 the PN spreading waveform is typically biphase modulated on a carrier whose phase is as yet unknown at the receiver, the matched filter acquisition system must be implemented either in a band-pass version (Figure 1.25a) or an equivalent low-pass ver- sion (Figure 1.25b). In the former case, a band-pass matched filter is used whose maximum output is detected by a square-law envelope detector. In the latter case, inphase and quadrature carriers with arbitrary phase but known or estimated frequency are used to demodulate the received signal followed by baseband matched filtering of each demodulated signal. The matched filter outputs are then non-coherently combined to produce the desired correlation measure for threshold testing. Conceptually, the implementation of a matched filter for a finite length PN waveform is most easily visualized in the form of a tapped delay line fol- lowed by a passive filter matched to a single PN chip waveform (Figure 1.26). To see how this comes about, we recall that a matched filter is generically a passive device that maximizes the signal-to-noise ratio at its output when the signal at its input is imbedded in additive white Gaussian noise. Mathematically speaking, for an input signal s(t) of duration To seconds, the impulse response h(t) of the matched filter is given by the reverse of s(t) in its T,-second time slot, i.e., (1.167) otherwise RECEIVED SIGNAL BANDPASS SQUARE-LAW CODE PHASE THRESHOLD MATCHED ENVELOPE DEVICE PLUS NOISE FILTER DETECTOR DECISION Figure 1.25a. A band-pass version of a matched filter acquisiton system. BASEBAND SQUARE-LAW MATCHED DETECTOR FILTER 2 cos(w0t++) THRESHOLD RECEIVED SIGNAL CODE PHASE DEVICE PLUS NOISE DECISION 2 sin(w0i++a ) BASEBAND SQUARE-LAW MATCHED FILTER DETECTOR Figure 1.25b. A low-pass version of a matched filter acquisiton system. RECEIVED SIGNAL DELAY DELAY DELAY DELAY DELAY NOISE FILTER p*(w) Figure 1.26. A tapped delay line implementation of a matched filter for an M-chip PN sequence. Rapid Acquisition Using Matched Filter Techniques 