The next generation of cellular communication networks aims to enable ubiquitous connectivity with limited inter-cell interference through cell-free massive multiple-input multiple-output (CF-MMIMO) technology. Deploying an intelligent reflecting surface (IRS) in the cell-free (CF) architecture can significantly enhance coverage area and increase network spectrum efficiency. The signals reflected from IRS can be superposed coherently at the user by introducing the phaseshift with passive reflecting elements (PREs) on IRS. Non-terrestrial communications via unmanned aerial vehicles (UAVs) are critical in providing the seamless connection of the next generation of cellular communication systems. In the current terrestrial network, the signal strength of aerial platforms like UAVs is compromised as the access points (APs) are, in general, aimed at serving ground user ends (GUEs). This challenge can be addressed by incorporating IRS into the CF-MMIMO network. In this paper, we present an IRS-assisted CF-MMIMO network architecture that provides coverage for conventional terrestrial and evolving non-terrestrial aerial user equipment (UEs) simultaneously. The terrestrial UEs experience Rayleigh fading in this architecture, while the non-terrestrial aerial UEs experience Rician fading. To assess the performance of the considered system intuitively, we derive closed-form expressions for both the downlink (DL) spectral efficiency (SE) and the overall system outage probability. These analytical tools allow us to gain valuable insights into the design of CF systems for the next generation of communication systems. To further demonstrate the effectiveness of our developed analytical framework, we validate the developed theoretical tools with Monte Carlo computer simulations for various use cases of the CF-MMIMO network.
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