On recursive and fast recursive computation of the capon spectrum

The Capon spectrum, which is known to have better resolution than the periodogram, has been widely used in various applications. Normally, the Capon spectrum is estimated through the direct computation of the inverse of the data correlation (or covariance) matrix. This so-called direct inverse approach is, however, computationally very expensive due to the high computational cost involved in the matrix inversion. This paper deals with fast and efficient algorithms in computing the Capon spectrum. Inspired from the recursive idea established in the area of adaptive signal processing, we first derive a recursive Capon algorithm. This new algorithm does not require an explicit matrix inversion, and hence is more efficient to implement than the direct inverse method. We then develop a fast version of the recursive algorithm, which can further reduce the complexity of the recursive one by an order of magnitude.