Optimal Diversity and Coding Gains for Millimeter-wave Communication

We consider a millimeter-wave communication system where the fading channel follows the Nakagami-m distribution. We derive performance limits of such a system in terms of the diversity and coding gains. First, we argue that although traditional design criteria for space-time codes (STCs) are optimal for Rayleigh and Rician fading channels, they fail to capture the optimal diversity and coding gains for Nakagami- $m$ fading channels. Then, we derive a tight upper bound on the average pair-wise error probability at high signal-to-noise ratios. From such a bound, we obtain upper and lower bounds on the diversity and coding gains of any STC over the Nakagami-m fading channel. We then identify necessary and sufficient conditions for STCs to achieve the upper bounds, leading to a fundamental trade-off between maximizing the diversity and coding gains. We also investigate the effect of blockage using stochastic geometry. We show that the diversity and coding gains are limited by the non-line-of-sight link. Numerical simulations assuming different fading scenarios further illustrate that STCs that satisfy the new design achieve full diversity. Whereas, STCs that are otherwise optimal for Rayleigh and Rician channels do not. Furthermore, in a typical indoor environment, blockage reduces the coding gain by 1.5 dB for BERs less than 10 $^{-3}$ .