Gaussian Multiple Access Channels with One-Bit Quantizer at the Receiver †^,‡.

Area of Science:

• Information Theory
• Digital Communications
• Signal Processing

Background:

• The capacity of communication channels is fundamental to information theory.
• One-bit analog-to-digital converters (ADCs) offer power and bandwidth efficiency but introduce quantization challenges.
• Gaussian multiple access channels (MACs) are essential models for systems with multiple transmitters sharing a common channel.

Purpose of the Study:

• To determine the capacity region of a two-transmitter Gaussian MAC with a one-bit ADC under average input power constraints.
• To characterize the nature of input distributions that achieve the capacity region boundaries.
• To establish bounds on achievable sum capacity and explore practical transmission strategies.

Main Methods:

• Analysis of the capacity region for a two-transmitter Gaussian MAC.
• Investigation of input distributions under average power constraints with a zero-threshold one-bit ADC.
• Derivation of upper bounds on the number of mass points for optimal input distributions.
• Proposal of a lower bound for sum capacity using time division and power control.

Main Results:

• Proved that the input distributions achieving capacity region boundary points are discrete.
• Derived upper bounds on the number of mass points for these discrete distributions.
• Proposed a lower bound on the sum capacity achievable via time division with power control.
• Conjectured the tightness of the proposed lower bound based on numerical evidence.

Conclusions:

• The capacity region of the studied channel is fundamentally linked to discrete input distributions.
• The derived bounds provide theoretical insights into the performance limitations imposed by one-bit ADCs.
• The proposed lower bound offers a practical and potentially optimal strategy for sum capacity maximization in such systems.