Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems (1601.07340v1)

Abstract: Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks. In contrast to conventional multiple-input-multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters (ADCs) can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing (OFDM) modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.

• The paper presents alternating minimization algorithms that reformulate hybrid precoding as a matrix factorization problem to achieve near-optimal digital precoder performance.
• It employs manifold optimization and phase extraction techniques to design fully- and partially-connected architectures that outperform traditional methods like OMP.
• Simulation results demonstrate enhanced spectral and energy efficiency in both narrowband and broadband OFDM systems, validating the practical impact of the proposed designs.

An Overview of "Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems"

The paper "Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems" explores the critical design challenges and proposes sophisticated solutions for hybrid precoding in mmWave MIMO communication systems, which are essential for the evolution of 5G networks. Given the inherent limitations in performing fully digital precoding at mmWave frequencies due to high cost and power consumption of RF chains, the hybrid precoding architecture, which combines both digital and analog precoders, has attracted significant interest. This paper rigorously formulates the hybrid precoder design as a matrix factorization problem and introduces alternating minimization (AltMin) algorithms to optimize the precoders for both fully-connected and partially-connected structures.

Key Contributions

1. Manifold Optimization for Fully-Connected Structure:
   • The proposed manifold optimization-based AltMin (MO-AltMin) algorithm leverages the Riemannian manifold structure to directly handle the unit modulus constraints on the analog precoder entries. This approach does not rely on pre-determined candidate sets, making it more flexible and closer to the optimal fully digital precoder.
2. Low-Complexity Solution via Phase Extraction:
   • To address the complexity of the MO-AltMin algorithm, the paper introduces a low-complexity AltMin (PE-AltMin) algorithm by enforcing orthogonality on the digital precoder and utilizing phase extraction techniques. This method provides practical implementation benefits while still improving performance over existing methods like Orthogonal Matching Pursuit (OMP).
3. Semidefinite Relaxation for Partially-Connected Structure:
   • For the partially-connected structure, the paper develops a semidefinite relaxation-based AltMin (SDR-AltMin) algorithm. This approach optimally designs hybrid precoders by converting the problem into a convex semidefinite programming problem, thus effectively managing the unit modulus constraints and reducing implementation complexity.
4. Broadband Extension for OFDM Systems:
   • The effectiveness of the proposed algorithms is further extended to broadband settings with OFDM modulation, illustrating significant performance gains over existing hybrid precoding algorithms across multiple subcarriers.

Numerical Results and Insights

Simulation results demonstrate the efficacy of the proposed algorithms:

• The MO-AltMin algorithm achieves near-optimal performance in spectral efficiency, closely matching the fully digital precoder, even when the number of RF chains is limited.
• The PE-AltMin algorithm achieves notable performance improvements over the OMP algorithm and offers a valuable trade-off between complexity and efficiency.
• For partially-connected structures, the SDR-AltMin algorithm significantly outperforms analog beamforming techniques, with substantial gains observed especially at higher SNRs.
• When examining both spectral and energy efficiency, the fully-connected structure shows higher performance with a smaller number of RF chains, while the partially-connected structure becomes favorable in terms of energy efficiency as the number of RF chains increases, underscoring its potential for low-complexity, high-efficiency implementations in mmWave systems.

Practical and Theoretical Implications

The alternating minimization framework proposed in this paper:

• Provides a robust methodology to approach the design of hybrid precoders, moving beyond heuristic or suboptimal solutions typically employed.
• Offers theoretical insights into the behavior of hybrid precoding structures and their optimization under practical constraints.
• The findings related to energy efficiency are especially relevant for real-world applications where power consumption is a critical factor, providing network designers concrete metrics to balance performance and cost-effectiveness.

Future Directions

Future research could focus on extending the alternating minimization framework to:

• Multi-user mmWave MIMO systems, addressing the multiplexing and beamforming challenges in more dynamic environments.
• Incorporation of advanced machine learning techniques to further enhance the adaptive capabilities and efficiency of hybrid precoding designs, especially in rapidly changing channel conditions.
• Integration with 6G and beyond technologies, exploring broader frequency bands, and leveraging additional spectrum resources, including terahertz communication.

In conclusion, this paper comprehensively addresses the hybrid precoder design challenge in mmWave MIMO systems using sophisticated alternating minimization algorithms, providing substantial contributions to both theoretical foundations and practical implementations in next-generation wireless networks.