基于D-optimality准则的多输入多输出雷达阵列设计

为了最小化参数估计的均方误差，提出了基于D-optimality准则(DOBC)的多输入多输出雷达天线几何设计方法。严格推导了天线几何在DOBC准则下需要满足的约束条件；进行了敏感性分析，DOBC准则下的天线几何只与目标方位角之差有关，而与具体的方位角值无关；并推导了远场条件下参数估计的克拉美罗界(CRLB)，DOBC准则可以看成一种修正的CRLB，其为最大似然估计算法提供了更严格的下界约束。仿真结果表明，与最小冗余阵列、均匀阵列相比，DOBC准则下的天线几何具有更优越的参数估计性能，且其不受阵列孔径的约束，可以通过扩大孔径，进一步提高分辨力。但随着孔径的提高，方向图的伪峰值会升高，在低信噪比条件下，会造成很大的参数估计误差，因此需要根据实际应用需求，选择合适的孔径大小。

Antenna array design for MIMO radar based on D-optimality

An antenna geometry design method of Multiple-Input Multiple-Output(MIMO) radar based on D-optimality Criterion(DOBC) is proposed in order to minimize Mean Square Error(MSE) of the estimations. Firstly, the constraints of DOBC designs are derived; then, the sensitivity properties of the DOBC designs are analyzed, which are only affected by the separation of the targets and are independent of the azimuth of targets; the Cramer-Rao Lower Bound(CRLB) of the estimations in the far field condition is also deduced. DOBC criteria can be looked as the modified CRLB and provides a tighter bound for performance measure of the Maximum Likelihood Estimate(MLE) algorithm. Simulation results demonstrate that compared with minimum redundancy arrays and uniform arrays, DOBC designs have better performance in parameter estimation. Furthermore, it is not restricted by the array aperture. As the aperture increases, the resolution will be improved and the spurious peaks will become higher at the same time, which will result in a very large error in the DOA estimation with low SNR. Therefore, an appropriate aperture must be chosen according to the physical requirements.