A New Approach for the Differential Spectrum Using the Frobenius Norm

The SEAD method relies on the difference between the two largest singular values of an augmented spatial covariance matrix in order to generate a Differential Spectrum that provides accurate DOA estimation even for low values of SNR. However the SEAD method is highly dependent on the SVD, such that it has to be performed for each test angle on a sweeping range. We have found that the induced matrix 2-norm by vector, i.e. The largest singular value, corresponds to the dominant contributor to the Differential Spectrum. On the other hand, as the Frobenius norm requires far less computations than the SVD, in this paper we analyze the use of the Frobenius norm to yield a spectrum that allows estimating the DOA angles. The major contribution of this proposition is the ease of performing the calculation of the Frobenius norm as opposed to performing multiple SVD.