Performance Analysis of Discrete-Phase-Shifter IRS-aided Amplify-and-Forward Relay Network

DONG Rongen; XIE Zhongyi; MA Haibo; ZHAO Feilong; SHU Feng

doi:10.11999/JEIT240236

Volume 47 Issue 1

Jan. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(1): 138-146

DONG Rongen, XIE Zhongyi, MA Haibo, ZHAO Feilong, SHU Feng. Performance Analysis of Discrete-Phase-Shifter IRS-aided Amplify-and-Forward Relay Network[J]. Journal of Electronics & Information Technology, 2025, 47(1): 138-146. doi: 10.11999/JEIT240236

Citation:

DONG Rongen, XIE Zhongyi, MA Haibo, ZHAO Feilong, SHU Feng. Performance Analysis of Discrete-Phase-Shifter IRS-aided Amplify-and-Forward Relay Network[J]. Journal of Electronics & Information Technology, 2025, 47(1): 138-146. doi: 10.11999/JEIT240236

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Performance Analysis of Discrete-Phase-Shifter IRS-aided Amplify-and-Forward Relay Network

doi: 10.11999/JEIT240236

1.
School of Information and Communication Engineering, Hainan University, Haikou 570228, China
2.
Purple Mountain Laboratories, Nanjing 210094, China
3.
China Mobile Group Hainan Co., Ltd., Haikou 571250, China

Funds: The National Natural Science Foundation of China (U22A2002, 62071234), Hainan Province Science and Technology Special Fund (ZDKJ2021022), The Scientific Research Fund Project of Hainan University (KYQD(ZR)-21008), The Collaborative Innovation Center of Information Technology, Hainan University (XTCX2022XXC07)

Received Date: 2024-03-13
Rev Recd Date: 2024-07-17

Available Online: 2024-08-27

Publish Date: 2025-01-31

Abstract

Abstract

Objective Most existing research assumes that the Intelligent Reflecting Surface (IRS) is equipped with continuous phase shifters, which neglects the phase quantization error. However, in practice, IRS devices are typically equipped with discrete phase shifters due to hardware and cost constraints. Similar to the performance degradation caused by finite quantization bit shifters in directional modulation networks, discrete phase shifters in IRS systems introduce phase quantization errors, potentially affecting system performance. This paper analyzes the performance loss and approximate performance loss in a double IRS-aided amplify-and-forward relay network, focusing on Signal-to-Noise Ratio (SNR) and achievable rate under Rayleigh fading channels. The findings provide valuable guidance on selecting the appropriate number of quantization bit for IRS in practical applications. Methods Based on the weak law of large numbers, Euler’s formula, and Rayleigh distribution, closed-form expressions for the SNR performance loss and achievable rate of the discrete phase shifter IRS-aided amplify-and-forward relay network are derived. Additionally, corresponding approximate expressions for the performance loss are derived using the first-order Taylor series expansion. Results and Discussions The SNR performance loss at the destination is evaluated as a function of the number of IRS-1 elements (N), assuming that the number of IRS-2 elements (M) equals N (Fig. 2). It is evident that, regardless of whether the scenario involves actual or approximate performance loss, the SNR performance loss decreases as the number of quantization bit (k) increases but increases as N grows. When k = 1, the gap between the actual performance loss and the approximate performance loss widens with increasing N. This gap becomes negligible when k is greater than or equal to 2. Notably, when k = 4, the SNR performance loss is less than 0.06 dB. Furthermore, both the SNR performance loss and approximate performance loss gradually decelerate as N increases towards a larger scale. The achievable rate at the destination is evaluated as a function of the N, where M equals N (Fig. 3). It can be observed that, in all scenarios—whether there is no performance loss, with performance loss, or approximate performance loss—the achievable rate increases gradually as N increases. This is because both IRS-1 and IRS-2 provide greater performance gains as N grows. When k = 1, the difference in achievable rate between the performance loss and approximate performance loss scenarios increases with N. As k increases, the achievable rate with performance loss and approximate performance loss converge towards the no-performance-loss scenario. For example, when N = 1 024, the performance loss in achievable rate is about 0.15 bit/(s·Hz) at k = 2 and only 0.03 bit/(s·Hz) at k = 3. The achievable rate is evaluated as a function of k (Fig. 4). The performance loss in achievable rate increases with N and M. When k = 3, the achievable rate with performance loss and approximate performance loss decrease by 0.04 bit/(s·Hz) compared to the no performance loss scenario. When k = 1, the differences in achievable rate between the no performance loss, performance loss, and approximate performance loss scenarios grow with increasing N and M. Remarkably, the achievable rate for the system with N = 1 024 and M = 128 outperforms that of N = 128 and M = 1 024. This suggests that increasing N provides a more significant improvement in rate performance than increasing M. Conclusions This paper investigates a double IRS-assisted amplify-and-forward relay network and analyzes the system performance loss caused by phase quantization errors in IRS equipped with discrete phase shifters under Rayleigh fading channels. Using the weak law of large numbers, Euler’s formula, and Rayleigh distribution, closed-form expressions for SNR performance loss and achievable rate are derived. Approximate performance loss expressions are also derived based on a first-order Taylor series expansion. Simulation results show that the performance losses in SNR and achievable rate decrease with increasing quantization bit, but increase with the number of IRS elements. When the number of quantization bit is 4, the performance losses in SNR and achievable rate are less than 0.06 dB and 0.03 bit/(s·Hz), respectively, suggesting that the system performance loss is negligible when using 4-bit phase quantization shifters.
- Intelligent Reflecting Surface (IRS),
- Amplify-and-forward relay,
- Signal-to-Noise Ratio (SNR),
- Achievable rate

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References(23)

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