Analysis of Age of Information in Wireless Communication Networks

Abstract

The exponential growth of Internet-of-Things (IoT) applications in next-generation communications has led to increasingly connected devices in the communication infrastructures. These connected devices are responsible to generate and exchange information within different entities of the communication setup to support decision taking processes in IoT applications. Emergence of diverse IoT applications (i.e., intelligent transportation systems, smart environmental applications, Tactile Internet applications, etc.) required the information freshness at the edge users to be increased much as possible. Thus, it is essential to maintain freshness of the information received since outdated information can jeopardize reliability of the system output given rise to safety risks. Data freshness at the destination is a quite difficult objective to achieve in wireless communication. It is also noteworthy that data freshness is different and goes beyond the latency. As a contribution in this direction, this book chapter defines the basic building block of the new performance metric named age of information. It begins with an introduction to AoI, and then it is shown the way AoI can be modeled for simultaneous wireless information and power transfer (SWIPT)-enabled cooperative communication network considering hardware impairments. Next, we investigate the relationship of AoI with other traditional performance metrics such as outage probability and throughput. Then, we optimize resource allocation of the SWIPT-enabled communication setup to improve AoI performance adhering to the quality-of-service (QoS) requirements. Finally, important future directions of AoI toward beyond 5G are provided along with conclusion remarks.

Appendix 1

The outage probability of the proposed system can be defined as the probability that the end-to-end average SNDR of the update data packet falls below a desired threshold value γ ^th. Therefore, the system outage probability at the S ₁ ¹ can be expressed as

$$\displaystyle \begin{aligned} P_{out} = Pr(\gamma_{S_1}<\gamma^{th}), {} \end{aligned} $$

(7.37)

where γ ^th = 2^2R − 1 and R is the transmission rate of the terminals. In order to have a closed-form expression for outage probability, considering (7.37), we fix X ₁ at some value x ₁ and obtain the outage probability with respect to x ₁. Next, the average of the obtained function in terms of x ₁ with respect to the distribution of X ₁ is considered to acquire the closed-form expression for outage probability at S ₁. Thus, (7.37) can be rewritten as

$$\displaystyle \begin{aligned} P_{out} = \int_{0}^{\infty}\gamma_{0}(C_{4}x_{1}+c_{3}x_{1}+c_{2})f_{X_{1}}(x_{1})dx_{1}. {} \end{aligned} $$

(7.38)

Now, (7.38) can be rewritten as

$$\displaystyle \begin{aligned} &p_{out}= 1-\mu_{1}e^{-2K}\int_{0}^{\infty}\sum_{k=0}^{\infty}\sum_{l=0}^{\infty}\sum_{m=0}^{l} \frac{(\mu_{2}\gamma_{o})^{m}K^{l+k}}{(k!)^2m!l!} (c_{4}x_{1}\\ &+c_{3}x_{1}+c_{2})^{m} \times e^{-\mu_{2}\gamma_{0}(c_{4}x_{1}+c_{3}x_{1}+c_{2})} (\mu_{1}x_{1})^{k} e^{-\mu_{1}x_{1}} dx_{1}. \end{aligned} $$

(7.39)

Then, having $\mu _{3}=\mu _{1}e^{2K}e^{-c_{2}\mu _{2}\gamma _{0}}$ and by applying probability mass function with binomial coefficient, we can obtain

$$\displaystyle \begin{aligned} &P_{out} = \mu_{3}\sum_{l=0}^{\infty}\sum_{k=0}^{\infty}\sum_{m=0}^{l}\sum_{n=0}^{m}\sum_{p=0}^{n} \underbrace{\frac{K^{l+k}\mu_{1}^k\mu_{2}^m\gamma_{0}^mc_{4}^{m-n}c_{3}^{n-p}c_{2}^p}{(k!)^2l!p!(m-n)!(n-p)!}}_{V_{1}}\\ &\times \underbrace{\int_{0}^{\infty} x_{1}^{m-2n+k+p}e^{-(\mu_{1}+c_{4}\mu_{2}\gamma_{0})x_{1}-\mu_{2}\gamma_{0}c_{3}x_{1}}}_{V_{2}} dx_{1}, {} \end{aligned} $$

(7.40)

whereby using (8.321.1) in [27], V ₂ can be represented as the complete Gamma function, and thus, (7.40) can be expressed as

$$\displaystyle \begin{aligned} P_{out} = &\mu_{3}\sum_{k=0}^{\infty}\sum_{l=0}^{\infty}\sum_{m=0}^{l}\sum_{n=0}^{m}\sum_{p=0}^{n} V_{1} \varGamma(1+k+m-2n+p)(\mu_{1}+\mu_{2}\gamma_{0}(c_{4}+c_{3}))^{-l-k-m-2n-p}, \end{aligned} $$

(7.41)

where only if (k + m − 2n + p) > 1 && μ ₁ + μ ₂ γ ₀(c ₄ + c ₃) > 0. Thus, by letting and considering Equation (3.471.9) in [27], a closed-form expression for the outage probability is obtained as in (7.25).