d thus causing a dismissal of the true sync position. Thus, a compromise threshold value must be chosen which allows for a relatively quick dismissal of false sync positions but tends to allow the integrator output for the true sync position to remain above threshold. If this latter event occurs for a designated interval of time, say To, after which the test is terminated (see Figure 1.44c), then the signal is declared present and the cell being searched is declared as the true sync position. The test trun- cation time To is often referred to as the time-out of the sequential detector Pseudonoise Code Acquisition in Direct-Sequence Receivers and in some cases is replaced by a test against a second (positive-valued) threshold. In this instance, the declaration of signal present comes as soon as the integrator output rises above this positive-valued threshold rather than as a result of this output remaining above the lower (negative-valued) threshold for all 0 < t < To. Since the two-threshold sequential detection system is indeed the more classical type in that it represents a direct application of the sequential hypothesis testing originally discussed by Wald [10], we shall discuss its per- formance first before returning to the sequential detector with the upper threshold replaced by the time-out feature. Another reason for presenting the material in this order is that a good deal more attention (particularly of a theoretical nature) has been paid in the literature to the two-threshold type of system, some of which carries over to the time-out type of system. Unfortunately, both systems are extremely difficult to analyze, and thus, in most applications, one ordinarily relies on simulation results. 1.7.1 A Brief Review of Sequential Hypothesis Testing as Applied to the Non-Coherent Detection of a Sine Wave Signal in Gaussian Noise Consider the two hypotheses H and H corresponding, respectively, to the application of Gaussian noise only and sine wave signal plus Gaussian noise to a square-law envelope detector as,