1. Introduction

2. Related Work

3. RAW Mechanism in Wireless IoT Networks

4. DRL for RAW Parameters Optimization

4.2. PPO for Optimizing RAW Parameters

Given a policy approximator ${\pi }_{\theta }\left(a\right|s)$ with parameters $\theta$, policy-based policy gradient (PG) algorithms find the optimal $\theta$ to maximize the reward or value function. For a given input state $s_t$, the policy network directly outputs either the action or the probability associated with the action. It then selects the appropriate action based on the probability, allowing the output action to be a continuous value. The expected value function in PG algorithms can be represented in terms of the policy parameters as

$$\begin{array}{c}\hfill J\left(\theta \right)=\sum _s{d}^{{\pi }_{\theta }}\left(s\right)V^{{\pi }_{\theta }}\left(s\right)=\sum _s{d}^{{\pi }_{\theta }}\left(s\right)\sum _a{\pi }_{\theta }(s,a)Q^{{\pi }_{\theta }}(s,a),\end{array}$$

(8)

where $d^{{\pi }_{\theta }}$ is the stationary distribution of the Markov chain for ${\pi }_{\theta }$, and $Q^{{\pi }_{\theta }}(s,a)$ denotes the Q-value of the state-action pair $(s,a)$ following the policy ${\pi }_{\theta }$. The goal of PG is to find parameters $\theta$ that maximize $J\left(\theta \right)$ by ascending he gradient of the policy. The evaluation of the policy gradient ${\nabla }_{\theta }J\left(\theta \right)$ can be simplified as [36]

$$\begin{array}{c}\hfill {\nabla }_{\theta }J\left(\theta \right)={\mathbb{E}}_{\pi }[Q^{\pi }(s,a){\nabla }_{\theta }ln{\pi }_{\theta }\left(a\right|s))]={\mathbb{E}}_{\pi }[\sum _{t=1}^T{Q}^{\pi }(s_t,a_t){\nabla }_{\theta }ln{\pi }_{\theta }\left(a_t\right|s_t))],\end{array}$$

(9)

where the expectation is taken over all possible state-action pairs following the same policy ${\pi }_{\theta }$. The policy gradient ${\nabla }_{\theta }J\left(\theta \right)$ can be evaluated by sampling historical decision-making trajectories.

For each episode, all the $(s,a,r,s^{\prime })$ tuples acquired by the agent can be collectively represented as a state-action trajectory resulting from the agent’s interaction with the environment over the current episode, which is denoted as $\tau =(s_0,a_0,r_1,s_1,...,s_{T-1},a_{T-1},r_{T-1},s_T)\sim ({\pi }_{\theta },P\left(s_{t+1}\right|s_t,a_t))$. Let $G_t={\sum }_{k=t}^{T}r(s_k,a_k)$ be the reward for a trajectory $\tau$, and estimate the Q-value $Q^{\pi }(s_t,a_t)$ in (9) by $G_t$. Therefore,the policy gradient in each time step can be approximated by randomly sampling $G_t{\nabla }_{\theta }ln{\pi }_{\theta }\left(a_t\right|s_t))$, and the policy parameters can be updated as $\theta \leftarrow \theta +\alpha {\nabla }_{\theta }J\left(\theta \right)$ , where $\alpha$ denotes the step size for gradient update. To reduce prediction variability and improve learning efficiency, the value function $V_{\pi }\left(s\right)$ can be used as the baseline, and the advantage function $A_{\pi }(s,a)\triangleq Q^{\pi }(s,a)-V_{\pi }\left(s\right)$ is further introduced to replace $G_t$.

To address high-dimensional state and action spaces while stabilizing the learning process, actor-critic (AC)-based DRL algorithms introduce a DNN with weight parameters $\omega$ to approximate the Q value. AC algorithms update both the policy network and the Q-value network. Specifically, at each learning step t, the actor updates the policy network by updating the policy parameters $\theta \leftarrow \theta +{\alpha }_{\theta }{Q}_{\omega }(s,a){\nabla }_{\theta }ln{\pi }_{\theta }\left(a\right|s))$, while the critic updates the Q network by minimizing a loss function and updates the parameters $\omega \leftarrow \omega +{\alpha }_{\omega }{\delta }_t{\nabla }_{\omega }{Q}_{\omega }(s,a)$ by gradient ascent, where ${\delta }_t=r_t+\gamma Q_{\omega }(s^{\prime },a^{\prime })-Q_{\omega }(s,a)$ denotes the TD error. To further stabilize the training process, the deep deterministic gradient policy (DDPG) algorithm [36] utilizes two DNNs with different parameters, i.e., the online Q-network $Q_{\omega }(s,a)$ and the target Q-network $Q_{{\omega }^{\prime }}(s,a)$. The TD error is rewritten as ${\delta }_t=r_t+\gamma Q_{{\omega }^{\prime }}(s^{\prime },a^{\prime })-Q_{\omega }(s,a)$.

