This paper presents an over-the-air post-distortion method that employs an embedded transmitting antenna to radiate a distortion-correcting waveform toward the intended user direction, enabling spatial-domain linearization of phased-array transmitters. The proposed approach achieves significantly improved linearization performance compared with conventional digital predistortion (DPD) and avoids the additional computational burden imposed on user equipment by receiver-side post-distortion approaches. A proof-of-concept implementation on a four-element 28 GHz beamforming array validates the proposed method. When driven with a 100 MHz OFDM waveform using 256-QAM subcarriers, the proposed method improves the adjacent-channel power ratio (ACPR) and error vector magnitude (EVM) at the receiver from −26.5/−28.3 dBc to −47.5/−47.25 dBc and from 10.7% to 1.5%, respectively. Under identical model complexity (nonlinearity order and memory depth), DPD achieves −40.9/ –41.2 dBc ACPR and 2.2% EVM.

This work presents a robust digital predistortion (DPD) framework for linearizing load-modulated balanced amplifiers (LMBAs) operating under varying signal conditions, as developed for the 2025 IEEE International Microwave Symposium (IMS) Student Design Competition 9 (SDC9). The proposed approach employs a complexity-reduced Volterra (CRV) model combined with a hybrid indirect-direct learning strategy to achieve accurate linearization with fast convergence. Several signal processing enhancements are integrated, including peak-to-average power ratio (PAPR) reduction, adaptive coefficient pruning, and bandwidth-aware basis function filtering to improve robustness under limited feedback bandwidth. Furthermore, a configuration-robust training methodology is introduced, enabling a single DPD model to maintain effective linearization across multiple carrier configurations. Experimental results demonstrate that the DPD achieves substantial improvements in the adjacent-channel power ratio (ACPR) and error vector magnitude (EVM) when the device under test (DUT) (LMBA) is driven with signals with various configuration settings. The proposed solution provides a practical, computationally efficient, and scalable DPD design suitable for adaptive transmitter architectures in future 5G and 6G systems.

Motivated by the need to use spectrum more efficiently, this paper investigates fine grained spectrum sharing (FGSS) in Multi-User massive MIMO (MU-mMIMO) systems where a neutral host enables users from different operators to share the same resource blocks. To be accepted by operators, FGSS must i) guarantee isolation so that the load of one operator does not impact the performance of another, and ii) avoid cross-subsidization whereby one operator gains more from sharing than another. We first formulate and solve an offline problem to assess the potential performance gains of FGSS with respect to the static spectrum sharing case, where operators have fixed separate sub-bands, and find that the gains can be significant, motivating the development for online solutions for FGSS. Transitioning from an offline to an online study presents unique challenges, including the lack of apriori knowledge regarding the performance of the fixed sharing case that is required to ensure isolation and cross-subsidization avoidance. We overcome these challenges and propose an online algorithm that is fast and significantly outperforms the static case. The main finding is that FGSS for a MU-mMIMO downlink system is doable in a way that is “safe" to operators and brings large gains in spectrum efficiency (e.g., for 4 operators, a gain above 60% is seen in many cases).

This letter proposes an active calibration method for millimeter-wave (mm-Wave) beamforming arrays that estimates the complex excitation of each element under realistic operating conditions. The method leverages a sequence of far-field transmission coefficient measurements collected while the array is rotated toward different angles. From these measurements, the complex excitation at each element is estimated without imposing any assumptions on the beamforming circuitry behavior. With all elements active during measurements, the estimated excitations inherently capture effects of mutual coupling and loading, which traditional elementwise calibration fails to account for. The method is validated on a 4 & times; 4 phased array operating at 38.5 GHz. Radiation patterns reconstructed from the estimated excitations match the measured patterns with a normalized root-mean-square error (NRMSE) better than -30 dB, confirming that the estimated excitations closely represent the true active-array behavior. In contrast, reconstructing the pattern using excitations obtained from elementwise measurements yields an NRMSE of only -8 dB. Furthermore, when beamforming toward boresight, the proposed active calibration method improves the measured boresight gain by 1.4 dB relative to passive calibration and reduces sidelobe-level imbalance by 2.4 dB. Finally, when the proposed method is applied for boresight null-steering, it achieves a null-depth that is 21.2 dB deeper than that obtained from passive calibration.

