Finite-SNR Diversity-Multiplexing Tradeoff for spectrum-aggregated transmission

The finite-SNR Diversity-Multiplexing Tradeoff (DMT) problem is studied in the context of spectrum aggregation, where there exist multiple noncontiguous (discrete) spectrum segments each of which has its own power limit. Firstly, we give an optimal power allocation strategy to achieve the ergodic capacity under Rayleigh fading. Secondly, two different coding schemes, i.e., coding without across sub-channels and coding across, are presented to achieve the lower and upper bound of diversity gain of this system under the same multiplexing gain. Then the finite-SNR DMT under i.i.d Rayleigh fading is derived, and its accurate expression for the coding-without-across scheme and the upper bound for the coding-across scheme are achieved respectively. The asymptotic performances of both schemes are also obtained. Under the equal sub-channel bandwidth setting, for infinite SNR, the coding-across scheme achieves M (the number of sub-channels) times diversity gain against the without-coding-across scheme. The loss of diversity gain caused by non-identical bandwidth and power limit is also analyzed.