A Cumulant-Based Method for Direction Finding in Uniform Linear Arrays With Mutual Coupling

The problem of direction finding in uniform linear arrays (ULAs) with unknown mutual coupling is considered. A new fourth-order cumulant (FOC)-based method for estimating directions of arrivals (DOAs) of far-field signals is developed. In our proposed method, an FOC matrix is first derived. Then, it is shown that the null space of the Khatri-Rao (KR) product of the steering matrices can be obtained via the eigen decomposition of the FOC matrix. Finally, by taking advantage of the banded complex symmetric Toeplitz structure of the mutual coupling matrix (MCM), a determinant-based spatial spectrum is introduced to determine the DOAs. Computer simulations for different signal-to-noise ratios (SNRs) and numbers of snapshots are included to demonstrate the superior performance of the proposed method over its conventional counterpart.