Convexity of the Capacity of One-Bit Quantized Additive White Gaussian Noise Channels

In this study, the maximum error-free transmission rate of an additive white Gaussian noise channel with a symmetric analog-to-digital converter (ADC) was derived as composite function binary entropy function, Q-function, and square root assuming that convex on set all non-negative real numbers. However, because mathematically proving convexity near zero is difficult, studies in field have only presented numerical results for small values domain. Because low-signal-to-noise (SNR) regime considered to be major application area one-bit ADCs wireless communication, deriving concrete proof SNR (non-negative zero) important. Therefore, study proposes novel convexity, which satisfied values, based continuity involved functions.