We consider a communication scenario involving an m x n multiple input multiple output (MIMO) flat fading channel whose input is a symbol stream multiplied prior to transmission by an n x n spatial-temporal formatting matrix X and whose output is fed into an m x n linear combiner Z. We show how to choose the matrices X and Z to maximize the signal-to-noise ratio (SNR) of the linear combiner output data that are used for detection, under the total power constraint (TPC), the elemental power constraint (EPC), or the total and elemental power constraint (TEPC). The TEPC design (considered here for the first time) is shown to include the TPC and EPC designs (previously considered by the authors) as special cases and, hence, to provide a theoretically and practically interesting unifying framework. We make use of this framework to discuss various tradeoffs of the three space-time formatting designs considered, such as transmission rate and requirements for channel state information at the transmission side. Additionally, we show that the EPC design, which is the only one of the aforementioned designs that does not require channel information at the transmission side, is also the maximum SNR design in the worst channel case under a TPC.
