5.5.2 Evaluation of P(E) for Simple Cases What I'll do here is teach by example. We'll take a look at BPSK and study the P(E) for a BPSK modulator-demodulator pair. The BPSK Modulator Remembered Take a look at Table 5.4, which summarizes the BPSK modulator. There, you can see that a 0 is mapped to SO (t) and a 1 mapped to S1 (t). Also, peeking back at Section 5.3.2, you can uncover that the orthonormal basis for BPSK is simply the one signal {Q(t) }, and SO (t) and S1 (t) are easily represented on Q (t) by sond S11* Figure 5.21 shows you a visual plot of the two BPSK symbols, plotted on their basis {Q(t) }. The BPSK Demodulator: A Summary As we saw in our earlier work, a demodulator consists of two parts: (1) a receiver front end, and (2) a decision device. The receiver front end takes r(t) and maps it to r . The details of how it works and how you build it are all in Section 5.4. If you just follow that, you'll find in the case of BPSK that the receiver front end is just like the picture in Figure 5.31 (look to the left of the dotted line). -20°2 In p(s01) 111-501 Choose table (bits) 1-1-11-11 -20°2 In p(s11) receiver front end decision device Figure 5.31 BPSK demodulator Getting It from Here to There: Modulators and Demodulators The decision device takes r and figures out which symbol Sm was sent. How it works and how to build it are once again the topics of Section 5.4, and if you look that over and apply it to BPSK, you'll discover that the decision device looks just as it's drawn on the right side of Figure 5.31. Also, you'll find that the equation that the decision device is carrying out is simply Si = = argmin (5.66) We'll assume equally likely symbols (that is, p(sil) = constant), which means that the decision device is carrying out the equation (5.67) That is, the decision device carries out the simple rule: output the symbol which is closest to the received 1. Evaluating the P() Now that we've recapped the modulator and the demodulator for BPSK, we're ready to move full-steam ahead and find the P(e). In