In this paper, we investigate widely-linear channel estimation and data detection for the uplink of the massive multiple-input multiple-output (MIMO) with in-phase or quadrature-phase imbalance (IQI). We firstly investigate widely-linear minimum mean square error (WL-MMSE) estimation for the effective channel which is the product of the IQI coefficients and the wireless channel. We reuse pilots among different user terminals (UTs) to reduce pilot overhead and derive a lower bound of the estimation MSE. Based on the optimal condition under which the lower bound is achieved, we show that if we assign the same pilot for the UTs of which the covariance matrices are orthogonal, the pilot interference does not affect the MSE performance. Then according to the obtained estimates of the effective channel, we further propose WL-MMSE data detection that is robust to the estimation error. The proposed widely-linear approach can cope with the IQI and multi-user interference jointly. With some results of operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed robust WL-MMSE data detection. The performance of the proposed widely-linear processing approach is verified by the numerical results.

中文翻译：

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具有 IQ 不平衡的大规模 MIMO 上行链路的宽线性处理：信道估计和数据检测

在本文中，我们研究了具有同相或正交相位不平衡 (IQI) 的大规模多输入多输出 (MIMO) 上行链路的广泛线性信道估计和数据检测。我们首先研究了有效信道的广泛线性最小均方误差 (WL-MMSE) 估计，该信道是 IQI 系数和无线信道的乘积。我们在不同的用户终端 (UT) 之间重用导频以减少导频开销并得出估计 MSE 的下限。基于达到下界的最佳条件，我们表明，如果我们为协方差矩阵正交的 UT 分配相同的导频，则导频干扰不会影响 MSE 性能。然后根据得到的有效信道估计，我们进一步提出了对估计误差具有鲁棒性的 WL-MMSE 数据检测。所提出的宽线性方法可以联合应对 IQI 和多用户干扰。利用算子价值自由概率理论的一些结果，我们推导出了所提出的稳健 WL-MMSE 数据检测的遍历可实现总和率的渐近确定性等价物。数值结果验证了所提出的宽线性处理方法的性能。