On block noncoherent communication with low-precision phase quantization at the receiver

Abstract

We consider communication over the block noncoherent AWGN channel with low-precision Analog-to-Digital Converters (ADCs) at the receiver. For standard uniform Phase Shift Keying (PSK) modulation, we investigate the performance of a receiver architecture that quantizes <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">phase</i> of the received signal; this has the advantage of being <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">implementable</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">automatic</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gain</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">control</i> , using multiple 1-bit ADCs preceded by analog multipliers. We study the structure of the transition density of the resulting channel model. Several results, based on the symmetry inherent in the channel, are provided to characterize this transition density. A low complexity procedure for computing the channel capacity is obtained using these results. Numerical capacity computations for QPSK show that 8-bin phase quantization of the received signal recovers more than 80-85% of the capacity attained with unquantized observations, while 12-bin phase quantization recovers above 90-95% of the unquantized capacity. Dithering the constellation is shown to improve the performance in the face of drastic quantization.