We present a maximum likelihood method for delay estimation in a CDMA wireless communication system. An antenna array is used at the receiver, which facilitates the concomitant estimation of the direction of arrival (DOA) of each user. In addition, the amplitude of each user is also estimated. A single path is considered for each user thereby resulting in uncorrelated signals at the receiver. The delay estimation reduces to the solution of a set of quadratic equations while the DOA estimation problem is equivalent to an eigenvalue problem.