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Joint Power and Bit Allocation for Precoded Massive MIMO Channels

Shuiyin Liu, Amin Sakzad

TL;DR

This work tackles the joint design of power and bit allocation for precoded massive MIMO systems using discrete input alphabets, introducing an adaptive QAM (A-QAM) scheme that maintains a fixed gap to the Gaussian-input capacity and showing that mercury/waterfilling (MWF) reduces to classical waterfilling (WF) under this scheme. A key theoretical result is that, at large system dimensions, non-zero subchannel deactivation occurs under WF, MWF, and EWF, enabling truncated SVD to replace full SVD with substantial complexity savings while preserving performance. The authors develop a bit-allocation procedure to meet a target rate with complexity $O(n\log n)$, and demonstrate that truncating SVD combined with A-QAM and EWF achieves superior decoding performance versus conventional methods. Collectively, the approach reduces precoding complexity and BER without sacrificing rate, making it attractive for practical deployment in massive MIMO systems with discrete constellations.

Abstract

This work addresses the joint optimization of power and bit allocation in precoded large-scale n x n MIMO systems with discrete input alphabets, specifically QAM constellations. We propose an adaptive QAM scheme that maintains a fixed gap to the Gaussian-input capacity for a given n. A key finding is that, under the proposed scheme, the mercury/waterfilling (MWF) solution reduces analytically to the classical water-filling (WF) policy. Furthermore, the adaptive QAM configuration can be precomputed under the large-system assumption, enabling the replacement of full SVD with truncated SVD and yielding substantial computational savings. To support practical deployment, we develop a bit-allocation algorithm that meets a target transmission data rate while minimizing the overall decoding error rate and preserving computational complexity at O(n log n). Simulation results confirm that the proposed truncated SVD precoding, paired with the joint power and bit allocation, achieves superior decoding performance relative to conventional approaches, while operating at significantly lower complexity.

Joint Power and Bit Allocation for Precoded Massive MIMO Channels

TL;DR

This work tackles the joint design of power and bit allocation for precoded massive MIMO systems using discrete input alphabets, introducing an adaptive QAM (A-QAM) scheme that maintains a fixed gap to the Gaussian-input capacity and showing that mercury/waterfilling (MWF) reduces to classical waterfilling (WF) under this scheme. A key theoretical result is that, at large system dimensions, non-zero subchannel deactivation occurs under WF, MWF, and EWF, enabling truncated SVD to replace full SVD with substantial complexity savings while preserving performance. The authors develop a bit-allocation procedure to meet a target rate with complexity , and demonstrate that truncating SVD combined with A-QAM and EWF achieves superior decoding performance versus conventional methods. Collectively, the approach reduces precoding complexity and BER without sacrificing rate, making it attractive for practical deployment in massive MIMO systems with discrete constellations.

Abstract

This work addresses the joint optimization of power and bit allocation in precoded large-scale n x n MIMO systems with discrete input alphabets, specifically QAM constellations. We propose an adaptive QAM scheme that maintains a fixed gap to the Gaussian-input capacity for a given n. A key finding is that, under the proposed scheme, the mercury/waterfilling (MWF) solution reduces analytically to the classical water-filling (WF) policy. Furthermore, the adaptive QAM configuration can be precomputed under the large-system assumption, enabling the replacement of full SVD with truncated SVD and yielding substantial computational savings. To support practical deployment, we develop a bit-allocation algorithm that meets a target transmission data rate while minimizing the overall decoding error rate and preserving computational complexity at O(n log n). Simulation results confirm that the proposed truncated SVD precoding, paired with the joint power and bit allocation, achieves superior decoding performance relative to conventional approaches, while operating at significantly lower complexity.
Paper Structure (11 sections, 8 theorems, 35 equations, 2 figures, 1 algorithm)

This paper contains 11 sections, 8 theorems, 35 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. MIMO Channel Model
  4. SVD Precoding and Power Allocation Schemes
  5. Adaptive QAM (A-QAM)
  6. Problem Statement
  7. Non-Zero Subchannel Deactivation
  8. Adaptive QAM and Bit-Allocation
  9. The Proposed Adaptive QAM
  10. Bit-Allocation for a Specified Transmission Data Rate $R$
  11. Conclusion

Key Result

Theorem 1

The optimal power allocation for the EWF problem is unique and satisfy where $W(x)$ is the real-valued Lambert W function defined as the inverse of the function $f(w)=w\exp(w)$ for $w>0$, and The Lagrange multiplier $\lambda_{\mathsf{EWF}} > 0$ is found as a unique solution for $\sum_{i=1}^{n}p_i(\lambda_{\mathsf{EWF}})=P$.

Figures (2)

  • Figure 1: $32 \times 32$ MIMO at $\mathsf{SNR} = 10$ dB: Average capacity $\mathbb{E}(C_k)$ for different input types and power allocation schemes, with $k$ inactive weakest subchannels.
  • Figure 2: $96 \times 96$ MIMO: BER of different precoding schemes.

Theorems & Definitions (16)

  • Definition 1: Gaussian Random Matrix
  • Definition 2: SVD and Truncated SVD
  • Definition 3: EWF Power Allocation Problem
  • Theorem 1
  • Definition 4: Non-Zero Subchannel Deactivation Problem
  • Definition 5: Joint QAM Size Selection and Power Allocation Problem
  • Lemma 1: $k_{\text{opt}}$ with WF
  • Lemma 2: $k_{\text{opt}}$ with MWF
  • Lemma 3: $k_{\text{opt}}$ with EWF
  • Theorem 2
  • ...and 6 more