21. Channel Capacity of Single-User Transmission Systems

In this chapter, we allude to a topic which is important for the design of a communications system. We will answer the question how many bit/s can be transmitted per symbol or equivalently per channel use. For a certain bandwidth of the channel, the interesting point is how many bit/s per Hz bandwidth can be achieved as a maximum. The channel capacity was introduced by Ch. Shannon in his pioneering work Shannon (Bell Syst Tech J 27:379, 1948, [1]) in the year 1948 for single input single output (SISO) channels. The extension to MIMO channels was given by I. Telatar, (Eur Trans Telecommun 10:585, 1999, [2]). The capacity of various models for stochastic MIMO channels have been intensively studied, e.g., in Kiessling (Statistical analysis and transmit prefiltering for MIMO wireless systems in correlated fading environments, Ph.D. dissertation, University of Stuttgart, Institute of Telecommunications, Shaker 2004, [3]). In the following, we start with the SISO channel capacity for a real-valued signal, extend it to complex signals, and finally derive the channel capacity of a MIMO scheme.