To facilitate the agent’s utilization of past experiences and improve sample efficiency, PG can be transformed into off-policy learning through the utilization of importance sampling [37]. Sample collection can be conducted under a behavior policy ${\pi }_o(s,a)$ distinct from the target policy ${\pi }_{\theta }\left(a\right|s)$. To mitigate the effects of improper step size in policy optimization on training stability, the off-policy trust region policy optimization (TRPO) algorithm imposes an additional constraint on the gradient update [37], ensuring that the old and new policies do not diverge significantly. Let ${\rho }_{theta}=\frac{{\pi }_{\theta }(s,a)}{{\pi }_o(s,a)}$ denote the probability ratio of the divergence between the old and new policies. TRPO maximizes the objective by applying conservative policy iteration without limiting the probability ratio to an appropriate range. This could lead to an excessively large policy update. Intuitively, a smaller deviation between the behavior policy and the target policy is better. Hence, the PPO algorithm [34] modifies the objective by constraining ${\rho }_{\theta }$ in a region $[1-ϵ,1+ϵ]$, and penalizing changes to the policy that move ${\rho }_{\theta }$ away from 1. The objective in $PP{O}_{CLIP}$ is

$$\begin{array}{cc}\hfill \underset{\theta }{max}& L^{CLIP}\left(\theta \right)=\tilde{J}\left(\theta \right)={\mathbb{E}}_{{\pi }_o}[min\{{\rho }_{\theta }{\widehat{A}}_{{\pi }_o},clip({\rho }_{\theta },1-ϵ,1+ϵ){\widehat{A}}_{{\pi }_o}\}]\hfill \\ \hfill s.t.& D_{KL}({\pi }_o,{\pi }_{\theta })\le {\delta }_{KL},\hfill \end{array}$$

(10)

where $D_{KL}(P_1,P_2)\triangleq {\int }_{\infty }^{\infty }{P}_1\left(x\right)log(P_1\left(x\right)/P_2\left(x\right))dx$ denotes a distance measure in terms of the Kullback-Leibler (KL) divergence between two different probability distributions. The advantage function $A_{{\pi }_o}$ in the objective of problem (10) is the approximation of the actual advantage $A_{{\pi }_{\theta }}$ corresponding to the target policy ${\pi }_{\theta }$. PPO constrains the parameters search within a region by introducing the inequality constraint in problem (10), which ensures that the KL convergence between ${\pi }_{\theta }$ and ${\pi }_o$ is bounded by ${\delta }_{KL}$. The clip function returns ${\rho }_{\theta }\in [1-ϵ,1+ϵ]$, and the hyper-parameter $ϵ=0.2$ by default.

During the training of the DNNs, PPO employs fixed-length(e.g. T time steps) trajectory segments. A truncated advantage estimation is computed to replace the advantage function in problem (10) as

$${\widehat{A}}_t^{{\pi }_o}={\delta }_t+\gamma {\delta }_{t+1}+\cdots +{\gamma }^{T-t+1}{\delta }_{T-1},$$

(11)

where ${\delta }_t=r_t+\gamma V\left(s_{t+1}\right)-V\left(s_t\right)$. The loss function of PPO is

$$L_t\left(\theta \right)={\mathbb{E}}_t[L_t^{CLIP}\left(\theta \right)-c_1{L}_t^{VF}\left(\theta \right)+c_{2}S\left[{\pi }_{\theta }\right]\left(s_t\right)],$$

(12)

where $L^{VF}=V_{\theta }\left(s_t\right)-V_t^{target}$ is the mean squared error loss, $c_1,c_2$ are coefficients, S is an entropy bonus.

The PPO algorithm for optimizing RAW parameters in networks built in NS-3 is summarized in Algorithm 1. PPO utilizes two DNNs to approximate the policy networks. In each learning episode, the PPO agent runs the old/behavior policy ${\pi }_{{\theta }_o}$ (i.e., RAW parameters), observes network throughput obtained from the NS-3 network simulations environment for T time steps, and stores T transition tuples $(s_t,a_t,r_t,s_{t+1}),t\in T$ in the experience replay buffer. Then, it samples mini-batches of transition tuples from the replay buffer and computes advantage estimates ${\widehat{A}}_1^{{\pi }_o},\cdots ,{\widehat{A}}_T^{{\pi }_o}$. Subsequently, weight parameters of the target policy network ${\pi }_{\theta }$ are updated by using mini-batches randomly sampled from the replay buffer through importance sampling and by optimizing the surrogate loss in (12). Weight parameters of the behavior policy network are updated by ${\theta }_o\leftarrow \theta$. Limiting the probability ratio of the two policies ${\rho }_{\theta }\in [1-ϵ,1+ϵ]$ ensures that the probability distribution of the output actions from the two policy networks remains similar.

The uniform grouping scheme is verified to perform better in homogeneous networks [38]. Considering the networks with periodic and random traffic in this paper, we employ the uniform grouping scheme, where STAs are evenly distributed in each RAW. Consequently, the slot duration and number of slots in each RAW group are considered to be equal. As a result, the actions of the MDP can be further simplified to the number of RAW groups, the number of slots in one RAW group, and the slot duration in one RAW group.

