中文摘要：

该文针对随机布局多天线信号联合时差估计Cramer—Rao下界（CRLB）开展研究，在深入研究多路联合参数估计和经典时差估计算法的基础上，首先建立信号模型，进而得到频域的联合概率密度函数，然后推导出Fisher信息矩阵和Cramer—Rao下界的解析表达式。最后，对结果进行了讨论分析，并同两路时差估计Cramer—Rao下界进行了对比。结果表明，多天线联合时差估计能够利用各信号的相同信息，有效提升时差估计性能，而且在低信噪比条件下估计性能改善更为明显。此外，可以看到增加天线数目不可能无限降低时差估计Cramer—Rao下界，其受待估时差的两路信号信噪比限制。

英文摘要：

In this paper, the Cramer-Rao lower bound （CRLB） for time delay estimation between signals received at multiple randomly distributed antennas is considered. Fourier Transform of the received signals is used to derive the proba- bility density function （PDF） in the frequency domain. The Fisher information matrix （ FIM ） is then deduced and the CRLB is obtained in the end. Furthermore, the result is discussed in two special cases and is compared with the CRLB in two-antenna case. It is remarkable that the estimation accuracy increases as the number of antenna elements increases. Mo- reover, it is shown that that increasing the number of results in a small advantage at high SNR values. However, the advan- tage becomes more significant for low SNR conditions. Besides, the CRLB between two signals cannot decrease infinitely, which is limited by the SNRs of the antenna pair, even by employing more antennas.