In this paper, we investigate the impact of channel aging on the performance of cell-free (CF) massive multiple-input multiple-output (MIMO) systems with both spatial correlation and pilot contamination. We derive novel closed-form uplink and downlink spectral efficiency (SE) expressions that take imperfect channel estimation into account. More specifically, we consider large-scale fading decoding and matched-filter receiver cooperation in the uplink. The uplink performance of a small-cell (SC) system is derived for comparison. The CF massive MIMO system achieves higher 95%-likely uplink SE than the SC system. In the downlink, the coherent transmission has four times higher 95%-likely per-user SE than the non-coherent transmission. Statistical channel cooperation power control (SCCPC) is used to mitigate the inter-user interference. SCCPC performs better than full power transmission, but the benefits are gradually weakened as the channel aging becomes stronger. Furthermore, strong spatial correlation reduces the SE but degrades the effect of channel aging. Increasing the number of antennas can improve the SE while decreasing the energy efficiency. Finally, we use the maximum normalized Doppler shift to design the SE-improved length of the resource block. Simulation results are presented to validate the accuracy of our expressions and prove that the CF massive MIMO system is more robust to channel aging than the SC system.

中文翻译：

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信道老化对空间相关信道上无蜂窝大规模 MIMO 的影响

在本文中，我们研究了信道老化对具有空间相关性和导频污染的无小区 (CF) 大规模多输入多输出 (MIMO) 系统性能的影响。我们推导出新的封闭形式的上行链路和下行链路频谱效率 (SE) 表达式，这些表达式考虑了不完美的信道估计。更具体地说，我们考虑了上行链路中的大规模衰落解码和匹配滤波器接收器合作。导出小小区 (SC) 系统的上行链路性能以进行比较。CF 大规模 MIMO 系统实现了比 SC 系统更高的 95% 可能的上行链路 SE。在下行链路中，相干传输的每用户 SE 的 95% 可能性比非相干传输高四倍。统计信道协作功率控制 (SCCPC) 用于减轻用户间干扰。SCCPC 的性能优于全功率传输，但随着信道老化的加剧，优势逐渐减弱。此外，强空间相关性降低了 SE 但降低了信道老化的影响。增加天线数量可以提高 SE，同时降低能量效率。最后，我们使用最大归一化多普勒频移来设计资源块的 SE 改进长度。仿真结果验证了我们表达式的准确性，并证明了 CF 大规模 MIMO 系统比 SC 系统对信道老化具有更强的鲁棒性。增加天线数量可以提高 SE，同时降低能量效率。最后，我们使用最大归一化多普勒频移来设计资源块的 SE 改进长度。仿真结果验证了我们表达式的准确性，并证明了 CF 大规模 MIMO 系统比 SC 系统对信道老化具有更强的鲁棒性。增加天线数量可以提高 SE，同时降低能量效率。最后，我们使用最大归一化多普勒频移来设计资源块的 SE 改进长度。仿真结果验证了我们表达式的准确性，并证明了 CF 大规模 MIMO 系统比 SC 系统对信道老化具有更强的鲁棒性。