ome rather ugly things), but this noise model is one of the most common ones. To characterize the noise term n(t), the most common noise model, and the one we'll work with, is called AWGN, shorthand for additive white gaussian noise. Each word has a meaning: Additive: tells us the noise signal n(t) is added to the sent signal Sm(t); Gaussian: tells us, first, that the noise signal n(t) is a random process. Second, if you consider a sample of that noise n(t), it is a random variable with a gaussian distribution. That is, in the concise language of math, (5.14) White: tells us that the noise n(t), a random process, has the autocorrelation function: R,(7)=o,"d(t). Chapter Five What this function means in words is that samples of n(t) are completely independent from one another. Noise: this little word means that n(t) is an unwanted signal introduced by the channel. Putting it all together, we know that n(t) is added to the sent signal, it's a random process, and we know its first- and second-order statistics (p(n) and R,(T)). 5.4.3 Building a Demodulator, Part I-the Receiver Front End I can describe the demodulator in two parts, each part having an important role to play in detecting the received signal. The first part is called the receiver front end. What it does The signal r(t)=s.,(t)+n(t) (5.15) jumps into the receiver front end. The receiver front end says to itself: "It would be easier for the rest of the receiver to work with numbers (or a vector of numbers), rather than this continuous time function r(t) ." So it decides to represent r(t) as a vector. One way to do this is to find an orthonormal basis for r(t), such that r(t) can be written as (5.16) In this case, r(t) can be represented as r = The rest of the receiver could then work with this vector, which is easier than working with r(t) And that's what it does the receiver front end turns r(t) into r, a term easier for the rest of the receiver to work with. The details follow. An orthonormal basis for r(t) The first thing the receiver front end is asked 