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The code timing acquisition problem of bandlimited long-code based DS-CDMA systems operating in doubly-selective time-varying multipath channels is considered. We extend the unstructured schemes proposed by Buzzi to long-code spreading, which first estimates the Symbol Weighted Composite Channel Impulse Response (SW-CCIR) vectors and then extracts the timing informations. We also propose novel structured acquisition schemes, which directly estimate the multipath propagation delays by exploiting the a priori knowledge of the chip waveform. Both the structured and unstructured schemes are blind, since they require no other a priori information but the aperiodic spreading code of the desired user. Our numerical results demonstrate that the structured acquisition significantly outperforms both its unstructured counterpart and the classic correlator-based acquisition at a reasonable complexity increase.