Over-the-Air Linearization of Phased Array Transmitters Affected by Load Modulation

Digital predistortion (DPD) of a phased array requires that multiple transmit paths must be measured by a feedback (FB) receiver (Rx), This paper proposes a simplified FB architecture to be used for phased array DPD. A single FB line collects the waveform samples from the parallel paths to the FB Rx. The gain and phase of the common FB line is obtained by comparing the FB outputs to over-the-air (OTA) measurements. The overall DPD training is done by collecting the PA outputs with the common FB line, post-equalizing them to model the main lobe waveform and combining them to create the object used for array DPD. The DPD performance was verified by OTA measurements with 5GNR waveform and 28 GHz 8-path phased array transmitter. The DPD trained through the local FB line with the proposed calibration method achieved < -45dB ACPR which was close to OTA DPD performance.

This letter proposes a stable-sample-level (SL)-based digital predistortion (DPD) technique for 2-D phased array with fixed-position over-the-air (OTA) feedback (FB) to overcome significant SL fluctuation when the beam is steered. It is achieved by optimizing the phase of the beamformer based on the DPD requirement, which can control the SL at a given value without affecting the main lobe of radiation pattern, relaxing the requirement of FB dynamic range. The radiation pattern and DPD performances are measured on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> phased array at 26 GHz. The measured results show that the proposed method can realize the stable SL with good DPD performance.

This paper proposes a near-field dual-polarized feedback (NFDPF) technique for tracking real-time status and improving linearity of 5G RF-beamforming millimeter-wave (mm-wave) phased array. The feedback signal captured by NFDPF can be used for array self-calibration and digital predistortion (DPD). A 2×2 dual-polarized 24.25-27.5-GHz phased array prototype with integrated NFDPF is designed for validation of the scheme. Using NFDPF, four RF chains of dualpolarizations are calibrated which is similar to far-field (FF) calibration. Furthermore, the DPD is applied to validate the performance of feedback structure. Experimental results show that the adjacent channel power ratio (ACPR) and normalized mean squared error (NMSE) can be improved from -40dBc and 28dB to -51dBc and -40dB respectively, which is close to the performance of FF DPD.

Joint sensing-and-communication is envisioned to play a major role in emerging mm-Wave wireless systems to perform rapid tracking of wireless nodes for reliable wireless communication and ubiquitous distributed sensing. Phased arrays are essential to realize high array gains and enhance the communication distance. However, their pencil sharp beams require precise localization and tracking of wireless nodes to maintain beam alignment and reliable communication, especially in mobile wireless links. In parallel, array-based mm-Wave radars require large arrays for precise angular resolution that is fundamentally limited by the form factor and power consumption of the radar systems. We propose a frequency modulated array (FMA) transmitter (Tx) to convert locations/positions to timing information, which supports dual-modes for joint sensing-and-communication: rapid and precise full field-of-view (FoV) receiver (Rx) localization in the Tx/Rx localization mode for wireless communication and target angular detection in its radar mode. Exploiting its unique joint space-time-frequency dependent signals, the FMA distinguishes spatial signatures far below its array 3-dB beamwidth, i.e., achieving super-resolution and can simultaneously localize multiple Rx nodes or detect multiple targets in “one-shot.” Moreover, FMA only adds minimal circuit/computation overhead on traditional multi-in multi-out (MIMO) arrays. A proof-of-concept 28-GHz four-element multi-mode FMA Tx array is implemented in a 45 nm CMOS silicon on insulator (SOI) process. Over-the-air (OTA) measurements with Rx nodes in the communication-mode or reflectors in radar-mode demonstrate the four-element FMA Tx array operations and achieve a full-FoV coverage with <2°–4° accuracy in angular localization with a 10 ns timing resolution (i.e., 100 MHz digital clock in Rx). Sensing aided communication is demonstrated to create sharp and secure constellation decomposition array (CDA) 64 quadratic-amplitude modulation (QAM) beams toward target Rx at low rms error vector magnitude (EVM) of < 5.33% using the sensed data from FMA based Rx localization scheme.

