k at what we now know. First, we know that the decision device receives r, and tries to figure out which Sm was sent. It makes its decision by choosing the Sm based on equation (5.45) (or (5.46) if all symbols are equally likely-that is, p(sm) equals a constant). Once the decision device decides on which Sm was sent, it then figures out which bits the modulator stored in that Sm (or, equivalently, that Sm(t)), and it outputs those bits. That's pretty much everything there is to know about deci- sion devices. The only thing left to talk about is how to build them. The Correlator Receiver Figure 5.28 shows the complete demodulator, beginning with the receiver front end and following with the decision device. When we build the demodulator according to Figure 5.28, people call it the correlator receiver. The receiver front end part is the part before (to the left of) the dotted line and looks just like the implementation I drew earlier in Figure 5.26. As we'd expect, it takes the r(t) and hands out the r. To the right of the dotted line in the figure, I've drawn the decision device. It works like this: (1) processor: the processor receives r = It outputs M values, where M is the number of possible Sm(t) signals (for example, for 4-PSK, it outputs four values). Specifically, for each Sm(t), the processor outputs r-sml2. (2) adders: there are M adders, one for each output from the processor. The jth adder receives the processor output and adds to it -20, In p(s)). So, to state the obvious, the jth adder's output is (3) choose min: the "choose min" device receives M inputs, r-sil-20, In[p(s) )] for 2, M. It outputs one value, the Sj, which has the smallest value of r-sil-20, In[p(s))] Combined, these three pieces carry out Si = argmin r-sil-20,1 In[p(s))]. Getting It from Here to There: Modulators and Demodulators 01(t) -20°2 'In p(s1) (i+1)T 1r-s1/2 Choose table (bits) (i+1)T 1r-sm12 ON (t) -20 21 p(s) receiver front end decision device Figure 5.28 Correlator Receiver Example 5.5 Describe the decision device in a BPSK 