基于哈达玛积扩展子空间的到达时间和波达方向联合估计

摘要

In the joint estimation for time of arrival (TOA) and direction of arrival (DOA) in the narrow-band orthogonal frequency division multiplexing (OFDM) system with antenna arrays, the estimation accuracy is not high in the situation of few numbers of arrays. Especially, DOA cannot be estimated if the number of multiple paths is more than that of the arrays. For these problems, a joint estimation algorithm for TOA and DOA based on the subspace of the extended hadamard product is proposed. First of all, the algorithm constructs an extended channel response in frequency domain via channel estimation for each array in the frequency domain. Then, auto-correlation matrix of extended channel response in the frequency domain is estimated by sampling many times. This estimation method of channel response in the frequency domain can use the fast Fourier transform algorithm. And the hadamard product in the extended noise subspace is obtained by eigenvalue decomposition. Finally, the pseudo-spectral function is constructed and used to search for spectrum peaks, so as to realize the joint estimation of TOA and DOA. The proposed algorithm requires no parameter paring but needs a two-dimensional searching. Monte Carlo algorithm can be used to reduce computational complexity. Simulation results show that the root mean square error of the joint TOA and DOA estimation which can be matched automatically is closer to the Cramer-Rao bound than that using present algorithms. And the proposed algorithm can be still applied when the number of multiple paths is more than number of arrays.%在窄带阵列天线正交频分复用系统的到达时间和波达方向联合估计中，针对阵元数目较少时波达方向估计精度不高，特别是多径数目大于阵元数目导致的波达方向无法估计问题，提出一种基于哈达玛积扩展子空间的到达时间和波达方向联合估计算法。该算法首先利用各阵元上的频域信道估计构成扩展信道频域响应矢量，然后计算扩展信道频域响应矢量自相关矩阵，并进行特征值分解得到哈达玛积扩展噪声子空间，最后构造伪谱函数并进行二维谱峰搜索，从而实现到达时间和波达方向的联合估计。仿真结果表明，与现有算法相比，在复杂度没有大幅提高的前提下，该算法的估计结果均方根误差更加接近克拉美罗界，且到达时间和波达方向估计能够自动配对，在多径数目大于阵元数目时依然适用。