A Robust Design for BackCom Assisted Hybrid NOMA

TL;DR

The paper addresses uplink power minimization for BackCom-assisted H-NOMA under imperfect CSI by formulating a worst-case robust optimization problem that accounts for generalized channel gain errors and residual SIC interference. It derives tractable convex surrogates via Lagrange duality and applies a majorization-minimization (MM) framework, augmented with slack-variable penalties to temper conservatism. The resulting iterative algorithm is proven to converge to a KKT point, with complexity dominated by solving convex conic-quadratic programs per iteration. Numerical results show the robust scheme achieves favorable power efficiency and high feasibility under CSI uncertainties, outperforming OMA and competing with nominal H-NOMA approaches in realistic conditions.

Abstract

Hybrid non-orthogonal multiple access (H-NOMA) is inherently an enabler of massive machine type communications, a key use case for sixth-generation (6G) systems. Together with backscatter communication (BackCom), it seamlessly integrates with the traditional orthogonal multiple access (OMA) techniques to yield superior performance gains. In this paper, we study BackCom assisted H-NOMA uplink transmission with the aim of minimizing power with imperfect channel state information (CSI), where a generalized representation for channel estimation error models is used. The considered power minimization problem with aggregate data constraints is both non-convex and intractable. For the considered imperfect CSI models, we use Lagrange duality and the majorization-minimization principle to produce a conservative approximation of the original problem. The conservative formulation is relaxed by incorporating slack variables and a penalized objective. We solve the penalized tractable approximation using a provably convergent algorithm with polynomial complexity. Our results highlight that, despite being conservative, the proposed solution results in a similar power consumption as for the nominal power minimization problem without channel uncertainties. Additionally, robust H-NOMA is shown to almost always yield more power efficiency than the OMA case. Moreover, the robustness of the proposed solution is manifested by a high probability of feasibility of the robust design compared to the OMA and the nominal one.

Figures (6)

• Figure 1: Illustration of BackCom assisted hybrid NOMA. During $T_{t}$, users $u>t$ are allowed to transmit their data using the BackCom mode. The data rate of user $u$ during time slot $t\geq u$ is denoted by $R_{ut}$. The channel gains are ordered in a decreasing order $|h_{1}|^{2}>|h_{2}|^{2}>\cdots>|h_{U}|^{2}$ and SIC is carried out in an increasing order to detect users's signals. BackCom between user $u$ in time slot $t$ and transmission in its dedicated time slot is shown in the same color.
• Figure 2: Variation of total consumed power and PF with threshold data rate. The uncertainty parameter $\rho$ is set as 0.025.
• Figure 3: Convergence behaviour of Algorithm \ref{['alg:RHNOMA']} for different $\tau_0$. The parameter $\rho$ is fixed as $0.025$, $r_p=2$ m and $r_c=15$ m.
• Figure 4: CDF plot of data rate (bps/Hz) of a typical user. We take $\rho=0.025$, $\mathcal{T}=3$ bps/Hz, $r_p=2$ m and $r_c=15$ m.
• Figure 5: PF vs variance of channel gain errors of $g_{ut}$. The magnitude of channel estimation error of $h_{u}$ is kept fixed at $10^{-2.5}$. The threshold data rate $\mathcal{T}=4$ bps/Hz, $r_p=2$ m and $r_c=15$ m.

Theorems & Definitions (6)

• Remark 1
• Theorem 1
• Lemma 1
• Lemma 2
• Lemma 3
• Remark 2