Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nyström method

•The new method avoids estimating the whole sample covariance matrix and its EVD.•The new method is more computationally efficient than the conventional methods.•The new DOA estimation method has a very high estimation accuracy.•The asymptotic variances of the proposed method are derived in this paper.

A low-complexity ESPRIT algorithm for direction-of-arrival (DOA) estimation is devised in this work. Unlike the conventional subspace based methods, the proposed scheme only needs to calculate two sub-matrices of the sample covariance matrix, that is, R11∈CK×KR11∈CK×K and R21∈C(M−K)×KR21∈C(M−K)×K, avoiding its complete computation. Here, M is the number of sensors of the array, K   satisfies P≤K≤min(M,N)P≤K≤min(M,N) with P being the number of source signals and N   being the number of snapshots. Meanwhile, a Nyström-based approach is utilized to correctly compute the signal subspace which only requires O(MK2)O(MK2) flops. Thus, the proposed method has the advantage of computational attractiveness, particularly when K⪡MK⪡M. Furthermore, we derive the asymptotic variances of the estimated DOAs. Numerical results are included to demonstrate the effectiveness of the developed DOA estimator.