Hybrid combiner and precoder architectures, radio frequency (RF) chain, analog phase shifters, digital-to-analog converter (DAC), and analog-to-digital converter (ADC) are components of a millimeter wave cellular system. Prior works in the area of millimeter wave cellular system design employ receiver with infinite bit and large amount of RF chain that scales linearly with the quantity of transmitting and receiving antennas. This mode of design no doubt increases power demand or requirement of a typical millimeter wave system. In this work, hybrid architecture with few RF chains and small number of ADC bits are proposed and are used as candidate for millimeter wave channel estimation and cellular communication. In that connection, least square (LS), orthogonal matching pursuit (OMP), compressed sampling matching pursuit (CoSAMP), and deep learning (DL) techniques are utilized for analytical investigation. Indeed, computational results reveal that, when ADC consisting of uniform mid- rise quantizer is employed, the performance of 4 and 6 bits at signal-to-noise ratio (SNR) values of − 10 dB and 20 dB is at par with infinite bit (unquantized case). As a validation, DL compares favorably well with adaptive compressed sensing (ACS) technique previously used in the literature for channel estimation, while OMP and CoSAMP show better performance than ACS.