Optimal and Successive Approaches to Signal Design for Multiple Antenna Physical Layer Multicasting
Optimal and Successive Approaches to Signal Design for Multiple Antenna Physical Layer Multicasting
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DOI：
10.1109/tcomm.2011.060911.080464
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发表时间：
2011-06
影响因子：
8.3
通讯作者：
I. Kim;D. Love;S. Park
中科院分区：
文献类型：
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作者：
I. Kim;D. Love;S. Park
在现代无线通信中，广泛需要发送公共信息流的系统（称为多播系统）来分发诸如电视或广播之类的内容。本文研究了多天线物理层多播信道，在该信道中，一条公共消息同时发送给多个单天线用户。为了实现这种多播设置的容量，需要确定发射信号矢量的协方差矩阵，使所有用户的最小最大可达速率最大化。在假定信道状态信息在发射机处完全可用的情况下，我们开发了一种简单的连续算法来确定信号矢量的协方差矩阵。我们首先刻画了容量实现协方差矩阵的性质，并推导了双用户情况下该矩阵的封闭表达式。然后，我们推导了两个用户情况下速率最大化波束形成器的封闭表达式，并提出了一种连续波束形成算法，该算法产生的波束形成矢量具有较低的计算复杂度。在本文提出的预编码设计方案中，通过对每个用户信道向量所张成的子空间进行正交化，依次构建协方差矩阵，直到递归次数达到最大值（即发射天线数与用户数的最小值）。将该方案的可实现速率与最优传输容量、发射波束形成容量、天线子集选择容量和不需要发射端CSI的开环传输容量进行了比较。随着用户数量和/或天线数量的增加，所提方案的平均可达速率在降低计算复杂度的同时实现了与真实容量相同的平均可达速率缩放。
In modern wireless communications, systems that send a common information stream (called multicasting systems) are widely needed for distributing content such as television or radio. In this paper, the multiple antenna physical layer multicasting channel is considered, in which a common message is simultaneously transmitted to multiple single-antenna users. To achieve the capacity of this multicasting set-up, the covariance matrix of the transmit signal vector needs to be determined to maximize the smallest maximum achievable rate among all the users. In this paper, we develop a simple successive algorithm to determine the covariance matrix of the signal vector under the assumption that channel state information (CSI) is perfectly available at the transmitter. We first characterize properties of the capacity achieving covariance matrix and derive a closed-form expression for the matrix in the two-user case. We then derive a closed-form expression for the rate maximizing beamformer in the case of two users and propose a successive beamforming algorithm that generates the beamforming vector with low computational complexity. In the proposed precoding design scheme, the covariance matrix is successively constructed by orthogonalizing the subspace spanned by each user's channel vector until the maximum number of recursions (which is the same as the minimum of the number of transmit antennas and the number of users) is reached. The achievable rate of the proposed scheme is compared with the capacity of optimal transmission, transmit beamforming, antenna subset selection, and open-loop transmission which does not require CSI at the transmitter. As the number of users and/or antennas grows large, it is shown that the average achievable rate of the proposed scheme achieves the same average achievable rate scaling as the true capacity while reducing the computational complexity.