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A Low Complexity Blind Estimator of Narrowband Polynomial Phase Signals

机译:窄带多项式相位信号的低复杂度盲估计

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Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio.
机译:考虑估计由传感器阵列观察到的多个多项式相位信号的参数的问题。在实践中,很难维持精确校准的阵列。然后假定阵列歧管是未知的,并且该估计被称为盲估计。迄今为止,仅建议使用近似最大似然估计器(AMLE)来盲目估计每个信号的多项式系数。但是,该估计器需要在整个系数空间上进行多维搜索。相反,我们提出了一种基于两个步骤的估计方法。首先,使用盲源分离技术分离信号,该技术利用了信号的恒定模量特性。然后,使用应用于估计信号的展开相位的最小二乘法来估计每个多项式的系数。该估计量不涉及系数空间中的任何搜索。所提出的估计器的计算复杂度相对于多项式阶数呈线性增加,而AMLE的计算复杂度则呈指数增长。仿真结果表明,所提出的估计器在中等或较高信噪比下均达到了Cramér-Rao下界。

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