,... 15(t)} for 16-QAM build it for yourself. But, first, we'll want to define the demodulator. What is it? The demodulator is a device that gets the signal sent across the channel, and turns it back into bits. 5.4.1 What Demodulators Do Let's start with a picture. Take a look at Figure 5.25. There, you can see how the signal (t) leaves the modulator, packing its bags and taking a journey across the channel. Finally, after its long journey, it arrives at the receiver side. Just like all us travellers, after a long trip our hair is a mess and our stomachs may be turned upside-down. Well, the signal Sm(t) is no different than we are-it looks a little shaken up. Specifically, by the time the signal arrives at the receiver, it's no longer its old sm(t) self, but rather it's become r(t)=s.,(t)+n(t) (5.13) where n(t) is the noise added by the channel as our signal Sm(t) headed along from transmitter to receiver. The demodulator doesn't know Sm(t) was sent across the channel. All it knows is that, for example, a 4-PSK signal from the set {s,(t),s(t),s,()),s,(t)} was sent. Its job is to do the best it can to figure out which Sm(t) was sent across the channel, given r(t) Once it figures this out, it uses a look-up table to find out what information bits are stuffed in the signal it thinks was sent. It then outputs those bits. The key to building a good demodulator is to minimize the effects of noise and give the highest probability of guessing the correct sent signal. This will make sure Getting It from Here to There: Modulators and Demodulators Modulator information 5m(t) Channel Demodulator output Figure 5.25 The modulator and demodulator that the bits that leave the demodulator (receiver side) are as close as possible to the bits that come into the modulator (transmitter side). 5.4.2 The Channel and Its Noise We've modeled the channel as an unpleasant fellow that takes the signal you sent, tires it out, and ultimately adds a noise to it. This is not the only channel model, and chan- nels can do a lot of other things (s