On Capacity of Large-Scale MIMO Multiple Access Channels with Distributed Sets of Correlated Antennas (1209.5513v2)

Abstract: In this paper, a deterministic equivalent of ergodic sum rate and an algorithm for evaluating the capacity-achieving input covariance matrices for the uplink large-scale multiple-input multiple-output (MIMO) antenna channels are proposed. We consider a large-scale MIMO system consisting of multiple users and one base station with several distributed antenna sets. Each link between a user and an antenna set forms a two-sided spatially correlated MIMO channel with line-of-sight (LOS) components. Our derivations are based on novel techniques from large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the terminals approach to infinity with a fixed ratio. The deterministic equivalent results (the deterministic equivalent of ergodic sum rate and the capacity-achieving input covariance matrices) are easy to compute and shown to be accurate for realistic system dimensions. In addition, they are shown to be invariant to several types of fading distribution.

• The paper derives deterministic equivalents for ergodic sum rate in large-scale MIMO using random matrix theory, offering efficient performance estimation.
• The study proposes an algorithm for calculating capacity-achieving input covariance matrices based on statistical CSI, optimizing transmit strategies in large MIMO systems.
• The methods significantly reduce computational complexity and enhance scalability for analyzing large systems, offering practical insights for next-generation wireless network design.

Large-Scale MIMO Multiple Access Channels: Capacity Achievements with Correlated Antennas

The paper presents a significant advancement in the field of communication systems, specifically addressing the challenges and potential of large-scale multiple-input multiple-output (MIMO) systems with spatially distributed and correlated antennas. As wireless systems continue to experience high demands for increased throughput and spectral efficiency, the implementation of large-scale MIMO becomes instrumental. This work critically examines the ergodic sum-rate capacity and proposes an algorithm for deriving capacity-achieving input covariance matrices in such complex wireless environments.

Key Contributions

The paper provides two primary contributions:

1. Deterministic Equivalents for Ergodic Sum Rate: The authors derive deterministic equivalents of the ergodic sum rate for large-scale MIMO multiple access channels by employing techniques from large-dimensional random matrix theory (RMT). This achievement is instrumental in efficiently estimating system performance as it offers computational simplicity over traditional Monte Carlo methods, especially as the system scales with more users and antennas.
2. Capacity-Achieving Input Covariances: An algorithm is proposed to calculate the capacity-achieving input covariance matrices under practical scenarios where only statistical channel state information (CSI) is available at the transmitter. This facilitates the optimization of transmit strategies in practical large MIMO systems, thus enhancing the link reliability and data rates.

System Model and Assumptions

A large-scale MIMO scenario with distributed antenna sets is scrutinized, where:

• Each user and base station utilizes spatially correlated channels with line-of-sight (LOS) components.
• The paper assumes environments where user terminals and base stations are equipped with potentially infinite antennas at a fixed ratio.

This assumption plays a crucial role in employing large-dimensional RMT techniques to model and analyze the channel. Furthermore, the paper extends the analysis beyond Gaussian entries, handling channels with various small-scale fading distributions.

Analytical Insights

The interplay of correlation matrices across both users and base station antenna sets is resolved ingeniously by:

• Proposing a set of equations for evaluating deterministic equivalents, ensuring robustness against different fading distributions.
• Demonstrating the convergence of the deterministic sum-rate approximations with the actual values as system dimensions grow infinitely large.

The method employed involves the innovative use of Gaussian methods and Lindeberg's principle to extend results from Gaussian to non-Gaussian models.

Practical Implications

Incorporating deterministic equivalents into the design of input covariance matrices allows:

• Reduced complexity: The proposed algorithm significantly reduces computational demands compared to direct simulations, making feasible the analysis of systems with hundreds of users and antennas.
• Enhanced scalability: The methods are adaptable to real-world large networks where computational efficiency and quick adaptations to CSI are prerequisites.
• System design implications: These findings open avenues for practical transmitter designs and adaptations in contemporary networks like 5G and beyond.

Future Directions and Impact

The deterministic equivalent approach lays down the groundwork for further exploration in system designs, especially focusing on the optimization of scheduling, cell planning, and interference management in large-scale MIMO systems. Future research could extend these results to include the impact of spatial correlation on the diversity and multiplexing trade-offs.

Overall, this research significantly broadens our understanding of capacity limits in large-scale MIMO settings and provides a feasible approach to exploit spatially correlated channels, thus furthering the enhancement of wireless communication capacities.