ermining when synchronization was achieved. Such a system is also referred to in the literature as a sliding correlator PN acquisition circuit [12], [18], [19]. Since the test for synchronization was based on the crossing of a threshold by the output of either a coherent or non-coherent detector, when compared with the serial realization of the maximum-likelihood technique discussed earlier, this scheme trades off shorter acquisition time (i.e., the search can terminate anywhere within the uncertainty region rather than having to wait till the end of the code period) against reduced accuracy in detection of synchronization. When compared with Ward's sequential estimation technique, the serial search technique, as mentioned, will yield shorter acquisition time for input signal-to-noise ratios less than approximately 15 dB. Although at first glance -15 dB input SNR might seem unusually slow, PN spread-spectrum communication systems which operate at, or below, this value are becoming increasingly common. The primary reason for this is that with modern tech- nology we can now produce devices capable of handling the rapid switch- ing rates needed to generate the high chip rate codes required for large processing gain. The need for a high code chip rate carries with it the atten- dant requirement of a compatibly high detector input bandwidth, which in turn results in a low input SNR. Since in addition to the above considera- tions serial search techniques have the advantage of being easy to imple- ment, their application, particularly in SS receivers, is becoming increasingly popular. Although Sage's original analysis applied to the case where the Pseudonoise Code Acquisition in Direct-Sequence Receivers input signal was a carrier direct-modulated only by the PN code, the tech- nique is easily extended to include the case of angle-modulated (such as that produced by data modulation) carriers in which the non-coherent detector would include a post-detection filter between the envelope detector and threshold comparison [