## 1 Introduction  
Recently, Internet of Things (IoT) systems have been rapidly deployed at an unprecedented pace with the growing demand in various emerging applications in the realms of sixth-generation (6G) networks [1]. The International Data Corporation (IDC) reveals that 41.6 billion connected IoT devices will generate 79.4 zettabytes of data by 2025 [2]. Hence, the design of 6G cellular IoT networks needs to satisfy the growing demands and expectations, e.g., huge capacity, low latency, seamless coverage, and global connectivity [3]. Direct communication between devices in close proximity (D2D communication) has emerged as a significant enabler of the 6G-based IoT networks [4]. In D2D communications, devices can communicate directly to exchange information, or they can relay data over the licensed cellular spectrum without forwarding it to a base station (BS) and without harmfully interfering with the licensed cellular users (this is called underlay communication). Thus, D2D communication is considered a promising offloading solution that enhances the overall network's performance by improving the spectral and energy efficiencies while reducing latency [5]. Due to the spectrum scarcity, there is a constant push for D2D users to share the under-utilized radio spectrum with cellular users (CUs). However, this might cause degradation in the quality-of-service (QoS) for the CUs due to unacceptable co-channel interference. Hence, interference management in underlay D2D communication has become a crucial challenge [5]. This can, however, be carefully tackled using efficient resource allocation [6], beamforming, and interference cancellation schemes [7]. On the other hand, due to transmit power limitations, the success rate of offloading is poor for those D2D users who are far away or hidden from each other. Moreover, the offloading communication links are prone to deep fade, blockages by obstacles, shadowing, etc. Therefore, an advanced framework for efficient D2D off-loading is necessary for satisfactory performance. Recently, the usage of intelligent reflecting surfaces (IRS) has emerged as a hardware solution to improve radio frequency (RF) signal propagation issues and, in addition, to realize a smart radio environment [8]. Specifically, the IRS is a two-dimensional man-made surface of electromagnetic (EM) material, namely a metasurface, that is composed of a large array of specially designed passive scattering elements. Using software, each scattering element can be programmed to maneuver the properties of the reflected RF signal, namely the phase and spacial angles compared to the incident signal. This can create a desirable multi-path effect. For instance, the reflected RF signals can be added coherently to improve the received signal power or be combined destructively to mitigate interference. The IRS can be applied as a coating on a building wall or even be carried by aerial platforms, paving the way to several smart functionalities. Hence, the IRS can turn a radio environment into a smart space with enhanced data rate, extended coverage, low power consumption, and more secure transmissions [8]. In contrast to the traditional relay communications, IRS can characterize a fully controllable signal propagation scenario without a constant power supply and active circuitry requirements [9]. This enhances the system capacity, spectral efficiency, and energy efficiency substantially. Therefore, an IRS-assisted D2D framework underlaying cellular system is very promising in eliminating the interference between the cellular and D2D users. Thus, this framework has the ability to boost the signal strengths of the cellular radio links, and it can help to meet the required data rate [10]. The research in this area has not yet been fully explored, which is the motivation behind this study on the IRS-assisted D2D framework. Most of the resource allocation problems in the literature are constructed as nonlinear non-convex optimization problems that are mathematically intractable [10].