The Approximation of Outage Probability and the Trade-off between Capacity and Diversity for the Frequency-Selective Channel

This paper addresses the trade-off between multiplexing gain and diversity gain for the frequency-selective channel. We derive this trade-off by considering the scaling law of the ergodic capacity, which determine the multiplexing gain, and the error probability, which determines the diversity gain at high SNR. It is proved that this trade-off only depends on the number of independent taps of the equivalent FIR channel filter. The error probability is bounded by the outage probability and the error probability without outage. The scaling law of the outage probability and the error probability without outage at high SNR is derived, as are approximations of the outage probability at both low and high SNR