Capacity Analysis of One-Bit Quantized MIMO Systems with Transmitter Channel State Information (1410.7353v3)

Abstract: With bandwidths on the order of a gigahertz in emerging wireless systems, high-resolution analog-to-digital convertors (ADCs) become a power consumption bottleneck. One solution is to employ low resolution one-bit ADCs. In this paper, we analyze the flat fading multiple-input multiple-output (MIMO) channel with one-bit ADCs. Channel state information is assumed to be known at both the transmitter and receiver. For the multiple-input single-output channel, we derive the exact channel capacity. For the single-input multiple-output and MIMO channel, the capacity at infinite signal-to-noise ratio (SNR) is found. We also derive upper bound at finite SNR, which is tight when the channel has full row rank. In addition, we propose an efficient method to design the input symbols to approach the capacity achieving solution. We incorporate millimeter wave channel characteristics and find the bounds on the infinite SNR capacity. The results show how the number of paths and number of receive antennas impact the capacity.

• The paper derives exact channel capacity for MISO systems over the entire SNR range and identifies capacity-achieving input distributions.
• The study establishes new finite SNR upper bounds and analyzes infinite SNR capacity for SIMO and general MIMO systems using geometric techniques.
• The research employs numerical optimization to propose capacity-approaching symbol designs and assesses the impact of sparse mmWave channels on system performance.

Analysis of One-Bit Quantized MIMO Systems with CSIT

The research paper explores the capacity of multiple-input multiple-output (MIMO) systems with one-bit quantized analog-to-digital converters (ADCs) under the assumption of channel state information at the transmitter (CSIT). The motivation for this exploration is the increased power consumption associated with high-resolution ADCs in next-generation wireless systems—especially those utilizing wide bandwidths around the gigahertz range. By employing one-bit ADCs, power consumption can be significantly reduced, albeit at a potential loss in communication capacity. The authors embark on characterizing this trade-off and optimizing transmission strategies for MIMO systems constrained by such low-resolution quantization.

Key Contributions

1. Channel Capacity Analysis: The paper derives the channel capacity for multiple-input single-output (MISO) systems with one-bit ADCs over the entire signal-to-noise ratio (SNR) range. It determines the exact channel capacity and the corresponding capacity-achieving input distribution.
2. Capacity at Infinite SNR: For both single-input multiple-output (SIMO) and general MIMO systems, the paper provides a capacity analysis at infinite SNR. It discusses upper and lower bounds on capacity derived from geometric considerations in multi-dimensional space, showcasing the dependency of capacity on system parameters such as the number of receive antennas and paths.
3. Finite SNR Bounds: The authors offer a new upper bound for MIMO capacity at finite SNR, which tightens prior results when the channel has full row rank. They propose a capacity-approaching symbol design method based on convex optimization for practical application when full channel information is available.
4. Impact of Millimeter-Wave Channels: By incorporating the unique characteristics of millimeter-wave channels, such as sparse multipath environments, the paper explores how capacity is influenced by the number of paths and determines strategic transmission tactics in single-path scenarios.
5. Numerical Optimization: The paper includes numerical techniques that allow for the optimization of input distributions to align closely with capacity-achieving configurations identified through theoretical analysis.

Implications and Potential for Future Research

This paper holds practical implications for the design of future wireless communication systems that aim to balance energy efficiency with performance. The findings are particularly relevant for the development of mmWave systems where hardware limitations and power constraints necessitate efficient solutions beyond traditional high-resolution ADCs. The characterization of MIMO capacities in the high SNR regime provides a framework for understanding the limitations and opportunities afforded by one-bit quantization.

Future research directions could explore the impact of imperfect channel state information (CSI), enhancing robustness against estimation errors, and developing adaptive strategies for real-time variations in channel conditions. Additionally, there might be potential in extending these results to multi-user scenarios or integrating them with advanced network architectures like massive MIMO or hybrid beamforming to address the challenges in next-generation millimeter-wave networks.

Overall, the paper provides a comprehensive theoretical treatment of one-bit quantized MIMO systems in the context of emerging wireless technologies, offering foundational insights that guide the direction of future technical advancements in the field.