Performance analysis and design of semi-blind beamforming for downlink MIMO–NOMA heterogeneous network

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.