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.