Unlicensed Assisted Ultra-Reliable and Low-Latency Communications

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.

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.