In this paper, we consider a particular class of selective fading channel corresponding to a channel that is selective either in time or in frequency. For this class of channel, we propose a systematic way to achieve the optimal DMT derived in Coronel and B "olcskei, IEEE ISIT, 2007 by extending the non-vanishing determinant (NVD) criterion to the selective channel case. A new code construction based on split NVD parallel codes is then proposed to satisfy the NVD parallel criterion. This result is of significant interest not only in its own right, but also because it settles a long-standing debate in the literature related to the optimal DMT of selective fading channels.
It turns out fron the geometrical interpretation that the outage event is reduced to the probability that the @math Jensen channel, denoted by @math in the rest of the paper, is in outage, which is the Jensen outage event in the Coronel and B "olcskei terminology @cite_0 . This means that the outage event is reduced to, @math Note that the straightforward generalization of the flat fading outage results to the block diagonal matrix in ) as in @cite_3 and @cite_2 does not take into account the impact of the coding among the channel blocks in the analytical outage derivation and does not lead to an accurate outage probability expression. In the following, we show how this optimal DMT can be achieved using a code derived from cyclic division algebra (CDA).
@cite_0 @cite_3 @cite_2
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Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. We propose the point of view that both types of gains can be simultaneously obtained for a given multiple-antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. For the richly scattered Rayleigh-fading channel, we give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes. In this paper we investigate the criteria proposed by for constructing MIMO MAC-DMT optimal codes over several classes of fading channels. We first give a counterexample showing their DMT result is not correct when the channel is frequency-selective. For the case of symmetric MIMO-MAC flat fading channels, their DMT result reduces to exactly the same as that derived by , and we therefore focus on their criteria for constructing MAC-DMT optimal codes, especially when the number of receive antennas is sufficiently large. In such case, we show their criterion is equivalent to requiring the codes of any subset of users to satisfy a joint non-vanishing determinant criterion when the system operates in the antenna pooling regime. Finally an upper bound on the product of minimum eigenvalues of the difference matrices is provided, and is used to show any MIMO-MAC codes satisfying their criterion can possibly exist only when the target multiplexing gain is small.