[Paper Review] Hybrid precoding and combining for frequency-selective mmWave MIMO Systems with per-antenna power constraints

Javier Rodríguez-Fernández, Roberto López-Valcarce+1 more|arXiv (Cornell University)|Dec 6, 2018

Millimeter-Wave Propagation and Modeling23 references4 citations

TL;DR

This paper proposes a hybrid precoding and combining framework for frequency-selective mmWave MIMO systems under per-antenna power constraints, using chordal distance minimization to approximate all-digital solutions. It achieves near-optimal spectral efficiency even with beam-squint and bandwidth expansion up to 3 GHz, outperforming total-power-constrained designs in practical hardware settings.

ABSTRACT

Configuring hybrid precoders and combiners is a major challenge to deploy practical mmWave communication systems. Prior work addresses the problem of designing hybrid precoders and combiner, yet focusing on finding solutions under a total transmit power constraint. The design of hybrid precoders and combiners in practical system, is constrained, however, by a per antenna transmit power, since each antenna element in the array is connected to a power amplifier (PA) that has to operate within its linear region. In this paper, we focus on the problem of hybrid precoding and combining with per-antenna power constraints, and under a frequency-selective bandlimited channel model. We first propose an all-digital solution to this problem, and develop a hybrid precoding and combining strategy that aims at matching this solution by minimizing the chordal distance between the all-digital precoders (combiners) and their hybrid approximations. Finally, since minimizing this metric does not guarantee that the final spectral efficiency will be maximized, we optimize the resulting spectral efficiency taking into account the per-antenna power constraints. Simulation results show the effectiveness of our all-digital and hybrid solutions, while emphasizing the differences with respect to the corresponding solution under a total power constraints. As shown in our numerical results, the proposed all-digital solution performs similarly to the case in which a total power constraint is considered. Further, our proposed hybrid solution is also shown to exhibit near-optimum performance, and the influence of different system parameters is also shown, thereby showing the suitability of our proposed framework to deploy practical mmWave MIMO systems.

Motivation & Objective

• Address the challenge of designing hybrid precoders and combiners in practical mmWave systems constrained by per-antenna power limits due to power amplifier linearity.
• Develop a hybrid precoding strategy that approximates an all-digital solution under frequency-selective, bandlimited channel models with realistic hardware constraints.
• Optimize spectral efficiency while accounting for beam-squint and per-antenna power limitations, avoiding the suboptimal power allocation of prior iterative methods.
• Provide a subspace-based framework that quantitatively captures the impact of bandwidth and frequency selectivity on hybrid precoder design.
• Demonstrate robustness to channel estimation errors and validate performance under imperfect CSI using advanced estimation algorithms.

Proposed method

• Propose an all-digital precoding and combining solution under per-antenna power constraints, serving as a performance upper bound.
• Design a hybrid precoder and combiner by minimizing the chordal distance between the all-digital precoders/combiners and their hybrid approximations.
• Use a Grassmannian-based optimization framework to align the analog precoder/combiner with the dominant singular subspaces of the frequency-selective channel across subcarriers.
• Formulate the hybrid design as a constrained optimization problem that respects per-antenna power limits and bandwidth expansion effects.
• Integrate beam-squint modeling into the channel model by incorporating frequency-dependent response and pulse-shaping effects at RF frontends.
• Apply a modified SS-SW-OMP+Th algorithm for channel estimation, enabling reliable CSI acquisition under practical training overhead constraints.

Experimental results

Research questions

• RQ1 How does per-antenna power constraint affect the design and performance of hybrid precoders and combiners in frequency-selective mmWave MIMO systems?
• RQ2 To what extent can chordal distance minimization between all-digital and hybrid precoders/combiners achieve near-optimal spectral efficiency under per-antenna power constraints?
• RQ3 How does beam-squint degrade performance in wideband mmWave systems, and can the proposed hybrid design mitigate this effect?
• RQ4 What is the impact of increasing bandwidth on the coherence of singular subspaces across subcarriers, and how does this affect hybrid precoder design?
• RQ5 Can the proposed framework maintain high spectral efficiency under imperfect CSI, particularly when using practical channel estimation algorithms?

Key findings

• The proposed all-digital solution under per-antenna power constraints achieves spectral efficiency comparable to the total-power-constrained case, validating its effectiveness as a performance benchmark.
• The hybrid precoding and combining design based on chordal distance minimization achieves near-optimal spectral efficiency, even with a 3 GHz bandwidth and significant beam-squint effects.
• Spectral efficiency degrades with increasing bandwidth due to reduced coherence between singular subspaces across subcarriers, as confirmed by the quality metric in (65).
• The quality metric in (65) demonstrates that higher subspace dimension $ d $ improves representation of frequency-selective channels, validating the need for sufficient degrees of freedom in hybrid designs.
• The SS-SW-OMP+Th channel estimation algorithm enables reliable CSI acquisition, allowing the hybrid system to achieve near-optimal spectral efficiency even with imperfect CSI.
• The proposed method outperforms prior iterative approaches in terms of training overhead and computational complexity, while avoiding error propagation from alternating optimization.