or output, which from (1.76) and (1.75) is given by NoBt or NoB(1 + y)t, depend- ing upon whether the cell being searched corresponds to a noise only or sig- nal plus noise condition. Equivalently, for both hypotheses, the integrator outputs tend to increase linearly with time but at different slopes. Suppose now that one subtracts a fixed bias voltage b from the signal before integra- tion. Then, if this bias is assigned a value between the means of the square- law detector outputs under the two hypotheses, i.e., NoB < b < NoB(1 + y), the integrator output will now tend to decrease linearly (with slope NoB - b) when noise only is present, and increase linearly (with slope NoB(1 + y) - b) when signal plus noise is present (see Figure 1.44b). If one now chooses a threshold n (of negative value) which causes a dismissal whenever the inte- grator output falls below it, then the smaller the magnitude of this threshold, the faster the output for the noise only condition will dip below it. This quick dismissal for the noise only condition is what forms the heart of the sequential detection system and provides the acquisition time advan- tage previously alluded to. Unfortunately, the smaller the magnitude of the RECEIVED SIGNAL SQUARE-LAW ENVELOPE (BANDWIDTH DETECTOR NOISE z(1)>0, O<i<To LOCAL CODE PHASE (f) <0 DECISION PN CODE LOGIC GENERATOR UPDATE z(t)>0, 1= TO DECLARE SIGNAL PRESENT Figure 1.43. A serial sequential detection PN acquisition system with timeout feature. PN Synchronization Using Sequential Detection SIGNAL + NOISE NOB(1+y)t NOISE ONLY Figure 1.44a. Integrator output with bias voltage absent. SIGNAL + NOISE [NOB(1+y)-b]r (NOB-D) NOISE ONLY Figure 1.44b. Integrator output with bias voltage present. TEST TERMINATES (DECLARE SIGNAL PRESENT) SIGNAL + NOISE NOISE DISMISSAL OCCURS (UPDATE CODE PHASE AND CONTINUE SEARCH) Figure 1.44c. Integrator outputs with threshold dismissal and test truncation. threshold, the more likely is the integrator output for the signal plus noise case to also dip below the threshol