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A Rank-Constrained Coordinate Ascent Approach to Hybrid Precoding for the Downlink of Wideband Massive (MIMO) Systems

José P. González-Coma, Óscar Fresnedo, Luis Castedo

TL;DR

The paper tackles the challenge of designing hybrid analog-digital precoders for the downlink of wideband massive MIMO under a frequency-flat analog front-end and a rank constraint on the transmit covariance. It introduces Rank-Constrained Coordinate Ascent (RCCA), which converts the problem to a dual uplink and imposes a frequency-flat covariance structure for each user, while allowing per-subcarrier power allocation to exploit bandwidth diversity. RCCA iteratively updates user subspaces and streams via a coordinated ascent over a common subspace basis and wideband gains, ensuring the rank constraint is met through selective stream augmentation and a waterfilling-like power policy. The approach yields substantial sum-rate gains over multiple baselines, demonstrates robustness to practical impairments (phase quantization, beam squint), and provides a tractable complexity profile suitable for realistic wideband deployment.

Abstract

An innovative approach to hybrid analog-digital precoding for the downlink of wideband massive MIMO systems is developed. The proposed solution, termed Rank-Constrained Coordinate Ascent (RCCA), starts seeking the full-digital precoder that maximizes the achievable sum-rate over all the frequency subcarriers while constraining the rank of the overall transmit covariance matrix. The frequency-flat constraint on the analog part of the hybrid precoder and the non-convex nature of the rank constraint are circumvented by transforming the original problem into a more suitable one, where a convenient structure for the transmit covariance matrix is imposed. Such structure makes the resulting full-digital precoder particularly adequate for its posterior analog-digital factorization. An additional problem formulation to determine an appropriate power allocation policy according to the rank constraint is also provided. The numerical results show that the proposed method outperforms baseline solutions even for practical scenarios with high spatial diversity.

A Rank-Constrained Coordinate Ascent Approach to Hybrid Precoding for the Downlink of Wideband Massive (MIMO) Systems

TL;DR

The paper tackles the challenge of designing hybrid analog-digital precoders for the downlink of wideband massive MIMO under a frequency-flat analog front-end and a rank constraint on the transmit covariance. It introduces Rank-Constrained Coordinate Ascent (RCCA), which converts the problem to a dual uplink and imposes a frequency-flat covariance structure for each user, while allowing per-subcarrier power allocation to exploit bandwidth diversity. RCCA iteratively updates user subspaces and streams via a coordinated ascent over a common subspace basis and wideband gains, ensuring the rank constraint is met through selective stream augmentation and a waterfilling-like power policy. The approach yields substantial sum-rate gains over multiple baselines, demonstrates robustness to practical impairments (phase quantization, beam squint), and provides a tractable complexity profile suitable for realistic wideband deployment.

Abstract

An innovative approach to hybrid analog-digital precoding for the downlink of wideband massive MIMO systems is developed. The proposed solution, termed Rank-Constrained Coordinate Ascent (RCCA), starts seeking the full-digital precoder that maximizes the achievable sum-rate over all the frequency subcarriers while constraining the rank of the overall transmit covariance matrix. The frequency-flat constraint on the analog part of the hybrid precoder and the non-convex nature of the rank constraint are circumvented by transforming the original problem into a more suitable one, where a convenient structure for the transmit covariance matrix is imposed. Such structure makes the resulting full-digital precoder particularly adequate for its posterior analog-digital factorization. An additional problem formulation to determine an appropriate power allocation policy according to the rank constraint is also provided. The numerical results show that the proposed method outperforms baseline solutions even for practical scenarios with high spatial diversity.
Paper Structure (13 sections, 2 theorems, 51 equations, 8 figures, 2 tables, 1 algorithm)

This paper contains 13 sections, 2 theorems, 51 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Initial Problem Formulation
  4. Reformulation of the optimization problem
  5. Frequency-flat transmission covariance matrix structure
  6. Frequency-selective power allocation
  7. Proposed algorithm
  8. Simulation results
  9. Performance under practical impairments
  10. Complexity and convergence analysis
  11. Conclusions
  12. Frequency-flat covariance matrix structure
  13. Analysis of the optimality of $N_s=N_\text{RF}$

Key Result

Proposition 1

The KKT condition in eq:KKTcondition holds for $K=1$ and $\boldsymbol{S}_u$ fulfilling $\left(\mathbf{I}_R+\boldsymbol{H}_{\bar{u}}[k]\boldsymbol{H}_{\bar{u}}^{\mathop{\mathrm{H}}\nolimits}[k]\boldsymbol{S}_u\right)^{-1}\boldsymbol{H}_{\bar{u}}[k]\boldsymbol{H}_{\bar{u}}^{\mathop{\mathrm{H}}\nolimit

Figures (8)

  • Figure 1: Achievable sum-rates of the different algorithms for a downlink scenario with the following configuration: $M=16, R=2, U=6, N_{\text{RF}}=4, N_p = 16$ and $K=16$.
  • Figure 2: Achievable sum-rates of the different algorithms for a downlink scenario with the following configuration: $M=32, R=2, U=6, N_{\text{RF}}=4, N_p = 32$ and $K=64$.
  • Figure 3: Achievable sum-rates vs. number of reflection paths for the different approaches and two SNR values: -5 dB and 10 dB. The configuration setup is: $M=32, R=2, U=6, N_{\text{RF}}=4$ and $K=64$.
  • Figure 4: Achievable sum-rates vs. number of RF chains at the BS for the different approaches and two SNR values: -5 dB and 10 dB. The configuration setup is: $M=32, R=2, U=12, K=64$ and $N_p = 32$.
  • Figure 5: Achievable sum-rates of RCCA for a downlink scenario with the following configuration: $M=32, R=2, U=6, N_{\text{RF}}=4, N_p=32$ and $K=64$ and different number of resolution bits $b={\infty,3,2}$.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof