inis 20(22): e4

Research Article

On the Capacity-Achieving Scheme and Capacity of 1-Bit ADC Gaussian-Mixture Channels

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  • @ARTICLE{10.4108/eai.31-1-2020.162830,
        author={Md Hasan Rahman and Mohammad Ranjbar and Nghi H. Tran},
        title={On the Capacity-Achieving Scheme and Capacity of 1-Bit ADC Gaussian-Mixture Channels},
        journal={EAI Endorsed Transactions on Industrial Networks and Intelligent Systems},
        volume={7},
        number={22},
        publisher={EAI},
        journal_a={INIS},
        year={2020},
        month={1},
        keywords={1-bit ADC, Capacity, Gaussian-Mixture, Kuhn-Tucker Condition, Mutual Information},
        doi={10.4108/eai.31-1-2020.162830}
    }
    
  • Md Hasan Rahman
    Mohammad Ranjbar
    Nghi H. Tran
    Year: 2020
    On the Capacity-Achieving Scheme and Capacity of 1-Bit ADC Gaussian-Mixture Channels
    INIS
    EAI
    DOI: 10.4108/eai.31-1-2020.162830
Md Hasan Rahman1, Mohammad Ranjbar1, Nghi H. Tran1,*
  • 1: Department of Electrical and Computer Engineering, University of Akron, Akron OH 44325, USA
*Contact email: Nghi.tran@uakron.edu

Abstract

This paper addresses the optimal signaling scheme and capacity of an additive Gaussian mixture (GM) noise channel using 1-bit analog-to-digital converters (ADCs). The consideration of GM noise provides a more realistic baseline for the analysis and design of co-channel interference links and networks. Towards that goal, we first show that the capacityachieving input signal is π/2 circularly symmetric. By examining a necessary and sufficient Kuhn–Tucker condition (KTC) for an input to be optimal, we demonstrate that the maximum number of optimal mass points is four. Our proof relies on Dubin’s theorem and the fact that the KTC coefficient is positive, i.e., the power constraint is active. By combining with the π/2 circularly symmetric property, it is then concluded the optimal input is unique, and it has exactly four mass points forming a square centered at the origin. By further checking the first and second derivatives of the modified KTC, it is then shown that the phase of the optimal mass point located in the first quadrant is π/4. Thus, the capacity-achieving input signal is QPSK. This result helps us obtain the channel capacity in closed-form.