# Joint Power and Time Allocation in Hybrid NoMA/OMA IoT Networks for Two-Way Communications
## 4 Simulation Analysis  
Since NoMA's detection complexity and delay increase with the number of terminals, a pair of user terminals, i.e., \(K=2\), are the most popular combination for NoMA. As a compromise, we choose \(K=3\) in the simulations. For the network topology, we considered the same scenario as adopted by [26]. In this scenario, all the communication nodes are distributed in a circular area of a 10 m radius, where the AP is located at the origin and the three terminals are uniformly distributed over three circular annulus with the inner radii of 1, 4, and 7 m, and the outer radii of 3, 6, and 10 m, respectively. The channel gain is defined as \(\left|l_{k}\right|^{2}=\beta(d_{k}/d_{0})^{-\alpha}\times\mathrm{Rice}(L)\), where \(\mathrm{Rice}(L)\) is the small-scale channel gain with a rice factor of \(L\); \(d_{k}\) is the transmission distance of the IoD \(k\); \(d_{0}\), \(\beta\), and \(\alpha\) are the reference distance, the channel gain at the reference distance, and the path loss exponential, respectively. In the simulations, \(L=10\), \(d_{0}=1\), \(\beta=-10\) dB, and \(\alpha=2.0\); and without loss of generality, let \(\tilde{R}_{\mathrm{D}}\xrightarrow{\tilde{R}}_{\mathrm{D,k}}\xrightarrow{ \tilde{R}}_{\mathrm{U}}\xrightarrow{\tilde{R}}_{\mathrm{U}}\xrightarrow{ \tilde{R}}_{\mathrm{U},k}\sigma_{\mathrm{AP}}^{2}=\sigma_{K}^{2}=10^{-6}\) W, for \(\forall k\). We first investigated the convergence performance of the iterative Algorithm 1. Under three transmission rate combinations \((\tilde{R}_{\mathrm{D}},\tilde{R}_{\mathrm{U}})\) with bits/s/Hz unit, Figures 2 and 3 plot the numerical relation curves between the system power and the UL time allocation proportion. Although only the UL time allocation proportion is given in the simulations, the DL time allocation proportion can be readily yielded by subtracting the UL time allocation proportion from one. Simulations from these plots show that both the system power and the time allocation proportion converge at a rapid speed. Only after several iterations, the system power and the time allocation proportion remained unchanged. Next we examined the numerical relationship between the time allocation proportion and the traffic difference on the DL and UL, as shown in Figure 3. For \((\bar{R}_{\rm D},\bar{R}_{\rm U})=(2,2)\), the UL time allocation proportion was about 46%, basically equal to the DL one of about 54%. For \((R_{\rm D},\bar{R}_{\rm U})=(1,3)\) and \((R_{\rm D},\bar{R}_{\rm U})=(3,1)\), the time allocation proportions for the UL and DL differed greatly. Specifically, for \((\bar{R}_{\rm D},\bar{R}_{\rm U})=(1,3)\), the UL time allocation proportion was about 71.5%, far exceeding the DL one of about 28.5%, and for \((\bar{R}_{\rm D},\bar{R}_{\rm U})=(3,1)\), the UL time allocation proportion was about 22%, much less than the DL one of about 78%. This is attributed to the asymmetric traffic on the DL and UL. For \((\bar{R}_{\rm D},\bar{R}_{\rm U})=(2,2)\), the traffic levels on the DL and UL are symmetric, and thus the DL and UL own almost the same transmission time. For \((\bar{R}_{\rm D},\bar{R}_{\rm U})=(1,3)\), the UL traffic is heavier than the DL, and of course requires more transmission time than the DL. On the contrary, for \((\bar{R}_{\rm D},\bar{R}_{\rm U})=(3,1)\), the DL traffic is heavier than the UL, and naturally requires more transmission time than the DL. Figure 3: Convergence property of the uplink’s transmission time. Figure 2: Convergence property of the system’s power. the UL. The variations of the transmission time proportion with the traffic difference on the DL and UL just reflect the resource allocation of the optimization procedure. Next we examine different resource allocation methods for the proposed system. To be specific, we investigate two methods of the joint power and time allocation and the power allocation with fixed time allocation proportion.