In this article, we study closed-loop digital predistortion (DPD) systems and associated learning algorithms. Specifically, we propose various low-complexity approaches to estimate and manipulate the inverse of the input data covariance matrix (CM) and combine them with the so-called self-orthogonalized (SO) learning rule. The inherent simplicity of the SO algorithm, combined with the proposed solutions, allows for remarkably reduced complexity in the DPD system while maintaining similar linearization performance compared to other state-of-the-art methods. This is demonstrated with thorough over-the-air (OTA) mmW measurement results at 28 GHz, incorporating a state-of-the-art 64-element active antenna array, and very wide channel bandwidths up to 800 MHz. In addition, complexity analyses are carried out, which together with the measured linearization performance demonstrates favorable performance–complexity tradeoffs in linearizing mmW active array transmitters through the proposed solutions. The techniques can find application in systems where the power amplifier (PA) nonlinearities are time-varying and thus frequent or even constant updating of the DPD is required, good examples being mmW adaptive antenna arrays as well as terminal transmitters in 5G and beyond networks.

This article first analyzes the nonlinear behavior of frequency-multiplier (FM)-based radio frequency (RF) beamforming transmitters TXs) over a wide range of steering angles. Then, based on this analysis, a digital predistortion (DPD) scheme is proposed to linearize FM-based TX arrays. Specifically, a dual-input behavioral model of FM-based TX arrays is derived. This dual-input model is then transformed into an angle-dependent single-input–single-output (SISO) model. Next, the effect of load modulation on FM nonlinearity is studied using a circuit-inspired behavioral model, and a very distinctive feature is revealed. Notably, it is shown that FM-based RF beamforming arrays have reduced sensitivity to load modulation when compared to last-stage power-amplifier (PA)-based arrays. This is first validated in simulation using a frequency doubler and PA terminated with load impedances extracted from an 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 8 electromagnetically simulated array. Furthermore, experimental results are obtained using a 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 2 planar frequency-doubler-based RF beamforming TX operated at 28 GHz and driven with up to 400-MHz-wide orthogonal frequency-division multiplexing (OFDM) signals where the subcarriers are modulated using up to 256-QAM. It is experimentally demonstrated that a single set of SISO DPD coefficients can significantly improve the adjacent channel power ratio (ACPR) and error vector magnitude (EVM) over a wide steering range. Specifically, for the case of a 100-MHz signal, the ACPR and EVM improved from 20 dBc and 23% to, at worst, 48 dBc and 1%, respectively, when the array is steered from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-40^\circ $ </tex-math></inline-formula> to 40° and measured along the main beam direction. In light of the FM-based arrays reduced sensitivity to load modulation, this article also investigates different TX observation receiver (TOR) methods for DPD function training, namely, far-field-based TOR, coupler-based TOR, and single-element-based TOR, and their impacts on the linearizability of the FM-based RF beamforming TXs.

A 144-element phased array transceiver is realized using a modular tiled approach that supports 802.11ad, MCS12 single carrier 16-quadratic-amplitude modulation (QAM) 4.6 Gbps, in the 60-GHz band. It consists of a system-on-a chip (SOC) (MAC/PHY/BB to IF) in 28-nm CMOS, and one IF-to-60-GHz transceiver master chip driving twelve 60-GHz phased array transceiver slave chips fabricated in a 40-nm CMOS. Using the master-slave configuration, the 60-GHz transceiver with 12 phase-controlled TX/RX slices is expanded to 144 phase-controlled slices. Each final TX/RX slice is then connected to two patch antennas on LTCC substrate. A tiled approach is used to create the 288 patch antenna array out of six identical tiles each with two slave 60-GHz transceivers connected to a 48-element antenna array. The single tile phased array with 48 antennas has a measured beam steering scan angle of 60° in azimuth and 10° in elevation. The full phased array transceiver with 288 antennas has a measured over the air (OTA) max effective isotropic radiated power (EIRP) of 51 dBm at saturated power (PSAT), and EIRP of 44.8 dBm with -22 dB EVM for MCS12 (16QAM-4.6 Gbps) at broadside. It has an OTA measured sensitivity of -87.3 and -80.4 dBm for MCS9 (QPSK-2.5 Gbps) and MCS12, respectively, at broadside. A packet error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> was measured for MCS9 and MCS12 with an OTA input power of -85 and -77.5 dBm, respectively, for the full phased array transceiver at broadside.

