For massive multiple-input multiple-output (MIMO) antenna systems, time division duplexing (TDD) is preferred since the downlink precoding matrix can be obtained through the uplink channel estimation, thanks to the channel reciprocity. However, the mismatches of the transceiver radio frequency (RF) circuits at both sides of the link make the whole communication channel non-symmetric. This paper extends the total least square (TLS) method to the case of self-calibration, where only the antennas of the access points (APs) are involved to exchange the calibration signals with each other and the feedback from the user equipments (UEs) is not required. Then, the proof of the equivalence between the TLS method and the least square (LS) method is presented. Furthermore, to avoid the eigenvalue decomposition required by these two methods to obtain the calibration coefficients, a novel algorithm named as iterative coordinate descent (ICD) method is proposed. Theoretical analysis and simulation results show that the ICD method significantly reduces the complexity and achieves almost the same performance of the LS method.
将总体最小二乘算法拓展到自校准的场景下, 并且证明了总体最小二乘算法和最小二乘算法的等价性。进一步地, 提出迭代坐标下降校准算法, 在基本达到最小二乘算法性能的同时, 大大降低了实现的复杂度。
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Wei, H., Wang, D., Wang, J. et al. TDD reciprocity calibration for multi-user massive MIMO systems with iterative coordinate descent. Sci. China Inf. Sci. 59, 102306 (2016). https://doi.org/10.1007/s11432-015-5441-4
- reciprocity calibration
- total least squares
- coordinate descent
- large-scale MIMO