Spatial modulation over K multiplicative complex fading wireless channels

The authors apply spatial modulation over multiplicative complex fading wireless channels, where the multiplicative complex fading is represented by the product of K statistically independent and identically distributed standard complex Gaussian random variables, where K ≥ 2. The analytical bit-error rate (BER) approximation of symbol estimation is obtained in terms of a Meijer´s G function. The conditional pairwise error probability (PEP) of transmit antenna index estimation is a function of a stochastic parameter with an unknown distribution function. The authors propose a lognormal distribution to approximate the distribution of this stochastic parameter. Based on the lognormal distribution, the average PEP and the analytical error probability upper bound of transmit antenna index estimation are derived. A goodness of fit test successfully validates the proposed lognormal distribution being the approximate distribution of the stochastic parameter. The derived analytical BER approximations for both symbol and transmit antenna index estimation are successfully validated via Monte Carlo simulations.