Frequency Selective Hybrid Precoding for Limited Feedback Millimeter Wave Systems (1510.00609v4)

Abstract: Hybrid analog/digital precoding offers a compromise between hardware complexity and system performance in millimeter wave (mmWave) systems. This type of precoding allows mmWave systems to leverage large antenna array gains that are necessary for sufficient link margin, while permitting low cost and power consumption hardware. Most prior work has focused on hybrid precoding for narrowband mmWave systems, with perfect or estimated channel knowledge at the transmitter. MmWave systems, however, will likely operate on wideband channels with frequency selectivity. Therefore, this paper considers wideband mmWave systems with a limited feedback channel between the transmitter and receiver. First, the optimal hybrid precoding design for a given RF codebook is derived. This provides a benchmark for any other heuristic algorithm and gives useful insights into codebook designs. Second, efficient hybrid analog/digital codebooks are developed for spatial multiplexing in wideband mmWave systems. Finally, a low-complexity yet near-optimal greedy frequency selective hybrid precoding algorithm is proposed based on Gram-Schmidt orthogonalization. Simulation results show that the developed hybrid codebooks and precoder designs achieve very good performance compared with the unconstrained solutions while requiring much less complexity.

• The paper presents hybrid precoding design with RF codebook optimization that reduces complexity by expressing the baseband precoder as a function of the RF precoder.
• It introduces efficient codebook construction for wideband mmWave systems, minimizing the average mutual information loss compared to ideal unconstrained solutions.
• The study proposes a low-complexity greedy frequency-selective precoding algorithm that achieves near-optimal performance, as validated by extensive simulations.

Frequency Selective Hybrid Precoding for Limited Feedback Millimeter Wave Systems

This paper, authored by Ahmed Alkhateeb and Robert W. Heath Jr., focuses on the development of hybrid precoding strategies for millimeter wave (mmWave) communication systems operating on wideband channels. Traditional narrowband solutions do not adequately address the challenges posed by the frequency selectivity of wideband mmWave channels. The research herein addresses this limitation by proposing and analyzing robust hybrid analog/digital precoding techniques, aimed at optimizing system performance while maintaining manageable hardware complexity.

Key Contributions

1. Hybrid Precoding Design with RF Codebook Optimization:
   • The paper derives the optimal hybrid precoding matrix design given a quantized RF codebook, providing a benchmark for evaluating heuristic algorithms. This paper reveals that the optimal baseband precoder can be written as a function of the RF precoder, thus reducing the hybrid precoder design complexity.
2. Codebook Development for Wideband mmWave Systems:
   • Efficient codebooks are constructed for hybrid precoding applicable in wideband scenarios. A particular focus is on minimizing the average mutual information loss relative to ideal unconstrained solutions. The codebooks accommodate scenarios where the number of data streams equals or is less than the number of RF chains.
3. Low-Complexity Greedy Precoding Algorithm:
   • The paper introduces a greedy frequency-selective hybrid precoding algorithm leveraging Gram-Schmidt orthogonalization. This method achieves performance close to that of optimal solutions while significantly reducing computational complexity.

Numerical Results and Implications

Extensive simulations demonstrate that the proposed hybrid precoding frameworks achieve substantial performance improvements over traditional analog-only solutions with a manageable increase in complexity. The simulations validate the near-optimality of the proposed algorithms and the advantage of leveraging wideband characteristics in codebook design.

Practical and Theoretical Implications

The proposed methods present a pragmatic approach for 5G and beyond, where mmWave frequencies are expected to play a crucial role. By reducing complexity without significant performance sacrifices, these strategies offer practical benefits for implementing cost-effective large-scale MIMO systems. Theoretically, the paper enriches the understanding of hybrid precoding in frequency-selective environments and opens avenues for future research on hybrid and full digital trade-offs, channel estimation, and multi-user scenarios.

Speculations on Future Developments

Future research could extend this work by exploring:

• Multi-user hybrid precoding strategies that incorporate the spatial constraints and dynamics of wideband mmWave channels.
• Adaptive codebook updates based on environmental sensing to maintain performance amidst dynamic channel conditions.
• Integration with machine learning for real-time and context-aware precoding solutions, potentially reducing feedback overheads further.

In conclusion, this paper provides valuable insights into the design and optimization of hybrid precoding systems suitable for next-generation mmWave communication platforms, addressing both theoretical challenges and practical constraints.