Wireless Communications Systems Design

4Optimum Receiver

We defined a signal and random process in Chapter 2 and looked into wireless channels in Chapter 3. Now, we need to know how to detect a transmitted signal correctly in a receiver. The main purpose of the receiver is to recover the transmitted signal from the distorted received signal. Decision theory is helpful for finding the original signal. Decision theories are widely used in not only wireless communication systems but also other applications. Almost everything people face in their day-to-day life is related to decisions. For example, every day, we have to decide on the color of outfit that we have to wear, what to eat, and which route to drive. For example, if we need to find a shortcut to a particular place, then we have to decide based on the following: a priori information (or a prior probability) such as weather forecast or traffic report, an occurrence (or a probability of occurrence) such as traffic jam, and a posterior information (or a posterior probability) such as data collected regarding traffic jam. Likewise, we have to decide on the messages a transmitter sends in a wireless communication system. The decision depends on a priori information such as modulation type and carrier frequency, an occurrence such as a measured signal, and a posterior information such as channel state information. The decision theory of wireless communication systems is developed to minimize the probability of error. In this chapter, several decision theories are ...