What good is having a blog if you can’t offer a rant every once in a while? In this post I talk about what I call *textbook signals*, which are mathematical models of communication signals that are used by many researchers in statistical signal processing for communications.

We’ve already encountered, and used frequently, the most common textbook signal of all: rectangular-pulse BPSK with independent and identically distributed (IID) bits. We’ve been using this signal to illustrate the cyclostationary signal processing concepts and estimators as they have been introduced. It’s a good choice from the point of view of consistency of all the posts and it is easy to generate and to understand. However, it is not a good choice from the perspective of realism. It is rare to encounter a textbook BPSK signal in the practice of signal processing for communications.

I use the term *textbook* because the textbook signals can be found in standard textbooks, such as Proakis (The Literature [R44]). Textbook signals stand in opposition to signals used in the world, such as OFDM in LTE, slotted GMSK in GSM, 8PAM VSB with synchronization bits in ATSC-DTV, etc.

Typical communication signals combine a textbook signal with an access mechanism to yield the final physical-layer signal–the signal that is actually transmitted (My Papers [11], [16]). What is important for us, here at the CSP Blog, is that this combination usually results in a signal with radically different cyclostationarity than the textbook component. So it is not enough to understand textbook signals’ cyclostationarity. We must also understand the cyclostationarity of the real-world signal, which may be sufficiently complex to render mathematical modeling and analysis impossible (at least for me). (See also some relevant examples of real-world signals here and here.)