This paper investigates the problem of initial beam alignment that is crucial to beam-based communications used in 5G and envisioned for 6G. Our proposed method includes a beam sweeping using a learned codebook, and a beam prediction by a categorization neural network (NN) based on the measurements from the sweeping. Different from the straightforward supervised learning for the optimal beam index, we first design a compact representation of the optimal beam to reduce the complexity of the NN. Then, we show that learning the single optimal beam index can be problematic for realistic scenarios, and propose to use a new probabilistic spatial power distribution as the output. We show that our method is better suited for future wireless generations and can provide various information related to beam management by simulations.

This paper develops two novel containment control protocols for networked fractional-order systems with sampled position data. In the first scenario, time delay is not considered and the protocol is about the last and causal past sampled position data, while in the second scenario, time delay is considered and the protocol is about the last and time delay sampled position data. Successively, some necessary and sufficient criteria are derived for two classes of protocols. It is interesting to find that containment control of networked fractional-order systems cannot be reached under the developed control protocols without the help of the causal past sampled position data or time delay. Lastly, the effectiveness of theoretical results is verified through a simulation example.

Alternating direction method of multipliers (ADMM) is an efficient implementation of linear programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty terms to the objective function of the LP decoding model, ADMM variable node (VN) penalized decoding can suppress the non-integral solutions and improve the frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region. In this paper, we propose a novel ADMM check node (CN) penalized decoding algorithm. Codeword solutions which satisfy all parity-check equations will have smaller penalty values than non-codeword solutions, including the non-integral solutions. We discuss the required properties of CN-penalty functions, propose a few functions that satisfy those properties, and study their performance/complexity trade-offs. We also investigate the convergence properties of the proposed algorithm and prove that its performance is independent of the transmitted codeword. Using Monte Carlo simulations and instanton analysis, we then demonstrate that the proposed CN-penalized decoder outperforms ADMM VN penalized decoders in both waterfall and error floor regions. This comes at the expense of some increase in the decoding complexity.

A correction is made in the statement and proof of a lemma used to prove codeword symmetry. In addition, an important typo is noted and corrected.