Version Age of Information Minimization over Fading Broadcast Channels

TL;DR

The paper investigates minimizing the long-term weighted VAoI across users in a downlink fading BC using NOMA, where VAoI is captured by $\Delta_i(t)=z_i(t)-y_i(t)$. It develops two solution frameworks: a channel-only stationary randomized policy (CO-SRP) and a CMDP-based approach with Lagrangian relaxation, and shows a performance bound $V_{\rm SRP} \le 2 V_{\rm opt}$. An iterative method solves the CO-SRP’s non-convex objective, while the CMDP solution reveals threshold structure and uses a bisection search on the Lagrange multiplier to satisfy the power constraint. Numerical results for a two-user case indicate that CO-SRP is competitive with the CMDP approach and that NOMA outperforms TDMA under relaxed power constraints, highlighting scheduling and power allocation tradeoffs for information freshness in fading broadcast channels.

Abstract

We consider a base station (BS) that receives version update packets from multiple exogenous streams and broadcasts them to corresponding users over a fading broadcast channel using a non-orthogonal multiple access (NOMA) scheme. Sequentially indexed packets arrive randomly in each stream, with new packets making the previous ones obsolete. In this case, we consider the version age of information (VAoI) at a user, defined as the difference in the version index of the latest available packet at the BS and that at the user, as a metric of freshness of information. Our objective is to minimize a weighted sum of average VAoI across users subject to an average power constraint at the BS by optimally scheduling the update packets from various streams for transmission and transmitting them with sufficient powers to guarantee their successful delivery. We consider the class of channel-only stationary randomized policies (CO-SRP), which rely solely on channel power gains for transmission decisions. We solve the resulting non-convex problem optimally and show that the VAoI achieved under the optimal CO-SRP is within twice the optimal achievable VAoI. We also obtained a Constrained Markov Decision Process (CMDP)-based solution and its structural properties. Numerical simulations show a close performance between the optimal CO-SRP and CMDP-based solutions. Additionally, a time division multiple access (TDMA) scheme, which allows transmission to at most one user at a time, matches NOMA's performance under tight average power constraints. However, NOMA outperforms TDMA as the constraint is relaxed.

Figures (6)

• Figure 1: VAoI evolution for the CO-SRP. The expressions closer to the arrows represent the state transition probability; the other expressions above are the events that cause the transitions.
• Figure 2: Variation of the long-term expected average weighted sum of VAoI, with the average transmit power, $\bar{P}$, under the CO-SRP and the CMDP-based policy with NOMA and TDMA schemes. Parameters adopted are $\lambda_1 = \lambda_2 = 0.5$, $R^0_1=R^0_2=2$, $\mathcal{H}\in \{1, 0.1\}$, $\mathbb{P}(H_1=0.1) = \mathbb{P}(H_2=0.1) =0.2$, and $w_1 = w_2 = 0.5$.
• Figure 3: Probability of simultaneous transmissions to both users versus the average transmit power, $\bar{P}$, under the CO-SRP with NOMA scheme for $R^0_1 = R^0_2 = 2$, $\mathcal{H}\in \{1, 0.1\}$, $H_1 = H_2 = H$, $\lambda_1 = \lambda_2 = 0.8$ and $w_1 = w_2= 0.5$.
• Figure 4: Variation of the long-term expected average weighted sum of VAoI with respect to probability of packet arrival, $\lambda_1 = \lambda_2 = \lambda$, under the CO-SRP with NOMA and TDMA schemes. Parameters are set to $R^0_1= R^0_2 = 2$, $\mathcal{H}\in \{1, 0.1\}$, $\mathbb{P}(H_1=0.1) = \mathbb{P}(H_2=0.1) =0.5$, $w_1 = w_2 = 0.5$.
• Figure 5: The largest achievable long-term expected average VAoI region by NOMA and TDMA schemes under CO-SRP by varying the weights associated with users ($w_1, w_2$). Parameters adopted are $\bar{P} = 40$, $\lambda_1 = \lambda_2 = 0.9$, $R^0_1 = R^0_2 = 2$ and $\mathcal{H}\in \{1, 0.1\}$, and $\mathbb{P}(H_1=0.1) = \mathbb{P}(H_2=0.1) =0.5$.

Theorems & Definitions (10)

• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof
• Lemma 5
• proof