Statistical Resolution Limits and the Complexified
Statistical Resolution Limits and the Complexified
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DOI：
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发表时间：
2005
影响因子：
1.6
通讯作者：
S.T. Smith
中科院分区：
文献类型：
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作者：
S.T. Smith
阵列分辨率限制和多个信号参数的准确度界限（例如，方位角、仰角、多普勒、距离、横向距离、深度、频率、啁啾、偏振、振幅、相位等）阵列处理算法的估计是评价系统性能的重要工具。信号的复振幅未知的情况具有特别的实际意义。对于确定性和未知信号幅度的情况，给出了这些边界的计算有效公式（从推导和分析的角度）。利用未知复信号参数及其复共轭，给出了一种新的推导方法。新的穆拉是很容易适用于获得无论是符号或数值解估计界的一类非常广泛的问题，在自适应传感器阵列处理中遇到的。此公式示出产生几个标准的Cramer-Rao结果的阵列处理，沿着新的结果的基本兴趣。具体而言，对于任何渐近无偏超分辨率算法（例如，音乐，ESPRIT）。统计分辨率极限被定义为等于其自身的Cramer-Rao界的源分离，提供了任何高分辨率方法的分辨率上的算法独立界。结果表明，阵列或相干积分窗的统计分辨极限约为信噪比相对于弧度的傅立叶分辨极限（大量阵元）。也就是说，可实现的最高分辨率与信噪比（SNR）四次方根的倒数成正比，这与标准精度界限的平方根SNR相关性相反。这些理论结果是consistent与以前公布的界限为特定的superresolu- tion算法推导出的其他方法。它还表明，通过分离两个共线阵列（合成超宽带），每个具有固定的孔径波长的波长（假设大），获得的潜在的分辨率提高是近似的，相反，分辨率提高的全孔径。这些问题的精确封闭形式的结果，其渐近逼近。
Array resolution limits and accuracy bounds on the multitude of signal parameters (e.g., azimuth, elevation, Doppler, range, cross-range, depth, frequency, chirp, polarization, ampli- tude, phase, etc.) estimated by array processing algorithms are es- sential tools in the evaluation of system performance. The case in which the complex amplitudes of the signals are unknown is of particular practical interest. A computationally efficient formula- tion of these bounds (from the perspective of derivations and anal- ysis) is presented for the case of deterministic and unknown signal amplitudes. A new derivation is given using the unknown com- plex signal parameters and their complex conjugates. The new for- mula is readily applicable to obtaining either symbolic or numer- ical solutions to estimation bounds for a very wide class of prob- lems encountered in adaptive sensor array processing. This for- mula is shown to yield several of the standard Cramer-Rao results for array processing, along with new results of fundamental in- terest. Specifically, a new closed-form expression for the statistical resolution limit of an aperture for any asymptotically unbiased su- perresolution algorithm (e.g., MUSIC, ESPRIT) is provided. The statistical resolution limit is defined as the source separation that equals its own Cramer-Rao bound, providing an algorithm-inde- pendent bound on the resolution of any high-resolution method. It is shown that the statistical resolution limit of an array or co- herent integration window is about SNR relative to the Fourier resolution limit of radians (large number of array elements). That is, the highest achievable resolution is pro- portional to the reciprocal of the fourth root of the signal-to-noise ratio (SNR), in contrast to the square-root SNR dependence of standard accuracy bounds. These theoretical results are con- sistent with previously published bounds for specific superresolu- tion algorithms derived by other methods. It is also shown that the potential resolution improvement obtained by separating two collinear arrays (synthetic ultra-wideband), each with a fixed aper- ture wavelengths by wavelengths (assumed large), is approx- imately , in contrast to the resolution improvement of for a full aperture. Exact closed-form results for these prob- lems with their asymptotic approximations are presented.