tion for the integral I want to rewrite this equation in more common notation, SO that if you happen to open another telecommunications book, you can easily follow their notation. First, there's Es : it's easy to show that the energy of the BPSK signal, Es, , is given by Additionally, it's to express the noise variance of common N1 as Plugging this into our P(e) equation gives us the end result: P(E)=01/25 (5.75) The Q () function can be looked up in a table. So, if you give me the energy of the BPSK signal (or its A and T from which I can get its energy), and you give me the noise variance, then I'll give you the P(e). Actually, all you've got to do is give me the ratio of the energy of the BPSK signal to the channel noise variance (that is, just give me which is often called the signal-to-noise ratio or SNR, and I'll give you the P(E). Take a look at Figure 5.33. There you can see a plot of P(E) for BPSK that was generated Eg/No(dB) using Equation (5.75). What you'll notice is that, as the signal-to-noise ratio gets higher, the Figure 5.33 BPSK performance P(e) decreases rapidly-very rapidly. Chapter Five 5.5.3 Some Well-known P(E)'s While we could calculate all the P(e)'s for all the modulation schemes in a manner similar to that in the last section, we simply don't have to. People have done a lot of for us. I'm going to give you some commonly used P(e)'s for you to use as you please. Just look at the last table of the chapter, Table 5.10. Modulation Performance M-PSK No M T B-FSK M-FSK Table 5.10 Modulation schemes and performance 5.6 What We Just Did Another one bites the dust. Let's take a moment to recap and summarize what we just went through. Modulators take the incoming bits and map them to a waveform ready to be sent over the channel. You've got baseband modulators (NRZ, RZ, and some others), and you've got bandpass modulators (ASK, PSK, FSK, and QAM). These modulator output signals fly across the channel. The channel introduces an unwanted element called a noise. The demodulator at the receiver end th