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Fundamental Tradeoffs for ISAC Multiple Access in Finite-Blocklength Regime

Zhentian Zhang, Christos Masouros, Kai-Kit Wong, Jian Dang, Zaichen Zhang, Kaitao Meng, Farshad Rostami Ghadi, Mohammad Javad Ahmadi

TL;DR

The paper addresses the fundamental tradeoff between communication rate and sensing accuracy in uplink ISAC multi-access under finite blocklength constraints. It introduces a geometric view where the NMSE sensing error decomposes as NMSE = e_{min} G_{η}, linking sensing performance to SNR and codeword correlation via the Gram matrix G. Achievability and converse bounds are derived for the rate–sensing tradeoff, with a universal Cramér–Rao bound connecting channel estimation to practical sensing parameters, and 3GPP-based parameter examples illustrating applicability. Numerical results corroborate the theory, showing the impact of blocklength, antenna count, and sensing requirements on the feasible region for joint communication and sensing. Overall, the work provides a rigorous framework for designing ISAC systems with short packets and low latency by quantifying how codebook geometry constrains sensing and rate.

Abstract

This paper investigates the fundamental communication--sensing tradeoffs of uplink dual-functional integrated sensing and communication (ISAC) multiple access under finite blocklength (FBL) constraints. Unlike conventional asymptotic analyses, we explicitly account for the limitations under FBL constraints imposed by short packets and low-latency transmission. By examining the unbiased channel state sensing estimator, we establish a geometric decomposition of the sensing error, indicating that it is jointly determined by the signal-to-noise ratio and the correlation structure of the information codebook. This insight reveals how cross-correlation among active users in the codebook geometry fundamentally constrains dual-functional ISAC performance. Consequently, we derive achievability and converse bounds that characterize the tradeoff between communication code rate and sensing accuracy in the FBL regime, with the converse further bounded by Shannon capacity. Moreover, by treating channel state sensing as a high-level sensing objective, a universal Cramér--Rao bound is derived to link channel estimation accuracy to practical sensing parameters. Examples of parameter sensing are also provided based on 3GPP standard. Numerical results validate the theoretical analysis and demonstrate the impact of blocklength, antenna dimensions, and sensing requirements.

Fundamental Tradeoffs for ISAC Multiple Access in Finite-Blocklength Regime

TL;DR

The paper addresses the fundamental tradeoff between communication rate and sensing accuracy in uplink ISAC multi-access under finite blocklength constraints. It introduces a geometric view where the NMSE sensing error decomposes as NMSE = e_{min} G_{η}, linking sensing performance to SNR and codeword correlation via the Gram matrix G. Achievability and converse bounds are derived for the rate–sensing tradeoff, with a universal Cramér–Rao bound connecting channel estimation to practical sensing parameters, and 3GPP-based parameter examples illustrating applicability. Numerical results corroborate the theory, showing the impact of blocklength, antenna count, and sensing requirements on the feasible region for joint communication and sensing. Overall, the work provides a rigorous framework for designing ISAC systems with short packets and low latency by quantifying how codebook geometry constrains sensing and rate.

Abstract

This paper investigates the fundamental communication--sensing tradeoffs of uplink dual-functional integrated sensing and communication (ISAC) multiple access under finite blocklength (FBL) constraints. Unlike conventional asymptotic analyses, we explicitly account for the limitations under FBL constraints imposed by short packets and low-latency transmission. By examining the unbiased channel state sensing estimator, we establish a geometric decomposition of the sensing error, indicating that it is jointly determined by the signal-to-noise ratio and the correlation structure of the information codebook. This insight reveals how cross-correlation among active users in the codebook geometry fundamentally constrains dual-functional ISAC performance. Consequently, we derive achievability and converse bounds that characterize the tradeoff between communication code rate and sensing accuracy in the FBL regime, with the converse further bounded by Shannon capacity. Moreover, by treating channel state sensing as a high-level sensing objective, a universal Cramér--Rao bound is derived to link channel estimation accuracy to practical sensing parameters. Examples of parameter sensing are also provided based on 3GPP standard. Numerical results validate the theoretical analysis and demonstrate the impact of blocklength, antenna dimensions, and sensing requirements.
Paper Structure (13 sections, 18 equations, 3 figures, 1 table)

This paper contains 13 sections, 18 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Fundamental Tradeoff Analysis: Achievability and Converse
  3. System Configurations
  4. Bridging Sensing and Communication
  5. Derivation of the Tradeoff Achievability Bound
  6. Derivation of the Tradeoff Converse Bound
  7. From Channel Estimation to Parameter Estimation
  8. Universal Parameter Sensing Lower Bound
  9. Practical Sensing Examples by 3GPP Standard
  10. Numerical Results
  11. Illustration of Tradeoff
  12. Illustration of Practical Sensing Examples
  13. Conclusion

Figures (3)

  • Figure 1: Tradeoffs: Code rate achievability and converse bound versus SNR under fixed sensing error $e_{th}\in \{10^{-3},10^{-2},5\times 10^{-3},2\times 10^{-2},5\times 10^{-2}\}$, $k=16$ active users, $n=1000$ channel uses, $m=10$ receiving antenna.
  • Figure 2: Illustrations of how blocklength affects the communication--sensing tradeoff with $k=16$ active users, $m=10$ receiving antennas, and $\mathrm{SNR}=10\,\mathrm{dB}$.
  • Figure 3: Illustrations on parameter estimation MSE lower bounds including AoA, range and velocity. Detailed parameter setups are listed in Tab. \ref{['tab:sim_params']}.