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In this paper, we present a game-theoretic approach for the purpose of deriving the problem of joint beamforming and power control in cognitive radio (CR) multiple-input multiple-output (MIMO) broadcast channels (CR MIMO-BCs), where the primary users (PUs) coexist with the secondary users (SUs) and they share the same spectrum. The cognitive base station (CBS), which is equipped with multiple antennas, is capable of transmitting data to the SU's multiple-antenna receiver by employing the technology of beamforming. The proposed approach is an application of separable games, which are formally stated by the subgames of beamforming and power control. Furthermore, based on the model of noncooperative separate games, separable cost functions for the parameters of beamforming and power control are also proposed, showing that these cost functions are convex. Therefore, the convex theory of a noncooperative game can be employed to investigate the best response strategies as well as existence of Nash equilibrium solutions. Finally, we propose an iterative algorithm to achieve the optimal Nash equilibrium of the proposed joint beamforming subgame and power control subgame. Numerical results verify both the convergence and the tracking properties of the proposed algorithm for variant scenarios.

This paper proposes a broad-band linear-to-circular polarization converter based on a multilayer stripline metasurface. The structure is constructed of three stripline metallic layers stacked with two dielectric plates, and it has different electromagnetic response characteristics in two orthogonal directions. Based on this, the amplitude of the two orthogonal components of the transmitted wave is equal, and the phase difference is 90°. To better understand the working principle of the proposed converter, a detailed equivalent circuit model is presented. The simulation results indicate that the converter can convert linearly polarized incident waves into circularly polarized transmitted waves in the frequency range of 4.96-12.44 GHz. For an increased incident angle of 50°, the device can still maintain an axial ratio bandwidth of 53.7% in the x-z and y-z planes. Because of its broadband, small size, and wide-angle, the proposed converter can be integrated into a linearly polarized antenna system to generate circularly polarized waves without significantly affecting antenna performance.

In recent years, many intriguing electromagnetic (EM) phenomena have come into being utilizing metasurfaces (MSs). However, most of them operate in either transmission or reflection mode, leaving the other half of the EM space completely unmodulated. Here, a kind of transmission-reflection-integrated multifunctional passive MS is proposed for entire-space electromagnetic wave manipulation, which can transmit the x-polarized EM wave and reflect the y-polarized EM wave from the upper and lower space, respectively. By introducing an H-shaped chiral grating-like micro-structure and open square patches into the unit, the MS acts not only as an efficient converter of linear-to-left-hand circular (LP-to-LHCP), linear-to-orthogonal (LP-to-XP), and linear-to-right-hand circular (LP-to-RHCP) polarization within the frequency bands of 3.05–3.25, 3.45–3.8, and 6.45–6.85 GHz, respectively, under the x-polarized EM wave, but also as an artificial magnetic conductor (AMC) within the frequency band of 12.6–13.5 GHz under the y-polarized EM wave. Additionally, the LP-to-XP polarization conversion ratio (PCR) is up to −0.52 dB at 3.8 GHz. To discuss the multiple functions of the elements to manipulate EM waves, the MS operating in transmission and reflection modes is designed and simulated. Furthermore, the proposed multifunctional passive MS is fabricated and experimentally measured. Both measured and simulated results confirm the prominent properties of the proposed MS, which validates the design’s viability. This design offers an efficient way to achieve multifunctional meta-devices, which may have latent applications in modern integrated systems.

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