Design criterion of linear dispersion codes (LDCs) in MIMO system from a new point of view

We propose the design criterion of LDCs over the whole range of signal to noise ratio (SNR) in quasi-static Rayleigh fading channel. Section 1 of the full paper briefs the MIMO system model. Section 2 explains our new design criterion; its core is that we present Theorem 1 and its proof. Section 3 presents the results of a numerical example and their analysis; its eqs. (4) and (5) are worth noticing; the results, given in Figs. 1 and 2, and their analysis show preliminarily that: (1) we obtain the optimal pair error probability (PEP) of a power-constrained MIMO system when the codeword difference matrix of any two codewords is in full rank and its singularity values are all the same; (2) in high SNR region, the rank criterion and determinant criterion of the MIMO system, taken together, is a special case of our design criterion for LDCs.