In this paper, beamforming for device-to-device multicast communication under channel uncertainty arising from incomplete channel state information is considered. The problem is first formulated as a non-robust minimization problem subject to signal-to-interference-plus-noise ratio, transmit power and interference constraints. Using semi-definite programming relaxation, a tractable convex robust counterpart of the beamforming problem was then formulated. Cases of deterministic and probabilistic interference constraints were considered. To simplify the probabilistic constraint, a cumulative distribution function substitution was used. The results show that the channel uncertainty error affects the optimal beamforming vector compared to the negligible effect of the probabilistic constraint.

在本文中，考虑了由于不完整的信道状态信息而导致的信道不确定性下的设备间组播通信的波束成形。首先将该问题表述为一个非鲁棒的最小化问题，该问题受到信号干扰加噪声比，发射功率和干扰约束的影响。使用半定规划松弛，然后制定了波束成形问题的可处理凸鲁棒对应项。考虑了确定性和概率性干扰约束的情况。为了简化概率约束，使用累积分布函数替换。结果表明，与概率约束的可忽略影响相比，信道不确定性误差影响最佳波束形成矢量。