Asymptotic Capacity for MIMO Communications With Insufficient Radio Frequency Chains

This paper presents an asymptotic capacity analysis for multiple-input multiple-output (MIMO) communications with insufficient transmit radio frequency (RF) chains and sufficient receive RF chains, which is named as iMIMO communications. We characterize the iMIMO channel capacity by the maximum mutual information given any vector inputs subject to not only an average power constraint but also a sparsity constraint. It is proven that an optimized Gaussian mixture input distribution is capacity-achieving in the high signal-to-noise-ratio (SNR) regime. The optimal mixture coefficients and the covariance matrices of the Gaussian mixtures are derived and also the corresponding asymptotic capacity. Furthermore, we discuss the impact of insufficient receive RF chains on the achievable spectral efficiency. We investigate the superiority of the capacity-achieving technique, which is an optimized non-uniform subspace modulation (NUSM), by comparing it with the best subspace selection (BSS) and the uniform subspace modulation (USM). The comparison results reveal that the optimized NUSM is optimal in the high SNR regime. Numerical results are presented to validate our analysis.