Precoding for Uplink Distributed Antenna Systems with Transmit Correlation in Rician Fading Channels

In this paper, we develop an optimal precoder and a suboptimal precoder for uplink distributed antenna systems with transmit correlation over Rician channels. The objective is to minimize a pairwise error probability (PEP) with constrained transmit power. The optimal scheme uses an efficient projection-based steepest descent algorithm to obtain the Gram matrix of the precoder, while the suboptimal scheme exploits the eigen-structure of the Gram matrix to obtain its unitary matrix (beamforming) and eigenvalues (power control). For a given beamforming (BF), an efficient power adaptation based on a fuzzy signal-to-noise ratio (SNR) is developed. The PEP analysis at low SNR is used to obtain a suboptimal BF. The derived BF and the fuzzy power adaptation have closed-form expressions that make the suboptimal scheme computationally efficient in comparison with existing methods. The BF can be re-optimized via the Riemannian steepest descent method to further reduce the PEP. Simulation results show that the proposed optimal scheme not only gives the performance the same as the existing optimal scheme when the latter can converge, but it also has lower computational complexity and faster convergence. Moreover, the suboptimal scheme can give a nearly optimal error rate.