In this paper, by considering the average mean squared error (AMSE) of channel estimation, we primarily obtain the closed-from expressions of the probability density function (PDF) and cumulative distribution function of AMSE for the least squares (LS)/minimum mean squared error (MMSE) estimation method as the line-of-sight (LOS) component is known, where the asymptotic analysis is executed in Rayleigh fading and strong LOS conditions. Secondly, the closed-form expressions for the expectation of AMSE ( Expamse) and variance of AMSE ( Varamse) are acquired, where Varamse is inversely proportional to the number of antennas ( M). As M becomes infinite, the PDF of AMSE at Expamse has an order of root M. When the pilot power decreases with M in a power law, the LS case keeps deteriorating while the MMSE case converges to a constant which basically depends on the Rician K-factor. Next, the spectral efficiency is investigated by considering AMSE. When Expamse accelerates, the spectral efficiency of the LS method keeps dropping and that of the MMSE method firstly is degraded and then is improved to a constant except Rayleigh fading. Finally, all results are validated via simulations.

中文翻译：

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具有莱斯衰落的大规模 MIMO 的信道估计感知性能分析


本文考虑信道估计的平均均方误差(AMSE)，初步得到最小二乘(LS)/最小均值的概率密度函数(PDF)和AMSE累积分布函数的闭表达式平方误差（MMSE）估计方法作为视线（LOS）分量是已知的，其中渐近分析是在瑞利衰落和强LOS条件下执行的。其次，得到AMSE期望(Expamse)和AMSE方差(Varamse)的闭式表达式，其中Varamse与天线数量(M)成反比。当 M 变得无穷大时，Expamse 处 AMSE 的 PDF 具有根 M 的阶。当导频功率按照幂律随 M 减小时，LS 情况不断恶化，而 MMSE 情况收敛到一个常数，该常数基本上取决于莱斯 K -因素。接下来，通过考虑 AMSE 来研究频谱效率。当Expamse加速时，LS方法的频谱效率不断下降，而MMSE方法的频谱效率先下降，然后提高到恒定值（瑞利衰落除外）。最后，所有结果都通过模拟进行验证。