ion Makers So the receiver front end has done its part-it's turned r(t) into r. Now it's up to the rest of the demodulator, which we call the decision device. What It Does The decision device receives r, which, for 4-PSK, corresponds to r=(r,1,r2) (5.30) (5.31) (5.32) In shorthand notation, we can write r=Sm+n. (5.33) The decision device thinks to itself: "All I see is which is a noisy version of (Sm),Sm2) I wonder which signal Sm(t), or correspondingly, which vector (SmI Sm2) (and there are four possibilities in 4-PSK), was sent to me by the modulator?" The decision device spends its time figuring out which (Sm), Sm2) (i.e., which Sm(t)) the modulator tried to send. Getting It from Here to There: Modulators and Demodulators Once the decision device figures 02(t) out which (Sm1,Sm2), or which Sm(t) is sent, its job is nearly done. It does one (S11,512) more simple thing: it looks to see which (r1, r2) bits the modulator stores in that Sm(t), and it outputs those bits, and, then, the demodulator has completed its job. 01(t) For example, take a look at Figure (S21,S22) (501,502) 5.27. There, the x's mark four possible (SmI,Sm2) values that may be output by a 4-PSK modulator. The 0 marks (1,1,22), the received values that come into the decision device from the * (531, 532) receiver front end. The decision device has the job of figuring out which Figure 5.27 Possible 4-PSK symbols (Sm1,Sm2) was sent, given that (r,12) and the received vector was received. Once the decision device decides which (Sm12Sm2) was sent, it then goes to Table 5.4. There, it can tell which bits are stored in the For example, if the demodulator decides (511,S12) was sent (corresponding to sending s(()), then it knows the bits sent were 01. This is the demodulator output. How It Works "Well", says the decision device, "I understand what it is I'm going to do, but I'm unclear about exactly how to do it. Specifically, how do I figure out which was sent when I look and see r = (1,12)?" In this section, we'll tell the decision device exactly how to