{'fraction_non_alphanumeric': 0.02099737532808399, 'fraction_numerical': 0.0, 'mean_word_length': 5.641114982578397, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Precoding Design for Correlated MIMO-AF Relay Networks With Statistical Channel State Information

An iterative precoding design of a two-hop amplify-and-forward (AF) multiple-input multiple-output relay network with one source, multiple relays, and one destination is presented. To provide a solution for general scenarios, the source-to-destination direct link and double correlated Kronecker Rician fading channels are considered. Statistical channel state information is used for the average capacity formulation for the sake of its robustness and infrequent update. The source and relay precoders are optimized to maximize a closed-form upper bound of the average capacity giving a suboptimal design. The non-convex design problem is divided into three sub-problems: source precoder, relay beamforming, and relay power allocation (PA). For optimizing the source precoder subject to multiple power constraints, rather than using computationally expensive penalty type algorithms, an efficient design procedure as a type of water-filling with multiple water levels is developed. Its negative PA is handled by a simple method of determining the eigen-modes of positive power. Using the Riemannian steepest descent method and a newly proposed power adaptation to optimize the relay beamforming and relay PA, respectively, the constrained optimization problems become unconstrained. Simulations show that the developed design procedure with trivial initialization provides nearly global optimum performance with fast convergence and efficient computation. The developed methods for the source precoder and relay PA outperform upon the augmented Lagrangian method with respect to convergence and computing time. Furthermore, the generality of the proposed scheme makes the design procedure applicable to AF relay networks with different simplified Kronecker channel models and with/without the direct link.