Capacity bound of mimo systems with mpsk modulation and superimposed pilots

Abstract

The enormous capacity potential of multiple-input multiple-output (MIMO) is based on some unrealistic assump- tions, such as the complete channel state information (CCSI) at the receiver and Gaussian distributed data. In this paper, in frequency-flat Rayleigh fading environment, we investigate the ergodic capacity of MIMO systems with M-ary phase-shift keying (MPSK) modulation and superimposed pilots for channel estimation. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. We also derive an easy-computing closed-form lower bound of the channel capacity. Furthermore, the optimal power allocation between the data and pilots is investigated by numerical optimization. It is shown that more power should be devoted to the data in low SNR environments and to the pilots in high SNR environments. I. INTRODUCTION In this paper, we investigate the MIMO channel capacity with MPSK modulation and superimposed pilots. Since it is hard to derive the exact closed-form expressions, we tackle this problem by finding a closed-form lower bound of the capacity. Consider the communication over a wireless channel with N transmit and M receive antennas and distorted by additive white Gaussian noise (AWGN). We adopt a block-fading chan- nel model where the fading gains between all antenna pairs are independent and identically distributed (i.i.d.) Rayleigh fading and remain constant for coherence interval of length T (in symbols) before changing to a new independent realization. H ∈ C M ×N denotes the channel matrix. The entries of H and the AWGN matrix V ∈ C M ×T are i.i.d. complex Gaussian variables with zero mean and unit variance. We further assume that the transmitter has no channel information thus equal power allocation is adopted on the transmit antennas. Under superimposed pilots scheme, the pilot and data vec- tors are transmitted simultaneously. Thus the received signal matrix can be expressed as Y = ρ/NHX + V