We consider robust hybrid beamfocusing schemes against statistical and norm-bounded positioning errors in order to improve a total system data rate in near-field communications. To this end, baseband and analog beamfocusing designs are formulated as an ergodic sum rate maximization, which is solved via deterministic and stochastic optimization. In particular, a closed-form expression of the erdodic sum rate is introduced, which makes the problem tractable by deterministic optimization. In turn, a new stochastic optimization algorithm is proposed for further data rate improvements, which incorporates matrix fractional programming (FP) and element-wise phase derivatives into stochastic learning frameworks by penalize methods. The proposed stochastic algorithm theoretically guarantees convergence to stationary points of the original problem. Numerical results confirm that the proposed approaches achieve higher data rates than non-robust approaches and a singular value decomposition (SVD) beamfocusing with perfect position information.

In this paper, we consider near-field beams that can mitigate signal attenuation and blockage effects using a uniform linear array (ULA). In particular, closed-form expressions for phase distributions in a ULA are derived to generate Bessel beams and curving beams based on the desired propagation directions and trajectories. Based on the phase distributions, the maximum steering angle and propagation distance of Bessel beams with a ULA are revealed. In addition, from the sampling theorem in the spatial domain, the requirements for ULAs to properly generate Bessel beams are clarified. For curving beams, trajectories to reach a user while avoiding one obstacle are designed via the Lagrangian method. Numerical results obtained by electromagnetic wave simulations confirm the effectiveness of the analyses for Bessel beams and the curving beam designs. Furthermore, the characteristics of Gaussian beams, beamfocusing, Bessel beams, and curving beams are summarized in terms of the statistical behavior of their intensity and signal processing.

In this paper, the optimal wavefronts for maximum ratio transmission (MRT) are investigated under path blockage effects in the near-field region. To characterize the behavior of the optimal wavefronts, a new deterministic channel model is proposed in the presence of obstacles, which describes blockage effects by the variation of the electric field based on the uniform theory of diffraction (UTD). With the proposed channel model, the linear precoder designs are formulated as optimization problems to maximize the power density at the desired point under fully digital and analog array assumptions, where the amplitude and phase distributions of the solutions characterize the optimal wavefronts to achieve MRT. The optimal precoders reveal that the proposed channel modeling must be required to optimize near-field communications systems in the presence of obstacles, which, together with electromagnetic wave simulations, confirm that linear precoding with the proposed channel model achieves MRT under any blockage effect, and the optimal wavefront varies for each blockage situation.

We consider the joint design of time-domain equalization and hybrid transmit and receive beamforming schemes, so as to combat frequency-selective fading and path loss effects in single-carrier (SC) multiple-input multiple-output (MIMO) communications systems. In particular, considering the linear equalization and hybrid beamforming matrices as variables, a minimum mean square error (MMSE) problem to minimize the bit error rate (BER) of SC-MIMO systems is formulated and solved via an accelerated matrix quadratic transform (QT) and manifold optimization. The relationship between mean square error (MSE) minimization via joint MMSE equalization and beamforming, and the minimization of average BER over all data streams is expressed analytically, which together with numerical results confirm that the proposed SC scheme outperforms the SC systems whose linear equalizer and beamformers are designed separately.

We propose a scheme for the concomitant design of hybrid beamforming and per-carrier transmit power allocation to mitigate the effect of random path blockages in coordinated multi-point (CoMP) systems using orthogonal frequency division multiplexing (OFDM) in millimeter-wave (mmWave) channels. In order to optimize both the beamformers and power allocation while dealing simultaneously with outage minimization and sum rate maximization (SRM) requirements, a regularized sum-of-outage minimization problem is formulated. The problem is then transformed into an empirical risk minimization (ERM) problem, solved via block stochastic learning and manifold optimization, with required learning rates derived and tuned to guarantee convergence. The method, which demands only a few radio frequency (RF) chains and relies only on knowledge of blockage probabilities, is shown via simulation results not only to outperform state-of-the-art (SotA) alternatives, but to actually achieve outage probabilities comparable to those a fully digital CoMP-SRM scheme with perfect knowledge of instantaneous blockages.

We propose a hybrid beamforming for coordinated multi-point (CoMP) transmission using orthogonal frequency division multiplexing (OFDM) over millimeter-wave (mmWave) channels to combat random propagation path blockages. In particular, a sum-of-outage-probability minimization problem with manifold constraints is formulated, which designs the hybrid beamformers, the data rate allocation, and the power allocation over subcarriers jointly to meet the prescribed data rate requirement. A new block stochastic learning mechanism exploiting prior knowledge of the path blockages is also introduced to solve the problem efficiently. Numerical results confirm the effectiveness of the proposed approach in minimizing the outage probability of users according to their target rate. Furthermore, these results also show that the proposed hybrid CoMP transmission only with a few radio frequency (RF) chains and knowledge of blockage probabilities achieves comparable outage performance to a fully digital CoMP transmission alternative with perfect knowledge of instantaneous path blockages.