Direction of Arrival Estimation using Modified Maximum Likelihood Function Based on Nystrom Method

The maximum likelihood (ML) technique offers high performance for the direction-of-arrival (DOA) estimation but is computational expensive. Conventionally, this approach uses the sample covariance matrix (SCM) of the array output. The computation of SCM relies on the array size and available snapshots which consequently leads to a huge computational burden for large array and/or snapshot samples. If calculation of the SCM can be avoided, the reduction of computation complexity is evidently achievable. To circumvent this issue, a modified ML version is proposed. Exploiting the Nyström method allows us to eliminate the SCM computation. The resulting low-rank matrices can be used to construct an accurate signal subspace without calculating the SCM and its eigenvalue decomposition (EVD). Furthermore, the replacement of the SCM by the signal subspace establishes the modified ML function. Regarding to the computation complexity, the complex multiplications between matrices are compared. Several simulation results such as spatial spectrum, root mean squared error (RMSE) and simulation time are included to confirm the tradeoff between the computational time and DOA estimation performance.