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arXiv 2501.01632cs.ITmath.IT
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固定信道状态的通信与贝叶斯估计的集成

Integrated Communication and Bayesian Estimation of Fixed Channel States

Daewon Seo

AI总结:

本文研究集成感知与通信系统中信息率与精确均方误差的折中,提出利用渐近紧致BCRB分析刻画一般信道下的完整性能极限,并通过方差估计示例进行数值验证。

摘要:

本工作研究集成感知与通信(ISAC)系统的信息论性能极限,其中感知目标是估计随机连续状态。考虑均方误差(MSE)作为估计性能指标,文献中广泛使用贝叶斯Cramér-Rao下界(BCRB)作为MSE的代理;然而,除限制性分布外,BCRB通常即使在渐近意义上也不紧致。为此,我们改用渐近紧致BCRB(ATBCRB)分析(BCRB的一种近期变体)来刻画信息率与精确MSE之间的完整折中。只要满足正则条件,我们的刻画适用于一般信道,且证明依赖于恒定成分码及基于该码的ATBCRB分析。我们还在频谱感知场景中常见的方差估计示例中对该折中进行了数值评估。

英文摘要:

This work studies an information-theoretic performance limit of an integrated sensing and communication (ISAC) system where the goal of sensing is to estimate a random continuous state. Considering the mean-squared error (MSE) for estimation performance metric, the Bayesian Cramér-Rao lower bound (BCRB) is widely used in literature as a proxy of the MSE; however, the BCRB is not generally tight even asymptotically except for restrictive distributions. Instead, we characterize the full tradeoff between information rate and the exact MSE using the asymptotically tight BCRB (ATBCRB) analysis, a recent variant of the BCRB. Our characterization is applicable for general channels as long as the regularity conditions are met, and the proof relies on constant composition codes and ATBCRB analysis with the codes. We also perform a numerical evaluation of the tradeoff in a variance estimation example, which commonly arises in spectrum sensing scenarios.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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