Minimizing the energy per bit for pilot-assisted data transmission over quantized channels

To communicate over a priori unknown channels, pilot sequences can be exploited to assist the receiver in obtaining the channel state information. The analog-to-digital converter (ADC) at the front end of the receiver samples and quantizes the input signal, including both pilot and data symbols. This results in a reduction of the receive signal-to-noise ratio (SNR) as well as deteriorated quality of channel estimation, which depends quantitatively on the bit resolution used by the ADC. In this work, we consider the point-to-point, training based communication between a single-antenna transmitter and a multi-antenna receiver over a Rayleigh block fading channel, and take into account the impact of the ADC for a joint optimization of the training length, the average receive SNR, the number of receive antennas, and the bit resolution of the ADC. Goal of the optimization is to minimize the energy per bit metric, where we include both transmit power and power dissipation of the ADC into the energy consumption model, and employ a capacity lower bound which depends on all aforementioned design parameters. Results from numerical simulations are demonstrated and analyzed, leading to a number of insightful observations and conclusions which are important for the energy efficient operation of the system.