## 1 Introduction  
As increasingly more 5G technology is being brought from concept to reality, the era of 5G has already started. A concept named reconfigurable intelligent surface (RIS) is proposed to achieve a higher data rate and increased availability and soon became a hot research topic. In practice, RIS is an artificial radio structure composed of low-cost units which can be programmed to reflect incoming radio-frequency waves to specified directions [1]. What makes RIS unique as a part of the environment is that it can control its reaction to the impinging radio wave by changing the inside current compared to the conventional surface [2, 3]. According to the physical laws, the traditional surface, such as a wall, has a fixed reflection characteristic. As RIS can adapt to time-varying wireless communication environments, it makes the concept of intelligent radio environments possible [3]. The propagation environments become reconfigurable by adding RISs into the wireless environments. The process of installing RISs on or removing RISs from walls or ceilings has a low implementation cost as the hardware footprints are relatively low [4, 5, 6, 7]. Therefore, RIS is expected to be the cost-efficient and energy-saving technology to improve system performance, becoming one of the hot topics in future communication networks [8, 9, 10, 11]. Through the research of channel modeling [12, 13], channel estimation [14], and performance evaluation of the communication system based on the RIS [15, 16, 17], the potential benefits of the communication environments based on RIS are discussed. In the resource allocation design of RIS-aided communication, large amounts of work focus on optimizing the spectral efficiency (SE) of the system [18]. Furthermore, we treat energy efficiency (EE), which is another important topic in the research on RIS [19, 20], as one of the optimization objectives. However, most of the existing work has focused on the optimization of either SE or EE. SE performance is sometimes sacrificed for the maximization of EE, especially when the value of Signal to Interference plus Noise Ratio (SINR) is large [21; 22]. Therefore, we try to find a way to attain a balance between EE and SE. In this paper, a trade-off between SE and EE is investigated while the transmitting precoding at the base station (BS) side and the phase shift values at the RIS of RIS-aided multi-user multiple-input single-output (MISO) downlink are jointly optimized. The main contributions made by this paper are listed as follows. We consider a RIS-aided multiuser downlink system to attain an EE-SE trade-off. Next, we propose an optimization framework for the problem in joint optimization. Then, we develop an optimization algorithm to design the transmitting precoding at the BS side and the phase shift values at the RIS to attain this trade-off. We first use the alternating optimization (AO) method to decouple the optimization variables. We also use quadratic transform and weighted minimization mean-square error (WMMSE) to turn the problem into a strictly convex problem. The rest of this article is organized as follows. We introduce the optimization problem of the RIS-aided multiuser MISO downlink system in Section 2. Then, we present an algorithm framework to handle the problem in Section 3. In Section 4, we present further numerical analysis according to simulation results. At last, we provide the conclusion of this paper in Section 5. **Notation 1**. : _We use \(\mathbf{A}\) to denote a matrix, while \(a_{i,j}\) and \(\mathbf{a}_{k}\) denote the \((i,j)\)-th element and the \(k\)-th column vector of matrix \(\mathbf{A}\), respectively. We also use \(\mathbf{x}\) to denote a column vector, while \(x_{i}\) and \(\|\mathbf{x}\|\) denote the \(i\)-th element and the Euclidean norm of vector \(\mathbf{x}\), respectively. An \(M\times M\) identity matrix is denoted by \(\mathbf{I}_{M}\) in this paper. The notation \(|b|\) denotes the modulus value of complex scalar \(b\).