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arXiv 2201.12940cs.ITmath.IT
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大规模MIMO LEO卫星上行传输的遍历和速率容量可达发射设计

Ergodic Sum Rate Capacity Achieving Transmit Design for Massive MIMO LEO Satellite Uplink Transmission

Ke-Xin Li, Xiqi Gao, Xiang-Gen Xia

AI总结:

研究仅有统计信道状态信息的大规模MIMO低轨卫星上行传输,提出基于低维矩阵转化和条件梯度法的遍历和速率容量最优发射协方差矩阵设计,并利用渐近表达式简化计算。

摘要:

本文研究了在用户终端(UTs)仅具有统计信道状态信息的情况下,大规模多输入多输出(MIMO)低轨(LEO)卫星通信的遍历和速率(ESR)容量可达上行(UL)发射设计。提出了在卫星和UTs端均采用均匀平面阵列配置的UL大规模MIMO LEO卫星信道模型。我们证明了每个UT的最优发射协方差矩阵的秩不超过其在UT侧的信道相关矩阵的秩,这揭示了从每个UT传输到卫星的独立数据流的最大数量。我们随后证明,发射协方差矩阵设计可以无损最优性地转化为低维矩阵设计。我们还获得了每个UT到卫星的单数据流传输能够实现ESR容量的充分必要条件。开发了一种条件梯度(CG)方法来计算实现ESR容量的发射协方差矩阵。此外,为避免穷举样本平均,我们利用ESR的渐近表达式,设计了一种简化的CG方法来计算发射协方差矩阵,从而能够近似ESR容量。仿真证明了所提方法的有效性。

英文摘要:

In this paper, we investigate the ergodic sum rate (ESR) capacity achieving uplink (UL) transmit design for massive multiple-input multiple-output (MIMO) low-earth-orbit (LEO) satellite communications with statistical channel state information at the user terminals (UTs). The UL massive MIMO LEO satellite channel model with uniform planar array configurations at the satellite and UTs is presented. We prove that the rank of each UT's optimal transmit covariance matrix does not exceed that of its channel correlation matrix at the UT side, which reveals the maximum number of independent data streams transmitted from each UT to the satellite. We then prove that the transmit covariance matrix design can be transformed into the lower-dimensional matrix design without loss of optimality. We also obtain a necessary and sufficient condition when single data stream transmission from each UT to the satellite can achieve the ESR capacity. A conditional gradient (CG) method is developed to compute the ESR capacity achieving transmit covariance matrices. Furthermore, to avoid the exhaustive sample average, we utilize an asymptotic expression of the ESR and devise a simplified CG method to compute the transmit covariance matrices, which can approximate the ESR capacity. Simulations demonstrate the effectiveness of the proposed approaches.

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