Employing Extreme Eigenvalues Ratio for Bind Channel Order Estimation
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摘要: 确定性辨识方法是盲信道辨识的主流方法，然而确定性方法性能受信道阶数估计的严重影响。本文针对大多数信道阶数估计算法在坏信道条件下失效问题，分析子空间方法中噪声子空间矢量构成特殊矩阵的奇异性与信道阶数之间的关系，对该特殊矩阵最大特征值最小特征值的变化情况进行对比分析，利用特征极值的比值来反映信号子空间到噪声子空间的变化情况，从而提出特征极值比定理。针对观测数据有限且含噪声的实际应用条件，提出一种盲信道阶数估计算法，该算法以不同信道阶数的特征极值比作为参数构造目标函数，得到在真实信道阶数处目标函数取全局最大值，同时对该算法进行了复杂度分析。最后针对两种常用仿真信道参数对算法进行了验证，结果表明，在短数据和低信噪比条件下，本文算法能以较高的估计概率得到好信道和坏信道的有效阶数。Abstract: Blind channel order estimation is a key technique for deterministic blind channel identification based on second order statistics; many blind channel order estimation methods are useless under ill-conditioned channel environment. In subspace method, when channel order is correct and over determined, the special toeplitz matrix constituted by the noise vectors is singular, the radio of maximum and minimum singular value is infinity. This paper employs the maximum and minimum singular value ratio of the special matrix to establish an extreme eigenvalues theorem (MMR theorem). Considering the finite and noisy observation samples, this paper proposes a new channel order estimation algorithm (MMRR algorithm) based on MMR theorem; the goal function of the MMRR algorithm uses extreme eigenvalues ratio according to different order values, this function can get the global maximum at the correct and/or effective channel order. Finally, this paper employs typical channel parameters(well-conditioned channel and ill-conditioned channel) for simulation and analysis, under the finite samples and moderate SNRs, the simulation results show that this method can correctly estimate effective order of well-conditioned and ill-conditioned channels with high probability, which outperforms other existing algorithms.
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