全相位FFT测相方差及其Cramer-Rao下限  

Variance of All-Phase FFT Measuring Phases and Its Cramer-Rao Lower Bound

作　　者：黄翔东[1] 王博[1] 杜宇彬[1] 王兆华[1] 

机构地区：[1]天津大学电子信息工程学院,天津300072

出　　处：《数据采集与处理》2013年第2期160-165,共6页Journal of Data Acquisition and Processing

基　　金：国家自然科学基金(61271069)重点资助项目;国家重点基础研究发展计划("九七三"计划)(2010CB327806)资助项目

摘　　要：为揭示全相位FFT(All-phase FFT,apFFT)相位测量法相比于现有方法精度提高的内在原因,在前人基础上,结合谱泄漏分布特征及其参数估计理论,推导出了适用于apFFT测相的两未知参数估计模型的克拉罗下限(Cramer-Rao lower bound,CRLB),以及apFFT测相误差与频偏分布的关系。指出该理论下限比传统三参数的CRLB低12dB,基于此总结出一系列在不同信噪比和不同频偏情况下的apFFT测相性能结论。仿真结果表明:在不同的信噪比环境和不同的频偏情况下,apFFT的测相方差都能被CRLB2所界定,验证了上述结论及其新的CRLB正确性。To disclose the underlying reasons of the superiority of apFFT in measuring phases compared with other existing methods, the distribution characteristics of spectral leakages and the theory of parameter estimation are combined. Therefore, one Cramer-Rao lower bound （CRLB） involving two-unknown-parameter estimation is deduced, which is suitable to apFFT measuring phases. Based on the deduction, the relationship of apFFT phase error and frequen- cy offset distribution is also obtained. Moreover, it is also pointed out that the novel CRLB is 12 dB lower than the traditional CRLB involving three parameters. Consequently, several con- clusions are drawn for apFFT measuring phases under different signal to noise ratios （SNRs） and different frequency offsets. Simulation results indicate that the phase measuring variance of apFFT can be defined by CRLB2 with different SNRs and different frequency offsets, verifying the above conclusions and the correctness of the novel CRLB.

关 键 词：全相位FFT 相位测量 克拉美罗下限 频偏 谱泄漏 

分 类 号：TM933.3[电气工程—电力电子与电力传动] TN911.72[电子电信—通信与信息系统]