[Paper Review] Large Intelligent Surface Assisted Non-Orthogonal Multiple Access: Performance Analysis

Lina Bariah, Sami Muhaidat+4 more|arXiv (Cornell University)|Jul 19, 2020

Advanced Wireless Communication Technologies34 references5 citations

TL;DR

This paper proposes a large intelligent surface (LIS)-assisted non-orthogonal multiple access (NOMA) system to enhance spectral and energy efficiency in 6G networks. By modeling the end-to-end fading channel via the sum of M half-Nakagami-m random variables, it derives closed-form expressions for pairwise error probability (PEP) and diversity order under imperfect successive interference cancellation, showing that LIS significantly improves error performance and achieves full diversity gain with large M.

ABSTRACT

Large intelligent surface (LIS) has recently emerged as a potential enabling technology for 6G networks, offering extended coverage and enhanced energy and spectral efficiency. In this work, motivated by its promising potentials, we investigate the error rate performance of LIS-assisted non-orthogonal multiple access (NOMA) networks. Specifically, we consider a downlink NOMA system, in which data transmission between a base station (BS) and $L$ NOMA users is assisted by an LIS comprising $M$ reflective elements. First, we derive the probability density function of the end-to-end wireless fading channels between the BS and NOMA users. Then, by leveraging the obtained results, we derive an approximate expression for the pairwise error probability (PEP) of NOMA users under the assumption of imperfect successive interference cancellation. Furthermore, accurate expressions for the PEP for $M = 1$ and large $M$ values ($M > 10$) are presented in closed-form. To gain further insights into the system performance, an asymptotic expression for the PEP in high signal-to-noise ratio regime, the achievable diversity order, and a tight union bound on the bit error rate are provided. Finally, numerical and simulation results are presented to validate the derived mathematical results.

Motivation & Objective

• To analyze the error rate performance of large intelligent surface (LIS)-assisted non-orthogonal multiple access (NOMA) systems in downlink transmission.
• To model the end-to-end fading channel between the base station and NOMA users as the sum of M half-Nakagami-m distributed random variables.
• To derive accurate closed-form expressions for pairwise error probability (PEP) under imperfect successive interference cancellation (SIC).
• To evaluate the diversity order and bit error rate (BER) performance in high signal-to-noise ratio (SNR) regimes.
• To validate the analytical results through numerical and simulation comparisons.

Proposed method

• Models the end-to-end channel gain as the sum of M independent half-Nakagami-m random variables, representing the combined pathloss and fading from base station to LIS and from LIS to each user.
• Derives the probability density function (PDF) of the total channel gain using moment-based density approximation and represents it as a Meijer’s G-function via Fox’s H-function approximation.
• Uses the moment-generating function and multinomial expansion to compute the first four moments of the sum of M half-Nakagami-m variables.
• Derives an approximate closed-form expression for the pairwise error probability (PEP) of NOMA users under imperfect SIC, valid for both M=1 and large M (>10).
• Establishes an asymptotic PEP expression in the high-SNR regime and derives the achievable diversity order using the PEP slope.
• Provides a tight union bound on the bit error rate (BER) based on the derived PEP expressions.

Experimental results

Research questions

• RQ1 How does the deployment of a large intelligent surface (LIS) affect the pairwise error probability (PEP) in a downlink NOMA system?
• RQ2 What is the impact of the number of reflective elements M on the diversity order and error rate performance in LIS-assisted NOMA?
• RQ3 How accurate are the closed-form PEP expressions for M=1 and large M (>10) under imperfect successive interference cancellation?
• RQ4 What is the asymptotic PEP behavior in the high signal-to-noise ratio (SNR) regime, and what diversity gain is achieved?
• RQ5 How does the proposed analytical model compare with simulation results in terms of BER performance?

Key findings

• The pairwise error probability (PEP) for NOMA users is derived in closed-form for both M=1 and large M (>10), enabling accurate performance evaluation.
• The diversity order of the system is shown to be M, indicating that full diversity gain is achieved as M increases, which is critical for reliable communication.
• The asymptotic PEP expression in the high-SNR regime confirms that the system achieves full diversity, with the PEP decreasing as O(SNR^(-M)) for large SNR.
• A tight union bound on the bit error rate (BER) is derived, which closely matches simulation results, validating the analytical accuracy.
• The derived Meijer’s G-function representation of the end-to-end channel PDF provides a highly accurate approximation using only the first four moments.
• Numerical results confirm that increasing M significantly improves error performance, with BER decreasing by several orders of magnitude as M grows.