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 $^{-3}$ .

中文翻译：

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毫米波通信的最佳分集和编码增益

我们考虑一个毫米波通信系统，其中衰落信道遵循 Nakagami- 百万美元分配。我们在多样性和编码增益方面推导出这种系统的性能限制。首先，我们认为，尽管空时码 (STC) 的传统设计标准对于瑞利和 Rician 衰落信道是最佳的，但它们未能捕捉到 Nakagami 的最佳分集和编码增益。 百万美元衰落的频道。然后，我们推导出高信噪比下平均成对错误概率的严格上限。从这样的界限，我们获得了 Nakagami 上任何 STC 的多样性和编码增益的上限和下限。 百万美元衰落通道。然后，我们确定 STC 达到上限的必要和充分条件，从而在最大化多样性和编码增益之间进行基本权衡。我们还使用随机几何研究了阻塞的影响。我们表明多样性和编码增益受到非视距链路的限制。假设不同衰落场景的数值模拟进一步说明满足新设计的 STC 实现了完全分集。然而，对于瑞利和莱斯信道而言最佳的 STC 则不然。此外，在典型的室内环境中，对于小于 10 $^{-3}$ .