Error exponents for Nakagami-m fading MIMO channels

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, as it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we consider 2 x 2 Nakagami-m fading channels and determine the exact closed-form analytical expression for the random coding error exponent which provides a significant insight regarding the ultimate limits to communications over multiple-input multiple-output (MIMO) channels. The important fact about this error exponent is that it determines the behavior of the probability of error in terms of the transmission rate as well as the code length that reflects the coding complexity required to achieve a certain level of reliability. We also improve the random coding bound by expurgating the bad codewords from the code ensemble, since random coding error exponent is determined by selecting the codewords independently according to the input distribution where good codewords and bad codewords contribute equally to the overall average error probability. Moreover, we find the closed-form analytical expressions for the cutoff rate, critical rate and expurgation rate.