1. An adaptive RAKE receiving apparatus constrained with at least one constraint in a mobile communication system, the apparatus comprising: input signal generating means for generating a complex received signal by gathering multi-path components during a corresponding transmitting signature; adaptive filtering means for filtering the complex received signal based on a tab weight that is adjusted at a predetermined period; channel estimating means for estimating a phase component and an amplitude component of a particular user channel by using the filtered signal from the adaptive filtering means to generate a channel estimating result signal; signal recovering means for recovering an original signal, which was transmitted from a particular user, by combining the filtered signals from the adaptive filter means for all multi-path components and the channel estimating result signal from the channel estimating means; selecting means for selecting one between a predetermined trained data signal and the recovered signal from the signal recovering means; reference signal generating means for generating a reference signal by using the selected signal from the selecting means and the channel estimation result signal from the channel estimating means; error calculating means for comparing the filtered received signal from the adaptive filtering means with the reference signal from the reference signal generating means to calculate error between these compared two signals; and tap coefficient adjusting means for adjusting tap coefficients of the adaptive filtering means based on MMSE (Minimum Mean Square Error) criterion with at least one constraint (constraint MMSE criterion).