This article presents a comprehensive design methodology for broadband Doherty power amplifiers (DPAs) based on an extended two-port <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula>-parameter solution set and irregular matching networks. Instead of designing the carrier, peaking, and post-matching networks separately, the entire output combining network (OCN) is modeled as a single two-port network, which captures the real interaction and load modulation mechanisms that determine wideband Doherty performance. To enlarge the feasible design space, the optimal load impedances obtained from load-pull simulations are processed using polygonal Boolean operations to extract their common high-efficiency, high-power region, followed by Poisson-disk sampling to generate a diverse set of impedance candidates. These impedances are converted into a large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula>-parameter solution set, any of which is acceptable for proper Doherty load modulation. An irregular microstrip matching structure is introduced to provide additional degrees of freedom and enable direct layout-level optimization. A two-stage selection and joint optimization is then developed, where passive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula>-parameter matching and active large-signal performance are jointly used to guide the design. To validate the proposed approach, a 1.2–3.1GHz DPA with an 88.4% fractional bandwidth is designed and fabricated. Measurements show saturated output power above 43.1dBm, saturated efficiency of 51.8%–70.6%, and 6-dB back-off efficiency of 50.3%–55.6%. With digital predistortion (DPD), the adjacent channel leakage ratio (ACLR) is better than −50 dBc.

With the prevalence of complex modulated signals, it is of utmost significance to research the extension of the dynamic power range of radio frequency (RF) power amplifiers (PAs). This article proposes a divisional load-modulated balanced amplifier (DLMBA) for extending the high-efficiency power range. The proposed DLMBA is composed of a local modulated Doherty PA (DPA) and a class-C biased balanced PA (BPA) pair. The output signal of the local DPA is fed into the isolation port of the output coupler of the BPA pair, forming a global load modulation. The design parameters of the DLMBA are derived after a comprehensive analysis. It is illustrated that the dynamic power range of the DLMBA can be extended beyond 12 dB by combining a local DPA and a BPA pair. Meanwhile, each subamplifier of the DLMBA is presented with a modulated impedance over the whole dynamic power range, avoiding voltage oversaturation. As a validation, a DLMBA operating over 1.85–2.05 GHz is fabricated and measured in this article. The fabricated DLMBA delivers a maximum output power of more than 44.8 dBm, a saturation drain efficiency (DE) of more than 53%, and a 13 dB back-off DE of more than 44% in the interested frequency band. Meanwhile, when the DLMBA is excited by a 20-MHz wideband signal with a peak-to-average ratio of 10.2 dB, the measured adjacent channel leakage ratio reaches −47.4 dBc after digital predistortion.

High throughput coherent optical transmitters are key components in future optical communication infrastructure. However, these transmitters are often distorted with the nonlinearity of their components. A potential approach for compensating nonlinearity is by applying digital pre-distortion methods based on the Volterra series or one of its derivatives. However, the Volterra series-based solution is complex to implement, difficult to scale, and its simplified versions may not yield the desired performance. Recently digital pre distortion solutions based on neural networks were proposed, which may benefit from the generality of neural networks and can be more easily scaled. These solutions are often based on non-standard neural network architectures which require complex neurons-based architectures or being based on indirect training approach which suffer from noise enhancement. In this article, a novel method for neural network-based pre-distortion with direct learning is proposed. The direct learning with neural network does not assume a specific transmitter model and does not suffer from noise enhancement. The method assumes standard neural network inference architecture and is applied to a coherent nonlinear optical transmitted with long-short-term memory neural network. The overall performance and complexity of the direct learning method is compared with the indirect approach and with the Volterra series-based solution, showing significant advantage in performance, especially in cases of severe nonlinearity and noise conditions.

This chapter summarizes the comprehensive review of the nonlinear ultrasonic phased array (PA) methods for the measurement of closed-crack depth. Various nonlinear ultrasonic PA methods are categorized into four groups: (I) subharmonics, (II) parallel and sequential transmission, (III) all-elements, odd-elements, and even-elements transmission, and (IV) utilization of thermal stress. Each method is described in the order of principles, experimental conditions and imaging results, key features.

