Non-orthogonal multiple access (NOMA) communication is a potential strategy for overcoming the limits of classic orthogonal multiple access schemes, and it can improve possible rates. In contrast, MIMO–NOMA improves them even more due to multiple antenna diversity advantages. On the other hand, future wireless communication will rely on heterogeneous networks (HetNets), which allow many wireless access networks to coexist hierarchically. However, channel reciprocity is invalid because of the shorter channel coherence time in 5G and 6G communications. As a result, channel estimation through an uplink (UL) pilot no longer holds for downlink (DL) transmission. To address this issue, a statistical beamforming approach is proposed that does not consider channel reciprocity for channel estimation. Consequently, the proposed method saves the pilot transmission overhead required for channel estimation resulting in increased spectral efficiency. To achieve this, we propose to employ the characterization of the ratio of the indefinite quadratic form (IQF) to obtain a closed-form formula for the outage probability in MIMO–NOMA HetNets. The analytical expression obtained is then utilized to design optimal beamforming weights using the genetic algorithm (GA) that solves a constrained multi-objective optimization task. In summary, advantages of our proposed method are (1) it provides spectral efficient method of beamforming, (2) it derives an exact characterization of outage probability in MIMO–NOMA HetNets in closed form, and (3) it develops a GA based optimization solution that solves a constrained multi-objective optimization task simulation results presented validate the theoretical analysis and show supremacy of the proposed method over classical statistical method.

非正交多址（NOMA）通信是克服经典正交多址方案限制的潜在策略，并且可以提高可能的速率。相比之下，MIMO-NOMA 由于多天线分集优势而进一步改善了它们。另一方面，未来的无线通信将依赖于异构网络（HetNet），它允许许多无线接入网络分层共存。然而，由于5G和6G通信中信道相干时间较短，信道互易性无效。结果，通过上行链路（UL）导频的信道估计不再适用于下行链路（DL）传输。为了解决这个问题，提出了一种统计波束成形方法，该方法不考虑信道估计的信道互易性。因此，所提出的方法节省了信道估计所需的导频传输开销，从而提高了频谱效率。为了实现这一目标，我们建议采用不定二次型（IQF）比率的表征来获得 MIMO-NOMA HetNet 中中断概率的封闭式公式。然后利用获得的解析表达式来使用遗传算法（GA）设计最佳波束形成权重，解决约束多目标优化任务。总之，我们提出的方法的优点是（1）它提供了波束成形的频谱有效方法，（2）它以封闭形式导出了 MIMO-NOMA HetNet 中中断概率的精确表征，以及（3）它开发了基于 GA 的优化解决约束多目标优化任务的解决方案仿真结果验证了理论分析并显示了所提出的方法相对于经典统计方法的优越性。