不完全复二阶循环平稳随机过程块处理的渐近FRESH性质化
Asymptotic FRESH Properizer for Block Processing of Improper-Complex Second-Order Cyclostationary Random Processes
摘要：
研究了离散时间（DT）非理想复二阶循环平稳（SOCS）随机过程的块处理问题。特别地，感兴趣的是找到能够实现计算上高效的接近最优的后处理的预处理操作。首先提出了一种可逆的线性共轭线性算子DT频率偏移（FRESH）性质化子。结果表明，DT FRESH properizer转换DT不正确复杂的SOCS随机过程输入到一个等价的DT正确复杂的SOCS随机过程输出，通过使用的信息，只有关于输入的周期。然后提出了一个可逆的LCL块处理算子，称为渐近FRESH properizer，它模仿DT FRESH properizer的操作，但处理DT非正常复杂SOCS随机过程的有限个连续样本。结果表明，渐近FRESH性质化器的输出不是真的，而是渐近真的，并且当块大小趋于无穷大时，其频域协方差矩阵收敛于一个具有对角块的高结构块矩阵.两个代表性的估计和检测问题，证明渐近最优的低复杂度后处理器可以很容易地设计利用这些渐近二阶性能的输出的渐近FRESH properizer。
英文摘要：
In this paper, the block processing of a discrete-time (DT) improper-complex second-order cyclostationary (SOCS) random process is considered. In particular, it is of interest to find a pre-processing operation that enables computationally efficient near-optimal post-processing. An invertible linear-conjugate linear (LCL) operator named the DT FREquency Shift (FRESH) properizer is first proposed. It is shown that the DT FRESH properizer converts a DT improper-complex SOCS random process input to an equivalent DT proper-complex SOCS random process output by utilizing the information only about the cycle period of the input. An invertible LCL block processing operator named the asymptotic FRESH properizer is then proposed that mimics the operation of the DT FRESH properizer but processes a finite number of consecutive samples of a DT improper-complex SOCS random process. It is shown that the output of the asymptotic FRESH properizer is not proper but asymptotically proper and that its frequency-domain covariance matrix converges to a highly-structured block matrix with diagonal blocks as the block size tends to infinity. Two representative estimation and detection problems are presented to demonstrate that asymptotically optimal low-complexity post-processors can be easily designed by exploiting these asymptotic second-order properties of the output of the asymptotic FRESH properizer.
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