Nowadays, more and more multimedia services are supported by Mobile Edge Computing (MEC). However, the instability of the wireless environment brings a lot of uncertainty to the computational offloading. Additionally, intelligent reflecting surface (IRS) is considered as a potential technology to enhance Quality of Service (QoS). Therefore, in this paper, we establish a framework for IRS-assisted MEC computational offloading to solve this problem and take fairness optimization as a key point involving communication and computing resources. Minimize user consumption by optimizing bandwidth allocation, task offloading ratio, edge computing resources, transmission power and IRS phase shifts. Firstly, we decompose the problem into three aspects, such as bandwidth allocation, computing resource allocation, transmission power and IRS phase shifts. Then, an alternative optimization algorithm is proposed to find the optimum solution and its convergence is proved. Secondly, since the optimization problem on transmission power and IRS phase shifts is non-convex, we propose Riemann gradient descent (R-SGD) algorithm to solve it. Finally, numerical results show that our proposed algorithm performs better than other algorithms and achieves a superiority in the framework.

如今，移动边缘计算（MEC）支持越来越多的多媒体服务。然而，无线环境的不稳定性给计算卸载带来了很多不确定性。此外，智能反射面（IRS）被认为是提高服务质量（QoS）的潜在技术。因此，在本文中，我们建立了一个 IRS 辅助 MEC 计算卸载的框架来解决这个问题，并将公平优化作为涉及通信和计算资源的关键点。通过优化带宽分配、任务卸载率、边缘计算资源、传输功率和 IRS 相移来最小化用户消耗。首先，我们将问题分解为带宽分配、计算资源分配、传输功率和IRS相移三个方面。然后，提出了一种替代优化算法来寻找最优解，并证明了其收敛性。其次，由于传输功率和IRS相移的优化问题是非凸的，我们提出了黎曼梯度下降（R-SGD）算法来解决它。最后，数值结果表明，我们提出的算法性能优于其他算法，并在框架中取得了优势。