Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels under Limited Feedback (0906.3682v5)

Abstract: In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas $M$ and the number of single-antenna users $K$ are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as $M,K\to\infty$. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive (i) for RZF the optimal regularization parameter, (ii) for ZF the optimal number of users, (iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal amount of feedback in large FDD/TDD multi-user systems. Numerical simulations suggest that the deterministic approximations are accurate even for small $M,K$.

• The paper develops deterministic SINR approximations for ZF and RZF precoding, reducing reliance on intensive simulations.
• It optimizes the RZF regularization parameter to maximize sum rate despite imperfect CSIT, guiding practical system design.
• The study introduces optimal power allocation and feedback/training scaling laws to efficiently manage resources in MISO systems.

An Analysis of Linear Precoding in Correlated MISO Broadcast Channels with Limited Feedback

The paper investigates the sum rate performance of zero-forcing (ZF) and regularized zero-forcing (RZF) precoding in large-scale multi-input single-output (MISO) broadcast systems. It focuses on scenarios where the transmitter lacks perfect channel state information (CSIT) and each user channel has its own correlation. The paper employs random matrix theory (RMT) to derive deterministic approximations for the empirical signal-to-interference-plus-noise ratio (SINR), which holds true as the number of transmit antennas $M$ and single-antenna users $K$ approach infinity while their ratio remains bounded.

Key Contributions

1. Deterministic SINR Approximations: The paper develops deterministic equivalents for the SINR of ZF and RZF precoding. These approximations enable the investigation of performance without intensive Monte Carlo simulations, offering precise results even for smaller system dimensions.
2. Optimization of RZF Regularization: By deriving the optimal regularization parameter for RZF, the paper identifies a condition for sum rate maximization. This parameter adapts to the imperfections in CSIT, providing insights into effective system optimization strategies.
3. Power Allocation Schemes: For channels with a common correlation and different CSIT qualities, a water-filling power allocation scheme is presented, which proves to be optimal under the given assumptions.
4. Feedback and Training Optimization: The paper analyzes the necessary amount of feedback in frequency-division duplex (FDD) systems and examines the optimal amount of training in time-division duplex (TDD) systems, presenting scaling laws that ensure a constant rate gap, thus maintaining full multiplexing gain.

Results and Implications

• Accurate Approximations: Numerical results validate the deterministic SINR approximations, demonstrating their accuracy and effectiveness for system dimensions as small as $M=K=16$.
• Optimization beyond Perfect CSIT: The findings indicate that imperfect CSIT can significantly impact the efficacy of linear precoding strategies, making parameter optimization crucial for maximizing performance.
• Feedback Bits Scaling: In large FDD systems, the required feedback scales with the number of transmit antennas, informing design choices for systems utilizing limited feedback.
• Training Interval Scaling: For large TDD systems, the analysis reveals that the training interval should scale proportionally to the square root of the coherence interval or inversely with the square root of the downlink SNR.

Future Directions

The insights from this work have several implications for future AI-driven communication systems:

• Adaptive Systems: By integrating adaptive strategies for power allocation and regularization parameters, AI models can enhance performance under varying CSIT conditions.
• Resource-Efficient Designs: Developing resource-efficient designs that account for both feedback and training trade-offs can improve real-time performance in dynamic environments.
• AI-Assisted Channel Estimation: Machine learning could further refine channel estimation processes, leading to more precise CSIT and improved precoding performance.

Overall, the paper provides a comprehensive framework for analyzing and optimizing linear precoding in MISO channels under realistic conditions, significantly contributing to the development of efficient multi-user communication systems.