4 1-rd ,fic ) dt COMPARISON LOCAL PN CODE CODE PHASE UPDATE GENERATOR Figure 1.6. Block diagram of a single dwell time PN acquisition system with non-coherent detection. The Single Dwell Serial PN Acquisition System then passed through a band-pass (pre-detection) filter. The filter output is then square-law envelope detected with the detector output being integrated for a fixed time duration, Td (the "dwell time"), in an integrate-and-dump (I & D) circuit (post-detection integration) and then compared to a preset threshold. An equivalent low-pass version of the single dwell acquisition system is illustrated in Figure 1.7. Here the received signal plus noise is first demod- ulated by inphase and quadrature carrier reference signals I(t) and Q(t) whose frequency is equal to that of the receiver carrier on which the PN waveform is direct modulated but whose phase is arbitrary. The demodulated and despread signals are now passed through identical low-pass filters which are the low-pass equivalents of the band-pass filter in Figure 1.6. Square-law detecting the filter outputs and summing produces the signal required for post-detection integration and threshold comparison. Although our analy- sis of the performance of the single dwell system will directly relate to the band-pass representation of Figure 1.6, our primary reason for introducing Figure 1.7 at this point is to allow for comparison later on in the chapter with an analogous configuration of a matched filter type of acquisition system. Also, in a later chapter on synchronization of frequency-hopped signals, we shall again draw a parallel with the low-pass version of the acquisition scheme as illustrated in Figure 1.7. 1.2.1 Markov Chain Acquisition Model The Markov chain nature of the acquisition model stems from the way in which the integrate-and-dump (I & D) output is processed. In particular, if the I & D output is above the preset threshold, then a "hit" is declared. If this hit represents a true hit (i.e., the correct code phase has been deter- mined), t