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The paper proposes a modified noncoherent sequential detection decision logic based on continuous accumulation in order to achieve fast PN code acquisition. In most reports on sequential schemes, the decision process is based on independent and identically distributed random variables, which requires the integrator to be reset periodically. This introduces loss in the effective signal-to-noise ratio. In this paper, on the contrary, the sequential scheme use continuous integration. To simplify the design and analysis, we deduce the equivalent relationship between the likelihood ratio of the current sample and that of all the previous samples. The scheme is proved to be an optimum sequential detection under certain assumptions. In addition, because the average sample number (ASN) can not be calculated through the methods applied to conventional sequential detection, an algorithm is also provided, which can estimate both the probability density function (PDF) and the upper threshold of ASN. The desired probability of false alarm and detection, as well as faster PN code acquisition compared to conventional sequential detection can be achieved by employing this structure. The correctness and advantage of the scheme was also verified by computer simulation. The performances of the proposed schemes were obtained and they suggested that the proposed non-coherent sequential detection is more desirable.