# A Novel Metasurface Lens Design for Synthesizing Plane Waves in Millimeter-Wave Bands
## 1 Introduction  
In recent years, 5G technology has been implemented and developed on a large scale. More specifically, 5G systems at frequency range two (FR2) have improved the channel capacities of systems by using the large bandwidths of millimeter waves [1; 2; 3]. Due to demands for higher data rates and increasing user terminals, massive multiple-input multiple-output (MIMO) was introduced as one of the key 5G technologies by the third-generation partnership project (3 GPP) for a higher spectrum efficiency in real networks. The radio performance of massive MIMO devices should be fully characterized in plane-wave conditions using radiated over-the-air (OTA) test methods [4; 5; 6]. OTA testing is seen as essential for mm-wave devices due to a highly integrated antenna and transceiver design [7]. In 3 GPP, there are several measurement scenarios requiring plane-wave conditions for device characterization: RF conformance with a specific angle of arrival, a simultaneous in-band and out-of-band emission analysis [8], radio resource management (RRM) conformance with different power levels from multiple angles of arrival, mobility management verification [9], and MIMO techniques to accurately reflect wireless propagation conditions [10]. Base stations are located in the far field of 5G millimeter-wave devices,and therefore, the electromagnetic waves from base stations can be recognized as plane waves, which can be recognized as real-world conditions. A far field is typically defined as beyond the Fraunhofer distance:  
\[R=\frac{2D^{2}}{\lambda}, \tag{1}\]  
where \(D\) is the maximum aperture of a device under test (DUT) and \(\lambda\) is the wavelength. By placing a probe antenna in the far field of a DUT, a plane-wave condition can be achieved and the phase curvature in the QZ is 22.5\({}^{\circ}\)[11]. For a typical millimeter-wave device with a dimension of 0.2 m \(\times\) 0.2 m, the far-field distance is 13.87 m at 26 GHz and the free-space path loss is roughly 83.58 dB with the following formula:  
\[L=32.4478+20\times\lg(f)+20\times\lg(d), \tag{2}\]  
where \(L\) is the path loss and \(d\) represents the distance between the transmitter and receiver. With such a measurement distance, an anechoic chamber is expensive to construct and impractical for measuring low-power emissions due to a high signal attenuation introduced by the long measurement distance. It is convenient and essential to carry out OTA measurements at distances that are significantly shorter than the Fraunhofer distance. The near-field to far-field (NF-FF) method was proposed for drastically reducing the measurement distance, and it can be used in passive antenna measurements. The NF-FF method [12] usually uses planar, cylinder, or spherical scanning in a near field to measure the phase and amplitude distributions of a device. Then, a NF-FF transformation [13] is applied to compute a far-field pattern. However, for modulated 5G millimeter-wave devices, cabled connections do not exist, and it would be technically problematic to derive the modulated far-field measurement results from power measurements. Therefore, the new-method plane-wave generator (PWG) using an active probe array to create a uniform plane wave over a QZ in a near field was proposed [14]. By designing the weights of amplitudes and phases on each probe, a plane wave with an acceptable deviation at a given distance from a PWG can be achieved [15]. In addition, in order to control the phase and amplitude of every probe, a large number of high-precision phase shifters is needed, and they are expensive and immature in a millimeter frequency band. Therefore, the compact-antenna test-range (CATR) technique was proposed to be used in high frequency measurements. The CATR [16] technique establishes a feeding antenna on the focal plane of a paraboloid reflector, which converts a spherical wave transmitted from the feeding antenna into a plane wave over a QZ and reduces the electromagnetic wave-propagation distance to compensate for the free-space path loss.