The error vector magnitude (EVM) is a comprehensive measure of the amplitude and phase distortion of digitally modulated signals and a potential tool for characterizing the performance of active beamforming arrays, especially at millimeter-wave frequencies, because of the high level of integration and limited spacing between the radiating elements. A review of the EVM measurement process and fundamental principles for time-domain demodulation with a vector signal analyzer (VSA) and spectral correlation with a vector network analyzer (VNA) was presented in <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> . This article demonstrates how researchers have modeled and measured impairments from antenna and phased array signal transmission to characterize their influence on the EVM of single and multicarrier digital signals. It presents examples of simulation models and measurements of the distortion from ultrawideband (UWB) passive antenna transmission, power amplifier (PA) nonlinearities, and phased array beam squint and beam scan intersymbol interference (ISI). A brief survey of over-the-air (OTA) test ranges for EVM analysis is also provided. This overview of state-of-the-art EVM simulation and measurement methods is intended to help interested readers understand and enhance the EVM performance analysis methods applied to antennas and phased arrays in this new era of millimeter-wave communications.

Digital linearization of a phased array transmitters is usually based on feedback measurements. Various arrangements can be used to measure multiple transmit paths by using conducted or radiated methods. We propose a technique for measuring any pair of transmit paths simultaneously by using a common feedback connected to two receivers, and a cancellation method that can make the measurements independent. Together with the feedback cancellation, a single feedback line with two output ports can be used to measure different transmit chain pairs coherently under varying load conditions present in phased arrays. The cancellation filters are trained by using a fifth-generation (5G) new radio waveform and verified by over-the-air (OTA) measurements along with the predistortion performance evaluation of a 28 GHz 8-element phased array transmitter. The method achieved 30 dB cancellation between the paths and the DPD trained with the feedback cancellation achieved 4.2 % EVM and -40.8 dBc ACPR.

High-symbol-rate coherentoptical transceivers suffer more from the critical responses of transceiver components at high frequency, especially when applying a higher order modulation format. We recently proposed a neural network (NN)-based digital pre-distortion (DPD) technique trained to mitigate the transceiver response of a 128 GBaud optical coherent transmission system. In this paper, we further detail this work and assess the NN-based DPD by training it using either a direct learning architecture (DLA) or an indirect learning architecture (ILA), and compare performance against a Volterra series-based ILA DPD and a linear DPD. Furthermore, we deliberately increase the transmitter nonlinearity and compare the performance of the three DPDs schemes. The proposed NN-based DPD trained using DLA performs the best among the three contenders. In comparison to a linear DPD, it provides more than 1 dB signal-to-noise ratio (SNR) gains at the output of a conventional coherent receiver DSP for uniform 64-quadrature amplitude modulation (QAM) and PCS-256-QAM signals. Finally, the NN-based DPD enables achieving a record 1.61 Tb/s net rate transmission on a single channel after 80 km of standard single mode fiber (SSMF).

In this communication, a dual-polarized millimeter-wave (mmWave) phased array antenna is proposed for the fifth-generation (5G)/B5G smartphones. The configuration of the antenna array is highly integrated with the up-to-date industry design (ID) of ultranarrow side frame, 3-D curved display, and covers, which are widely adopted in flagship smartphones and popular among consumers. The proposed antenna contains a minor portion of slotted metal frame and a cavity-backed antenna module. The air cavity and the multiple slots are employed to enhance the bandwidth. A strip bump is established on the metal frame to meet the ID requirement, which also improves the impedance matching simultaneously. A prototype of the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times $ </tex-math></inline-formula> 4 phased array assembled in a smartphone’s metal frame is fabricated and measured. The antenna array achieves a −10 dB impedance bandwidth from 23.2 to 29.7 GHz. At 27.0 GHz, the measured peak gain is greater than 11.2 dBi and the 3 dB scanning angle is larger than 77° for the two polarizations. Finally, the blockage issue of the curved cover is studied. In virtue of high integration with ID, compact size, wide bandwidth, good spatial coverage, and easy assembling, the proposed antenna scheme is promising for 5G/B5G smartphone designs.