<p>This paper develops tight ergodic-capacity approximations for intelligent reflecting surface (IRS)–assisted single-input single-output (SISO) wireless systems under practical hardware impairments and both Rayleigh and Rician fading. A physically consistent cascaded channel model is introduced that jointly incorporates electromagnetic mutual coupling, amplitude phase-dependent reflection, and distance-dependent attenuation, providing a realistic representation of practical metasurface behavior. Building on this model, the paper derives unified closed-form capacity approximations for arbitrary and sub-optimal phase-shift strategies using a second-order Taylor expansion tailored to the bilinear structure of the impaired S–R–D link. The analysis introduces generalized second and fourth-order IRS parameters that capture the coherent and non-coherent contributions of phase-aligned and arbitrarily phased elements under both scattering and Line of Sight (LoS) conditions. These expressions reduce naturally to their Rayleigh special cases, thereby offering a consistent analytical framework across different fading environments. The approximations are shown to be highly accurate, achieving root-mean-square errors on the order of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$8\times 10^{-2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>8</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> bps/Hz across a wide range of IRS placements, trajectory geometries, element counts, phase configurations, and transmit-power levels. The results quantify how hardware-induced distortions, geometric positioning, and mixed-phase allocation influence system performance, revealing that coherent phase alignment remains effective even under practical impairments. Numerical evaluations further highlight that sub-optimal phase shifts provide significant gains over arbitrary configurations and that the coherent benefit increases predictably with the number of aligned elements. Overall, the derived approximations offer a computationally efficient and physically grounded tool for analyzing and optimizing practical IRS-assisted communication systems.</p>

Practical IRS-Assisted 6G Wireless Communications: Tight Ergodic Capacity Approximations with Coupling and Amplitude-Phase Distortion

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发表日期：

2026年1月22日

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Md Sarfraz Alam,
Ganesh Prasad,
Deepak Mishra,
Abhishek Mondal,
Prabina Pattanayak

摘要

This paper develops tight ergodic-capacity approximations for intelligent reflecting surface (IRS)–assisted single-input single-output (SISO) wireless systems under practical hardware impairments and both Rayleigh and Rician fading. A physically consistent cascaded channel model is introduced that jointly incorporates electromagnetic mutual coupling, amplitude phase-dependent reflection, and distance-dependent attenuation, providing a realistic representation of practical metasurface behavior. Building on this model, the paper derives unified closed-form capacity approximations for arbitrary and sub-optimal phase-shift strategies using a second-order Taylor expansion tailored to the bilinear structure of the impaired S–R–D link. The analysis introduces generalized second and fourth-order IRS parameters that capture the coherent and non-coherent contributions of phase-aligned and arbitrarily phased elements under both scattering and Line of Sight (LoS) conditions. These expressions reduce naturally to their Rayleigh special cases, thereby offering a consistent analytical framework across different fading environments. The approximations are shown to be highly accurate, achieving root-mean-square errors on the order of $8\times 10^{-2}$ $8 \times 10^{- 2}$ bps/Hz across a wide range of IRS placements, trajectory geometries, element counts, phase configurations, and transmit-power levels. The results quantify how hardware-induced distortions, geometric positioning, and mixed-phase allocation influence system performance, revealing that coherent phase alignment remains effective even under practical impairments. Numerical evaluations further highlight that sub-optimal phase shifts provide significant gains over arbitrary configurations and that the coherent benefit increases predictably with the number of aligned elements. Overall, the derived approximations offer a computationally efficient and physically grounded tool for analyzing and optimizing practical IRS-assisted communication systems.