Diversity-Multiplexing Tradeoff with Arbitrary Doppler Spectrum

The original diversity-multiplexing tradeoff work by Zheng and Tse assumes multi-input-multi-output (MIMO) systems with frequency flat, spatially independent, and temporally block fading. Several following works have extended the tradeoff to either frequency selective or spatially correlated channels. However, all of them assume that fadings are temporally block. Compared with block fading assumption, it is more realistic to model Rayleigh temporal fadings as a zero-mean stationary complex Gaussian random process . Correspondingly, its power spectral density (or Doppler spectrum) is a sufficient description of the random process, because the correlation between two arbitrary fadings can be calculated through the Fourier transform of the Doppler spectrum. The main contribution of this paper is to derive the diversity- multiplexing tradeoff in frequency flat single-input-single-output (SISO) channels with arbitrary Doppler spectrum. Moreover, the derivation process itself, which is based on the spike sharpening effect, may be extended to facilitate other more complicated diversity-multiplexing tradeoff works.