Diversity and multiplexing tradeoff (DMT), tradeoff between the simultaneously achievable diversity order and multiplexing gain, is widely used to characterize the limiting performance of a communication system, and for comparison between different communication systems. We generalize the diversity order and the multiplexing gain to diversity profile (DP) and multiplexing profile (MP), respectively. By expanding the log of error probability function (or data rate function) into a iterated log function expansion (ILFE) in signal-to-noise ratio (SNR), the generalized profiles capture the traditional diversity order or multiplexing gain in the first order, but extend them to include higher order effects. Using the lexicographical order for ranking the profile, we show that schemes with hig...[ Read more ]

Diversity and multiplexing tradeoff (DMT), tradeoff between the simultaneously achievable diversity order and multiplexing gain, is widely used to characterize the limiting performance of a communication system, and for comparison between different communication systems. We generalize the diversity order and the multiplexing gain to diversity profile (DP) and multiplexing profile (MP), respectively. By expanding the log of error probability function (or data rate function) into a iterated log function expansion (ILFE) in signal-to-noise ratio (SNR), the generalized profiles capture the traditional diversity order or multiplexing gain in the first order, but extend them to include higher order effects. Using the lexicographical order for ranking the profile, we show that schemes with higher ranked diversity profiles (or multiplexing profiles) have better asymptotic error performance (or higher asymptotic data rate). We then investigate the tradeoff between these two profiles and consequently extend the DMT to diversity and multiplexing profile tradeoff (DMPT), which provides a more detailed analysis on the tradeoff between error probability and data rate in asymptotically high SNR.

We compare the traditional DMT and the DMPT of several communication systems, including point-to-point systems, systems with parallel channels, and systems with relays. We found that some systems or protocols with identical DMT curves, but quite different asymptotic limiting performance, can be differentiated using the new DMPT framework. Simulations verify the difference in the diversity profile, illustrating again that DMPT provides a more refined comparison between systems than DMT.