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By deriving a generalized Shannon capacity formula for multiple-input, multiple-output Rayleigh fading channels, and by suggesting a layered space-time architecture concept that attains a tight lower bound on the capacity achievable. Foschini (see Wireless Pers. Commun., vol.6, no.3, p.311-35, 1998) has shown a potential enormous increase in the information capacity of a wireless system employing multiple-element antenna arrays at both the transmitter and receiver. The layered space-time architecture allows signal processing complexity to grow linearly, rather than exponentially, with the promised capacity increase. This paper includes two important contributions. First, we show that Foschini's lower bound is, in fact, the Shannon bound when the output signal-to-noise ratio (SNR) of the space-time processing in each layer is represented by the corresponding "matched filter" bound. This proves the optimality of the layered space-time concept. Second, we present an embodiment of this concept for a coded system operating at a low average SNR and in the presence of possible intersymbol interference. This embodiment utilizes the already advanced space-time filtering, coding and turbo processing techniques to provide yet a practical solution to the processing needed. Performance results are provided for quasi-static Rayleigh fading channels with no channel estimation errors. We see for the first time that the Shannon capacity for wireless communications can be both increased by N times (where N is the number of the antenna elements at the transmitter and receiver) and achieved within about 3 dB in average SNR about 2 dB of which is a loss due to the practical coding scheme we assume-the layered space-time processing itself is nearly information-lossless.