On EXIT-Charts for Space-Time Block Codes

In this work, we consider the application of the well-known space-time block code (STBC), the Alamouti-scheme, as inner code within a “turbo” coding scheme for the multiple-input-multiple-output (MIMO) Rayleigh fading channel. We analyze therefore the applicability of the Alamouti-scheme for iterative space-time detection and decoding applied at the receiver. To this end, we use extrinsic information transfer characteristics (EXIT-charts) in order to predict the performance of the Alamouti-scheme. Furthermore, we analyze the impact of different mapping strategies on the information transfer of the soft-input-soft-output (SISO) space-time detector and show analytically that it is possible to improve the performance by employing other mapping schemes than Gray mapping. I. Characterizing different mappings by mutual information and EXIT-charts In the following, we analyze the impact of different 8PSK mappings (analogous to [1]) on the transfer characteristics of the detector for an AWGN channel. The extension to a Rayleigh fading channel is straightforward. With the chain rule of mutual information it can be shown that the mutual information I(s; r) = I(c; r) = I(c1, . . . , cm; r) between transmitted constellation symbol s = f(c) and received AWGN channel output r (assuming that all constellation symbols are equiprobable) can be decomposed into I(c; r) = ∑m−1 L=0 IL, where IL is the average mutual information [1], when L bits are already known to the receiver. Hence, for 8PSK (m=3) we have I0 = 1 m(m−1 0 ) m ∑ i=1 I(ci; r) ; I1 = 1 m(m−1 1 ) m ∑