Array manifold properties and performance of higher-order signal subspace techniques

The effective manifold of a linear array of sensors, i.e., the manifold associated with the fourth-order signal-subspace techniques, is investigated. It is shown that, like the manifold itself, the effective manifold has the shape of a hyperhelix. By using the rate of change of the arc-length, and the first curvature of this hyperhelix, three lower bounds on the performance of fourth-order signal subspace techniques are presented for arrays operating in the presence of independent sources. By evaluating these bounds it is shown that fourth-order signal subspace techniques provide an increase in the resolving and detecting power of an array as well as estimation errors of smaller variance.<>