In this paper, an adaptive algorithm is derived by considering that the beamforming vector can be decomposed as a Kronecker product of two smaller vectors. Such a decomposition leads to a joint optimization problem, which is then solved by using an alternating optimization strategy along with the steepest-descent method. The resulting algorithm, termed here Kronecker product constrained least-mean-square (KCLMS) algorithm, exhibits (in comparison to the well-known CLMS) improved convergence speed and reduced computational complexity; especially, for arrays with a large number of antennas. Simulation results are shown aiming to confirm the robustness of the proposed algorithm under different operating conditions.

在本文中，考虑到可以将波束成形向量分解为两个较小向量的Kronecker乘积，从而得出一种自适应算法。这种分解会导致联合优化问题，然后通过使用交替优化策略以及最速下降方法解决该问题。所得的算法在这里称为Kronecker乘积约束最小均方（KCLMS）算法，与已知的CLMS相比，具有更快的收敛速度和更低的计算复杂度。特别是对于具有大量天线的阵列。为了证实所提出算法在不同工作条件下的鲁棒性，给出了仿真结果。