Performance Bound for MIMO Systems Using One-Bit ADCs Over Rayleigh Fading Channels

This study explores the performance of multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs) over Rayleigh fading channels. We particularly aim to characterize the pairwise error probability (PEP) achieved by maximum likelihood detection (MLD), which provides the optimal detection performance of the considered systems. First, the upper bound of the PEP is derived by leveraging Jensen's inequality and the Chernoff bound. The asymptotic bounds of the PEP are then characterized to clarify the impact of the one-bit ADCs on the diversity order of the MIMO systems. Notably, the diversity order of the MIMO systems with one-bit ADCs is the same as the number of receive antennas only when transmitting two symbol vectors with the opposite sign. Except for this special case, the asymptotic bound of the PEP is saturated at a high signal-to-noise ratio due to the use of the one-bit ADCs. Using simulations, we verify that the analytical results coincide with the asymptotic behavior of the PEP of the MLD for MIMO systems with one-bit ADCs over Rayleigh fading channels.