5. DRL-guided NS-3 Simulation

5.2. Learning Performance in Periodic Traffic Networks

We first consider the RAW parameters optimization in networks with periodic traffic, where all STAs are assigned to one RAW group. The action of the MDP is $a_t=(K_{N_{RAW=1}},T_{N_{RAW=1}})$. In each iteration during the training process, the PPO agent observes throughput $s_t$ and other information $o_t$ from the wireless environment and employs policy $\pi$ to determine the RAW parameters setting $a_t$ for the next time step. The effectiveness of the RAW parameters is evaluated at the subsequent time step with the reward obtained from NS-3, and the RAW parameters for the following time step are determined accordingly. The PPO agent is trained through numerous interactions with network simulation environments bulit in NS-3.

5.2.1. Convergence to the Optimal RAW Parameters

We first validate the convergence performance of the PPO algorithm on a basic network topology. In the periodic traffic network, the traffic interval of all STAs is fixed (e.g., 0.1 ms). We train the PPO agent though numerous interactions with the network environment built in NS-3. The convergence performance of the PPO algorithm is shown in Figure 5, and Figure 6 demonstrates the convergence process of the PPO agent interacting with the network simulation environment in the NS-3 simulator. As the training iteration proceeds, the PPO agent learned better actions, leading to significantly increased normalized rewards obtained from interacting with the NS-3 simulation environment. After 10,000 training episodes, the reward stabilized at its maximum value. This indicates that the PPO agent has learned the optimal RAW parameters by the end of training and achieved the optimized network throughput in the periodic traffic network. We also observe the improvement of network throughput with the NS-3 simulator during the PPO agent’s training process. It can be seen in Figure 6 that the network throughput is ascending when the training process proceeds. Compared to the network throughput obtained with default settings ($K_{RAW}=1,TBI=100ms$), the network throughput with the optimal RAW parameters obtained by PPO agent is improved by about 70%. It is evident that employing DRL method for optimizing RAW parameters is feasible, and the RAW parameters derived from learning lead to a significant enhancement in network throughput compared to default settings.

Additionally, we depict the convergence performance of the slot count within a RAW and the slot duration with different number of STAs in the network. To provide a more straightforward demonstration, we calculate the approximate duration of a beacon interval as $T_{BI}=N_{RAW}·K·T_{slot}$ and use beacon interval dynamics to represent variations in slot duration in the following subsections. As shown in Figure 7, both parameters converge to stable values for different network sizes, further validating the algorithm’s convergence. As the network size is relatively small, the number of slots is similar when the number of STAs in the network is 40, 50 and 60 respectively. The duration of the beacon interval increases by about 40% when the number of STAs in the network increases from 40 to 60, indicating that the slot duration is adaptively adjusting to the network size with DRL.

Figure 7. Convergence performance of $K_{RAW}$.

Figure 7. Convergence performance of $K_{RAW}$.

Figure 8. Convergence performance of $T_{BI}$ ($w.r.t.T_{slot}$).

Figure 8. Convergence performance of $T_{BI}$ ($w.r.t.T_{slot}$).

5.2.2. Throughput Performance with Different Traffic Loads

In this section, we analyze the adaptive adjustment of RAW parameters obtained through PPO method with different network loads. We assume homogeneous traffic load 0.05 Mbps for each STA. Therefore, the traffic load in the network increases as the number of STAs in network increases. We observe the adaptive adjustments of RAW parameters and changes in network throughput as the number of STAs increases from 30 (10) to 100.

As shown in Figure 9, both the slot count and slot duration increase with the growing number of STAs and traffic load in network. The number of slots in a RAW increases stepwise with the network size and traffic load. Specifically, the slot count remains constant when the number of STAs is between 50-70 and 80-90. This is attributed to the fact that dividing fewer slots in a RAW significantly reduces contentions when the network size is small. Overall, the RAW mechanism ensures that the number of STAs in each RAW slot is not excessive. When the number of STAs in the network is less than 50, the slot duration increases significantly from $10ms$ to about $50ms$, approximately 4 times longer, with the increasing network size and traffic load.

This trend is consistent with the changes in network throughput depicted in Figure 10. When the number of STAs in the network is less than 40, the network throughput remains unsaturated with few STAs and low traffic load in the network. As the number of STAs increases from 10 to 40, along with the ascending network traffic load, the network throughput subsequently increases from $0.076Mbps$ to $0.248Mbps$, approximately 4 times larger. At a certain point, with number of STAs = 40, the network traffic load reaches its maximum capacity, leading to saturated network throughput under current network conditions. As the number of STAs in the network continues to increase from 40 to 90, contentions intensify, leading to a higher probability of transmission collisions. Meanwhile, when the network traffic load exceeds its capacity, constrained by the data transmission rate and the duration of a single simulation, the AP cannot handle all the traffic from STAs, resulting in a slight decrease by about 7% in network throughput. This trend is consistent with the variation of throughput with the number of STAs in IEEE 802.11 networks [14].

6. Conclusion

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