[Paper Review] Performance Analysis for Massive MIMO Downlink with Low Complexity Approximate Zero-Forcing Precoding

Cheng Zhang, Yindi Jing+2 more|arXiv (Cornell University)|Nov 1, 2017

Advanced MIMO Systems Optimization3 citations

TL;DR

This paper proposes the identity-plus-column Neumann series (ICNS) and ordered ICNS precoding methods for massive MIMO downlink, using a relaxation parameter and user-specific interference selection to reduce complexity while maintaining high sum-rate performance. The ICNS method achieves near-ideal ZF performance with significantly lower computational cost, especially in correlated channels and high loading scenarios.

ABSTRACT

Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink due to its near optimal performance. However, the high computation cost of the involved matrix inversion hinders its application. In this paper, we adopt the first order Neumann series (NS) for a low-complexity approximation. By introducing a relaxation parameter jointly with one selected user's interference to others into the precondition matrix, we propose the identity-plus-column NS (ICNS) method. By further exploiting the multi-user diversity gain via choosing the user with the largest interference to others, the ordered ICNS method is also proposed. Moreover, the sum-rate approximations of the proposed ICNS method and the competitive existing identity matrix based NS (INS) method are derived in closed-form, based on which the performance loss of ICNS due to inversion approximation compared with ideal ZF and its performance gain over INS are explicitly analyzed for three typical massive MIMO scenarios. Finally, simulations verify our analytical results and also show that the proposed two designs achieve better performance-complexity tradeoff than ideal ZF and existing low-complexity ZF precodings for practical large antenna number, correlated channels and not-so-small loading factor.

Motivation & Objective

• To address the high computational complexity of zero-forcing (ZF) precoding in massive MIMO systems due to matrix inversion.
• To develop a low-complexity approximation of ZF precoding that maintains high spectral efficiency, especially in correlated channels and high user loading.
• To derive closed-form sum-rate approximations for the proposed method and compare its performance loss relative to ideal ZF and existing low-complexity alternatives.
• To optimize the tradeoff between computational complexity and sum-rate performance through user selection and preconditioning.

Proposed method

• Proposes the identity-plus-column Neumann series (ICNS) method by incorporating the first column of the Gram matrix and a relaxation parameter into the precondition matrix.
• Introduces the ordered ICNS method by selecting the user with the largest interference to others to further exploit multi-user diversity.
• Derives closed-form sum-rate approximations for ICNS and the identity matrix-based NS (INS) method using random matrix theory and statistical channel modeling.
• Uses the first-order Neumann series expansion to approximate the inverse of the Gram matrix, reducing complexity from O(K^3) to O(K^2).
• Applies matrix decomposition and expectation calculations to derive analytical expressions for effective SINR and sum-rate, leveraging Lemma 2 for simplification.
• Validates the analytical results through simulations under practical massive MIMO scenarios, including correlated channels and high loading factors.

Experimental results

Research questions

• RQ1 How does the proposed ICNS method compare to ideal ZF precoding in terms of sum-rate performance and computational complexity?
• RQ2 What is the performance loss of ICNS due to matrix inversion approximation, and how does it compare to existing low-complexity ZF methods?
• RQ3 Can user selection based on interference power improve the performance-complexity tradeoff in ICNS?
• RQ4 How do channel correlation and user loading factor affect the sum-rate performance of ICNS and INS?
• RQ5 What is the closed-form sum-rate approximation for the proposed ICNS method under i.i.d. Rayleigh fading and correlated channels?

Key findings

• The proposed ICNS method achieves sum-rate performance very close to ideal ZF, with a performance loss of less than 10% in high SNR and high loading scenarios.
• The ordered ICNS method outperforms the standard ICNS and existing INS methods by exploiting multi-user diversity through optimal user selection.
• The sum-rate approximation for ICNS is derived in closed-form, enabling accurate performance prediction without Monte Carlo simulations.
• The ICNS method achieves a better performance-complexity tradeoff than both ideal ZF and existing low-complexity ZF precoders, especially in correlated channels and large-scale antenna arrays.
• Simulation results confirm that ICNS maintains near-optimal sum-rate even with large numbers of users and antennas, outperforming INS and other NS-based methods under practical conditions.
• The cubic equation derived for the SINR ratio between ICNS and ideal ZF allows for analytical determination of the SNR threshold at which ICNS achieves near-ideal performance.