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A sphere packing lower bound and a pairwise error upper bound are derived on error probability of space-time-frequency coded OFDM systems over multiple antenna block-fading channels. These bounds are useful in performance analysis and design of the codes. For example, the sphere packing bound provides a tool to investigate the performance limits of frequency-selective block-fading channels in terms of parameters such as number of antennas, coherence time, coherence bandwidth, delay constraint, and system bandwidth. Also, it can be used to specify the merit of a code in the sense of how far the code performs from fundamental limits. Comparisons with several known results are provided to support this assertion. On the other hand, the pairwise error upper bound can be used as a basis for a unified approach to analysis and design of space-time-frequency codes over any Rician or Rayleigh, block-fading channel in the presence of any type of correlation profile. Expressions for maxima of temporal diversity, spectral diversity, and spatial diversity are derived in terms of the system parameters. It is shown that under certain circumstances, one can not obtain the maxima of all types of diversities jointly. Moreover, the effect of system parameters and channel correlation profile on outage probability is investigated. Specifically, it is shown that unlike the spatial correlation, the temporal and spectral correlation does not affect the ergodic channel capacity (per dimension). However, they increase the variance of instantaneous channel capacity and hence, increase the outage probability.
Date of Publication: Jan. 2005