Receive Antenna Selection Under Discrete Inputs: Approximation and Applications

To analyze the achievable performance of antenna selection (AS) in practical multi-antenna systems, this paper studies the receive antenna selection (RAS) in single-input multiple-output (AS-SIMO) systems under discrete inputs. We first propose an approximate expression to evaluate the instantaneous mutual information (MI) of M-ary quadrature amplitude modulation (M-QAM) signaling over additive white Gaussian noise (AWGN) channels. Then, by exploiting this approximate formula, we develop a closed-form formula for the ergodic MI in AS-SIMO systems with M-QAM signaling. Additionally, we also analyze the asymptotic MI for a large number of receive antennas Nr. This asymptotic analysis suggests that the scaling rate of the MI with Nr becomes zero rate in contrast to the double logarithmic rate under Gaussian inputs. Besides, our result is also extended to discuss the mutual information of multiple-input multiple-output (MIMO) systems having discrete inputs with receive antenna selection, and an upper bound for the MI is derived. Finally, the derived result is applied to analyze several performance measures of the discrete inputs driven ASSIMO systems. Specifically, it is first used to discuss the relationship between the ergodic MI and the number of active antennas. Our investigation shows that this relationship follows Pareto principle, i.e., 80% of the MI of full-antenna selection can be achieved via 20% of the total antennas. Then, our proposed approximation is employed to analytically study the effective MI which takes channel estimation (CE) into consideration, indicating that CE is a main limit of large-scale systems. Moreover, the energy efficiency (EE) is explored on the basis of our results, and we find there exists an optimal number of active antennas to maximize the energy efficiency. In addition to theoretical derivations, all the analytical results are validated by numerical simulations.