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Unlicensed Assisted Ultra-Reliable and Low-Latency Communications

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Abstract

The ultra-reliable and low-latency communication (URLLC) in the fifth generation (5G) communication has emerged many potential applications, which promotes the development of the internet of things (IoTs). In this paper, the URLLC system adopts the duty-cycle muting (DCM) mechanism to share unlicensed spectrums with the WiFi network, which guarantees the fair coexistence. Meanwhile, we use the mini-slot, user grouping, and finite block length regime to satisfy the low latency and high reliability requirements. We establish a non-convex optimization model with respect to power and spectrum, and solve it to minimize the power consumption at the devices, where the closed-form expressions are given by several mathematical derivations and the Lagrangian multiplier method. Numerical simulation results are provided to verify the feasibility and effectiveness of the proposed scheme, which improves the system spectrum efficiency and energy efficiency.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 61771429), in part by the Okawa Foundation for Information and Telecommunications, in part by G-7 Scholarship Foundation, in part by the Zhejiang Lab Open Program under Grant 2021LC0AB06, in part by the Academy of Finland under Grant 319759, Zhejiang University City College Scientific Research Foundation (No. JZD18002), in part by ROIS NII Open Collaborative Research 21S0601, and in part by JSPS KAKENHI (Grant No. 18KK0279, 19H04093, 20H00592, and 21H03424).

Author information

Authors and Affiliations

  1. School of Information and Electrical Engineering, Zhejiang University City College, Hangzhou, 310015, China

    Jiantao Yuan, Rui Yin & Wei Qi

  2. School of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, 310007, China

    Qiqi Xiao

  3. Graduate School of Informatics and Engineering, University of Electro-Communications, Tokyo, 182-8585, Japan

    Celimuge Wu

  4. VTT Technical Research Centre of Finland, Oulu, 90570, Finland

    Xianfu Chen

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  1. Jiantao Yuan
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  3. Rui Yin
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Correspondence to Rui Yin.

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Appendix A: Proof of convexity

Appendix A: Proof of convexity

The objective function Eq. 9 includes three parts. We can replace the second part, \(\theta ^{(U)}_{i,k}\) and \(p^{(U)}_{i,k}\), with \(A^{(U)}_{i,k}\). And P(tot) can be written as

$$P^{(tot)} \!= \! \sum\limits_{i=1}^{N}\sum\limits_{j=1}^{J}p^{(L)}_{i,j} + \sum\limits_{i=1}^{N}\sum\limits_{k=1}^{K}A^{(U)}_{i,k} + \sum\limits_{i=1}^{N}\sum\limits_{k=1}^{K}(1 - \theta^{(U)}_{i,k})p^{(U)}_{s}.$$
(A1)

Therefore, the objection function is a linear and convex function with respect to \(p^{(L)}_{i,j}\), \(A^{(U)}_{i,k}\), and \(\theta ^{(U)}_{i,k}\). The data rate of the URLLC device i on licensed subchannel j can be written as

$$\begin{array}{cc} R^{(L)}_{i,j} &= \underbrace{\xi^{(L)}_{i,j}W^{(L)}\log\left( 1+\frac{p^{(L)}_{i,j}h^{(L)}_{i,j}}{\xi^{(L)}_{i,j}W^{(L)}N_{0}}\right)}_{C_{1}} \\ &-\underbrace{\xi^{(L)}_{i,j}W^{(L)}\sqrt{\frac{V^{(L)}_{i,j}}{l}}\frac{Q^{-1}(\varepsilon)}{\ln2}}_{C_{2}}, \end{array}$$
(A2)

we can divide \(R^{(L)}_{i,j}\) into two parts, denoted as C1 and C2. For the first part, in order to prove its convexity, we define a function

$$R_{1}(x,y) = -x\log\left( 1+\frac{y}{x}\right),$$
(A3)

the Hessian matrix of R1(x,y) can be derived as

$$H =\left\lvert \begin{array}{cc} \frac{y^{2}/x}{(x+y)^{2}} & -\frac{y}{(x+y)^{2}}\\ -\frac{y}{(x+y)^{2}} & \frac{x}{(x+y)^{2}} \end{array}\right\lvert ,$$
(A4)

which has two eigenvalues

$$\lambda_{1} = 0,~\lambda_{2} = \frac{x^{2}+y^{2}}{x^{3}+2x^{2}y+xy^{2}}.$$
(A5)

It is obvious that two eigenvalues are greater or equal to zero when x ≥ 0. Thus, the function R1(x,y) is a convex function when x ≥ 0. For the second part, when the SINR is greater than 10 dB, \(V^{(L)}_{i,j}\) is approximately equal to 1. Therefore, the second part can be written as

$$C_{2} = \xi^{(L)}_{i,j}W^{(L)}\sqrt{\frac{1}{l}}\frac{Q^{-1}(\varepsilon)}{\ln2},$$
(A6)

which is linear with respect to \(\xi ^{(L)}_{i,j}\). Then, \(R^{(L)}_{i,j}\) can be rewritten as

$$\hat{R}^{(L)}_{i,j}\!= \! - f\left( \xi^{(L)}_{i,j}W^{(L)},\frac{p^{(L)}_{i,j}h^{(L)}_{i,j}}{N_{0}}\right) - \xi^{(L)}_{i,j}W^{(L)}\sqrt{\frac{1}{l}}\frac{Q^{-1}(\varepsilon)}{\ln2},$$
(A7)

the combination of a concave function and a linear function is also a concave function. The data rate of the URLLC device i on unlicensed channel k can be expressed as

$$\begin{array}{cc} R^{(U)}_{i,k} &= \theta^{(U)}_{i,k}W^{(U)}\log\left( 1+\frac{p^{(U)}_{i,k}h^{(U)}_{i,k}}{N_{0}W^{(U)}}\right)\\ &-\theta^{(U)}_{i,k}W^{(U)}\sqrt{\frac{V^{(U)}_{i,k}}{l}}\frac{Q^{-1}(\varepsilon)}{\ln2}, \end{array}$$
(A8)

let \(A^{(U)}_{i,k} = \theta ^{(U)}_{i,k} \cdot p^{(U)}_{i,k}\), and \(R^{(U)}_{i,k}\) can be expressed as

$$\begin{array}{cc} R^{(U)}_{i,k} &= \theta^{(U)}_{i,k}W^{(U)}\log\left( 1+\frac{A^{(U)}_{i,k}h^{(U)}_{i,k}}{\theta^{(U)}_{i,k}N_{0}W^{(U)}}\right)\\ &-\theta^{(U)}_{i,k}W^{(U)}\sqrt{\frac{V^{(U)}_{i,k}}{l}}\frac{Q^{-1}(\varepsilon)}{\ln2}, \end{array}$$
(A9)

we can prove \(R^{(U)}_{i,k}\) is also a concave function in the same way as \({R}^{(L)}_{i,j}\). The data rate of the URLLC device i can be written as

$$R_{i} = \sum\limits_{j=1}^{J}{R^{(L)}_{i,j}}+\sum\limits_{k=1}^{K}{R^{(U)}_{i,k}},$$
(A10)

the combination of a concave function and a concave function is also a concave function. In brief, problem P1 is a convex optimization problem.

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Yuan, J., Xiao, Q., Yin, R. et al. Unlicensed Assisted Ultra-Reliable and Low-Latency Communications. Mobile Netw Appl 27, 2232–2243 (2022). https://doi.org/10.1007/s11036-022-02003-8

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