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本文研究了在确定的观察时间内,在有色高斯噪声中离散时间检测和估计的性能与样本数之间的关系。指出相邻样本之间相关系数在0.1—0.2范围内,广义信噪比就能相当接近极限值S~2(T)。在讨论二阶相关噪声时指出,由二阶微分方程描写的高斯过程的样本序列一般不是AR(2)模型,但是当样本间隔△→0时,却可用AR(2)模型近似描写序列,因此求极限信噪比时,可以较简便地采用AR(2)模型。最后指出最大似然估计与似然比检验之间和两者的性能测度之间的联系。
This paper investigates the relationship between the performance of discrete time detection and estimation and the number of samples in a colored Gaussian noise over a defined observation time. Pointed out that the correlation coefficient between adjacent samples in the range of 0.1-0.2, the generalized SNR can be quite close to the limit S ~ 2 (T). When discussing the second-order correlation noise, it is pointed out that the sample sequence of the Gaussian process described by the second-order differential equation is not generally the AR (2) model, but the AR (2) model can be used to approximate the sequence when the sample interval △ → 0 AR (2) model can be adopted simply when seeking the ultimate SNR. Finally, the link between the maximum likelihood estimation and the likelihood ratio test and the performance measure of the two are pointed out.