Finite-Precision Conjugate Gradient Method for Massive MIMO Detection

TL;DR

This work tackles the heavy computational burden of CG-based detection in massive MIMO, especially under correlated channels, by introducing a finite-precision CG (FP-CG) framework and a jointly finite-precision with block-Jacobi preconditioning CG (FP-BJ-CG). It derives attainable accuracy bounds, reveals that inner-product precision has little effect while matrix-vector products dominate error, and proposes a practical precision-selection heuristic. The BPJ-CG extension exploits near block-diagonal Gram matrices to reduce iterations and improve conditioning, yielding significant complexity reductions while maintaining BER performance close to LMMSE (e.g., ~1.2 dB BER loss at high SNR) and enabling low-precision operation (e.g., FP16). Simulations show FP-CG and FP-BJ-CG can achieve substantial computational savings (tens of percent to ~80%) with robust performance, making real-time, hardware-friendly massive MIMO detectors feasible.

Abstract

The implementation of the conjugate gradient (CG) method for massive MIMO detection is computationally challenging, especially for a large number of users and correlated channels. In this paper, we propose a low computational complexity CG detection from a finite-precision perspective. First, we develop a finite-precision CG (FP-CG) detection to mitigate the computational bottleneck of each CG iteration and provide the attainable accuracy, convergence, and computational complexity analysis to reveal the impact of finite-precision arithmetic. A practical heuristic is presented to select suitable precisions. Then, to further reduce the number of iterations, we propose a joint finite-precision and block-Jacobi preconditioned CG (FP-BJ-CG) detection. The corresponding performance analysis is also provided. Finally, simulation results validate the theoretical insights and demonstrate the superiority of the proposed detection.

Figures (9)

• Figure 1: Convergence curve of FP-CG detection using $\mathtt{bfloat16}$ with different $\zeta$ in SNR $=20$ dB. MV: matrix-vector products using $\mathtt{bfloat16}$. IP: inner products using $\mathtt{bfloat16}$. MV + IP: both using $\mathtt{bfloat16}$.
• Figure 2: Convergence curve of FP-CG detection using the heuristic method with different $\zeta$ in SNR $=20$ dB.
• Figure 3: Convergence curve of various detection using the heuristic method with $\zeta = 0.8$ in SNR $=20$ dB.
• Figure 4: BER performance of various detection against SNR with $\zeta = 0.8$ and $\mathcal{I} = 10$.
• Figure 5: BER performance of various detection against SNR with imperfect CSI, $\zeta = 0.8$ and $\mathcal{I} = 10$.

Theorems & Definitions (14)

• Example 1
• Definition 1: Finite-Precision Operator
• Definition 2: Standard Arithmetic Model
• Lemma 1: Real-valued Matrix Computations higham2002accuracygreenbaum1997estimating
• Theorem 1: Complex-valued Matrix Computations
• Theorem 2: Attainable Accuracy of Algorithm \ref{['alg: FP-CG']}
• Remark 1: Impact of Finite-Precision Arithmetic on Attainable Accuracy
• Remark 2: Impact of Finite-Precision Arithmetic on Convergence
• Theorem 3: Asymptotic Analysis of Correlated MIMO Channel
• Theorem 4: Attainable Accuracy of Algorithm \ref{['alg: FP-BJ-CG']}