ng Filter and MLSE First, congratulations. When you build a receiver as shown in Figure 9.19 you've got an optimal one. You pass the incoming signal through an optimal receiver front end to get r'; then you pass it through a whitening filter to get V. Finally, you pass it through an MLSE (which finds the closest path through a noiseless trellis), and that puts out the best guess on bits m'. However, there is a problem with the MLSE. In many communication systems, the number of states and the number of branches in the trellis can be very large. In fact, the trellis can be SO large that it becomes very expensive to build receivers that implement the MLSE. People began to look for inexpensive alternatives. In essence, the rest of this chapter is all about cheaper options. We want to find alternatives to using the whitening filter followed by the MLSE-alternatives that will perform well, and will be far more cost effective. COS Wct h(-t) r'(t) sin Wct Figure 9.19 The optimal receiver 9.6 Linear Equalizers We start here with Figure 9.20(a): we've got the new modulator putting out s(t), the new channel putting out r(t) s(t)*c(t)+n(t), and the optimal receiver front end putting out r'c. We know how to build an optimal rest-of-the-receiver, but it's SO darn expensive that we're looking for cheaper alternatives. The first alternative is called the linear equalizer. The use of the linear equalizer in the receiver is shown in Figure 9.20(b). It is simply a discrete filter with impulse response Ck that takes the input r's and turns it into a new variable called rk ; this rk is then passed through a decision device which outputs I'k, the best guess on the data symbol Ik The decision device always works in the same way, exactly the way decision devices were described in Chapter 5. Chapter Nine What is this impulse response Ck , and how do we choose it? There are many different possible choices for ck,and , we'll spend the next few sections discussing these choices (one section per choice). COS Wct ej(ccc) pulse coder shaper Re