can outperform RD compression by orders of magnitude at the same rate, motivating localization-aware compression for networked sensing and integrated sensing and communication systems.

On the Suboptimality of Rate--Distortion-Optimal Compression: Fundamental Accuracy Limits for Distributed Localization

Abstract

We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate-distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation model with a Gaussian wideband waveform. Using the Gaussian RD test-channel model together with a Whittle spectral Fisher-information characterization, we obtain an explicit frequency-domain Cramér-Rao lower bound. A two-band, two-level specialization yields closed-form expressions and reveals a rate-induced regime change: RD-optimal compression under a squared-error distortion measure can eliminate localization-informative spectral content. A simple band-selective scheme can outperform RD compression by orders of magnitude at the same rate, motivating localization-aware compression for networked sensing and integrated sensing and communication systems.
Paper Structure (9 sections, 2 theorems, 54 equations)

This paper contains 9 sections, 2 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. CRLB for RD-Optimally Compressed Signals
  4. CRLB via a spectral FI
  5. RD Is Not Localization-Optimal: A Two-Band Counterexample
  6. Two-band, two-level spectral model
  7. Closed-form CRLB under the two-band model
  8. Discussion and Outlook
  9. Derivation of the CRLB for the two-band model

Key Result

Theorem 1

Under the two-band, two-level spectrum model eq:two_level_psd--eq:flat_noise_psd_counter, RD-optimal compression eq:Bm_two_band and the symmetric setting eq:symmetric_rates, the FI rate for $\mathbf{p}\xspace\xspace$ based on $\widehat{\bm{\mathsf{x}}\xspace}(\cdot)$ over $[0,T]$ reads Consequently, for any unbiased estimator $\widehat{\mathbf{p}\xspace\xspace}$ of $\mathbf{p}\xspace\xspace$ based

Theorems & Definitions (3)

  • Theorem 1: Closed-form FI rate and CRLB under the two-band model
  • Remark 1
  • Lemma 1