On the Performance of IRS-Assisted Multi-Layer UAV Communications With Imperfect Phase Compensation
Mohammad Al‐Jarrah, Arafat Al‐Dweik, Emad Alsusa, Youssef Iraqi, Mohamed‐Slim Alouini
Abstract
This work presents the symbol error rate (SER) and outage probability analysis of multi-layer unmanned aerial vehicles (UAVs) wireless communications assisted by intelligent reflecting surfaces (IRS). In such systems, the UAVs may experience high jitter, making the estimation and compensation of the end-to-end phase for each propagation path prone to errors. Consequently, the imperfect phase knowledge at the IRS should be considered. The phase error is modeled using the von Mises distribution and the analysis is performed using the Sinusoidal Addition Theorem (SAT) to provide accurate results when the number of reflectors <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\leq 3$ </tex-math></inline-formula> , and the Central Limit Theorem (CLT) when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\geq 4$ </tex-math></inline-formula> . The achieved results show that accurate phase estimation is critical for IRS based systems, particularly for a small number of reflecting elements. For example, the SER at 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> degrades by about 5 dB when the von Mises concentration parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa =2$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L=30$ </tex-math></inline-formula> , but the degradation for the same <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> surges to 25 dB when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L=2$ </tex-math></inline-formula> . The air-to-air (A2A) channel for each propagation path is modeled as a single dominant line-of-sight (LoS) component, and the results are compared to the Rician channel. The obtained results reveal that the considered A2A model can be used to accurately represent the A2A channel with Rician fading.