SIPEX-G is a fast-converging, robust, gradient-based PCA algorithm that has been recently proposed by the authors. Its superior performance in synthetic and real data compared with its benchmark counterparts makes it a viable alternative in applications where subspace methods are employed. Blind multiuser detection is one such area, where subspace methods, recently developed by researchers, have proven effective. In this paper, the SIPEX-G algorithm is presented in detail, convergence proofs are derived, and the performance is demonstrated in standard subspace problems. These sub space problems include direction of arrival estimation for incoming signals impinging on a linear array of sensors, nonstationary random process subspace tracking, and adaptive blind multiuser detection.