Efficient Computation of Joint Direction-Of-Arrival and Frequency Estimation

The efficient computation of joint direction-of-arrival (DOA) and frequency estimation from the data matrix obtained from a sensor array is discussed. High-resolution ESPRIT/MUSIC algorithms are used to compute the estimates. A preprocessing step uses a two-sided DFT (computed using FFT) and applies a threshold to generate a sparse matrix from the given data matrix. The Lanczos method is used to compute the SVD/EVD of the sparse matrix. This results in a reduced computational complexity if the complexity of the preprocessing step is small compared to the reduction of the computational effort obtained by exploiting the sparsity of the matrix. We also compare this procedure with the estimations based on one sensor and one snapshot of the sensor array, respectively. In this case we can build Hankel matrices from the data samples and apply ESPRIT/MUSIC methods to these Hankel matrices and these matrices after the preprocessing step, respectively. This also yields a reduced computational complexity (again using Lanczos´ method) but decreases the accuracy of the estimates. We compare the computational effort and the mean square error (MSE) of the estimates for the different approaches.