On the diversity-multiplexing tradeoff for frequency-selective MIMO channels

We have previously (ISIT'05) introduced the optimal Diversity versus Multiplexing Tradeoff (DMT) for a FIR frequency-selective i.i.d. Rayleigh MIMO channel. This tradeoff is the same as for a frequency-flat MIMO channel with the larger of the number of receive or transmit antennas being multiplied by the delay spread. In this paper we provide alternative proofs and insights into this result. In particular, we consider the ordered LDU decomposition instead of the usual eigen decomposition of the channel Gram matrix. Popular approaches for frequency-selective channels use OFDM techniques in order to exploit the diversity gain due to frequency selectivity. We show that the minimum number of subcarriers that need to be involved in space-frequency coding to allow achieving the optimal tradeoff is the delay spread times the smaller of the number of transmit or receive antennas, thus answering a question that was open hitherto. Although the no-CSIT/full-CSIR case is considered here, we propose an alterative DMT interpretation based on negligible CSIT. This CSIT allows to exploit the ordered LDU decomposition.