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 calculating the SCM directly can be avoided, the reduction of computation complexity is achievable. To circumvent this issue, a modified ML version is made. Exploiting the Nyström method allows an avoidance of the SCM computation. The resulting 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 in the traditional ML function by the signal subspace establishes the modified ML function. Regarding to the computation complexity, the complex multiplications between matrices are analyzed to evaluate the performance of the modified ML function to greatly reduce the complexity. 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 estimation accuracy.
 

direction of arrival, maximum likelihood function, Nyström method