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In mobile communications the antenna arrays make it possible to estimate the path delay, angle of arrival (or angle), and amplitude for the multipath propagation channel. This paper considers the problem of joint angle and delay estimation (JADE) in a time-division code-division multiple access system. The angle/delay estimation is made from multiple slots by exploiting the angle/delay invariance of the channel regardless of the fast faded amplitude variation (i.e., angle/delay is assumed quasistatic). JADE can be approximated by methods that estimate the frequencies of the two-dimensional complex sinusoids where the faded amplitudes act as sources. The shift invariance method (JADE-ESPRIT) is chosen for its capacity to pair delay and angle for each path and each user. The consistency of JADE-ESPRIT for a large enough number of slots guarantees the feasibility of the method for spatially correlated noise. The performance of the JADE method for channel estimation is evaluated analytically and numerically in propagation environments with increasing complexity.