In this paper, a multiple-cluster downlink multiple-input single-output (MISO) nonorthogonal multiple access (NOMA) system is considered. In each cluster, there are one central user and one cell-edge user. The central user has a data buffer with finite storage units, which will decode the cell-edge user’s message and store it at the data buffer. To enhance the performance of the cell-edge user, the central user operates as a relay and helps forward the message to the cell-edge user. Our objective is to maximize the long-term average sum rates for the cell-edge users by designing the beamforming vectors and online power control, under the constraints of the data buffer causality, required information rates for central users, and transmit power at the base station and central users. Based on the current buffer state and the channel state information, we propose a low-complexity online Lyapunov optimization algorithm combined with a constrained concave-convex procedure (CCCP) to solve the causal and nonconvex problem. Furthermore, we verify the asymptotic optimality of the proposed online Lyapunov optimization algorithm. Simulation results demonstrate that our proposed scheme performs better than the greedy algorithm and the orthogonal multiple access (OMA) scheme.
Recently, nonorthogonal multiple access (NOMA) scheme is considered as a breakthrough key technology for the fifth generation networks and has attracted great attention [
In the practical and causal NOMA cooperative relaying system, the current information is reachable only when it arrives, which is involved with the online resource allocation problem. In [
A cellular downlink MISO NOMA system is being considered in our study, which consists of multiple clusters. In each cluster, there are one central user and one cell-edge user. The central user has a data buffer with finite storage units and operates as a relay to help forward the message to the cell-edge user. For cell-edge users with high quality of service (QoS) requirement, by designing optimal beamforming vectors and power allocation, our objective is to maximize the long-term average achievable information bits for the cell-edge users under the constraints of required number of achievable information bits for the central users and transmit power constraints. The optimization problem is causal and nonconvex and thus hard to solve. Based on the current buffer state and the channel state information, we propose a low-complexity online Lyapunov optimization algorithm combined with a constrained concave-convex procedure (CCCP). The asymptotic optimality of the proposed online Lyapunov optimization algorithm is also verified.
The rest of this paper is organized as follows: Section
For a vector,
We consider a buffer-aided cooperative NOMA downlink system consisting of a base station and
The model for a buffer-aided cooperative NOMA downlink transmission system.
The base station transmits signals to central users directly while transmits signals to cell-edge users with the cooperation of central users. We assume that the transmission time duration is partitioned into
In the
Accordingly, at the
During the remaining
The central users can store the information bits at the data buffers for later transmission. We assume the data buffers at the central users have finite storage units, denoted as
The dynamics of data buffer is
At the
For the cell-edge users with high QoS requirement, our objective is to maximize the long-term average achievable information bits for the cell-edge users under the constraints of required number of achievable information bits for the central users and transmit power constraints, which is formulated as
Problem
In this section, an online Lyapunov algorithm to solve problem
According to the Lyapunov optimization [
Accordingly, the per-time-slot Lyapunov drift with respect to the data buffer at the
Because of the dynamics involved in
For any feasible
From the dynamics of data buffer (
From (
Substituting (
The Lyapunov algorithm only needs the current system state, and thus, we turn it into a per-slot problem and minimize the drift-plus-penalty function’s upper bound. Since
In problem (
Using (
Problem
Note that when
The right-hand side of (
Similarly, the right-hand sides of (
Thus, in our iterative algorithm, given
Now, we summarize the proposed online Lyapunov algorithm in Algorithm
(
(
From (
Firstly, we give the feasible set and its complement on the possible range of
The main idea of this modified algorithm above is that we use the buffer state
In this section, the online Lyapunov algorithm’s performance is analyzed. From [
The asymptotic optimality of our proposed online Lyapunov algorithm is verified as follows.
We first define the following optimization problem related to
Problem
For any feasible solution of problem
Since
To continue, we have the following result for problem
Let
Then the asymptotic optimality of our proposed online Lyapunov algorithm is verified in the following lemma.
Denote
Since the objective of problem
From Lemma 1, we have
Since problem
In this section, we provide the simulation results of our proposed algorithm. We consider the NOMA system with complex Gaussian random channels, where the channel responses
Figures
Long-term average sum rate of cell-edge users versus time slot.
Long-term average sum rate of all users versus time slot.
From the perspective of time slots, Figures
Figure
Data buffer dynamics versus time slot.
Figure
Long-term average sum rate of cell-edge users versus transmit power constraints.
Considering the NOMA system with buffer-aided cooperative relaying, we have proposed the online Lyapunov algorithm combined with the constrained concave-convex procedure to solve the causal long-term average transmission sum rate maximization problem and verified the asymptotic optimality of the proposed online Lyapunov. Simulation results have shown that the proposed online Lyapunov algorithm outperforms the greedy algorithm and the conventional OMA scheme.
No data were used to support this study.
This research was a part of the project titled Optimization Design for Physical Layer Security of Nonorthogonal Multiple Access Wireless Networks, funded by the National Natural Science Foundation of China.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported in part by the National Natural Science Foundation of China under Grant 61802447, in part by the Guangdong Natural Science Foundation under Grants 2018B0303110016 and 2014A030310374 and Guangzhou Science and Technology Program under Grant 201804010445.