The shift toward millimeter-wave and sub-terahertz frequencies in communication systems presents significant challenges in transmitter design, particularly in generating wideband, high-data-rate signals with adequate power and linearity. Frequency multiplier (FX)-based architectures have emerged as promising solutions for signal generation at these frequencies, but the inherent nonlinearity of FXs poses challenges to maintaining signal integrity. This article reviews recent advancements in digital predistortion (DPD) techniques aimed at mitigating the nonlinear distortions in FX-based transmitters, particularly when driven by vector-modulated signals. By providing a comparative analysis of state-of-the-art DPD approaches and highlighting key innovations, this work offers critical insights into the strengths and limitations of current methods and outlines future research directions for enhancing the linearization of FX-based transmitters in next-generation communication systems.

This work develops a learning-based framework that directly exploits noisy pilots to optimize reconfigurable intelligent surface (RIS) systems while accommodating different service priorities and fairness via user weights. First, an adaptive beamforming configuration problem is formulated to generate the base station active beamforming vectors and RIS passive beamforming reflection coefficients that optimize the weighted sum-rate. Under mild regularity conditions, this problem is shown to attain a maximum. To learn approximate solutions, a novel hypernetwork-based beamforming (HNB) framework is proposed. Particularly, a beamforming network (BFN) exploits available information, including noisy pilots, to generate optimized beamforming configurations. Rather than learning one BFN, a hypernetwork is trained to dynamically generate BFN learning parameters from an input conditioning vector. When the conditioning vector is chosen as the user weights, the trained HNB can tune the BFN to the user weights without the need for retraining. Numerical experiments demonstrate that tuning allows the proposed HNB to perform close to an optimistic block-coordinate descent with perfect CSI benchmark and significantly outperform static learning where a BFN is directly trained to optimize beamforming configurations. Additionally, employing the HNB to also tune the BFN to location information considerably reduces the pilots needed to generate optimized beamforming configurations.

This paper presents a comparative study of two architectures for generating wideband modulated signals at sub-THz frequencies using a frequency bonding approach, focusing on achievable output signal quality. The first architecture generates a wideband signal at an intermediate frequency (IF) and up-converts it to sub-THz frequencies using a heterodyne mixer. The second approach generates multiple narrowband signals at IF, up-converts each to sub-THz, and then combines them. The study shows that, under linear up-converter operation, both architectures achieve similar signal-to-noise ratios (SNR) and are limited by the noise floor. However, replacing the combiner in the second architecture with a frequency duplexer improves the SNR by 3 dB. At higher IF power levels, where up-converter nonlinearity becomes significant, both architectures require digital predistortion to mitigate distortion. Despite this, the second architecture demonstrates superior adjacent-channel power ratio (ACPR). D-band measurements confirm that the second architecture enhances ACPR by up to 8 dB at high IF power levels when generating a modulated signal with a carrier frequency of 142.5 GHz and a modulation bandwidth of 1.2 GHz, while performance at lower power levels remains comparable.

This article introduces an active calibration scheme tailored for fully digital multiple-input multiple-output (MIMO) transmitters, a key step toward ensuring channel reciprocity. The theoretical analysis starts by examining the influence of antenna mutual coupling and power amplifier (PA) output impedances on the MIMO transmitter and channel reciprocity. This analysis highlights the significant impact of the inherently poor output matching, exhibited in high-efficiency PAs, exacerbating the effects of antenna mutual coupling on channel reciprocity. Consequently, an active calibration scheme is formulated to concurrently characterize and compensate for the nonflat responses of all radio frequency (RF) chains in the fully digital MIMO transmitter. To validate the proposed scheme, a proof-of-concept experiment is conducted using a custom-built 16-chain fully digital MIMO system, driven with 200-MHz orthogonal frequency-division multiplexing (OFDM) signals at 3.5-GHz center frequency. Measurement results demonstrate the efficacy of the calibration scheme in mitigating the impact of antenna coupling and PA output mismatch on channel reciprocity. The root normalized mean square error (RNMSE) after calibration is reduced from ${22\%}$ to ${1\%}$ .

While multi-user (MU) massive MIMO is a critical technology for next generation wireless systems, its complexity poses significant operational challenges as it entails several processes. These include user selection, precoding, power distribution among the users, and Modulation and Coding Scheme (MCS) selection. While many studies have been conducted on MU-MIMO, most have made invalid assumptions (e.g., every non-zero signal received at a user yields a non-zero rate) or excluded some essential steps (e.g., MCS selection). We revisit the problem of operating a single-cell massive MIMO network with zero-forcing precoding, and develop real-time network operation algorithms. First, we relax the real-time constraint and perform an offline study to obtain a target performance for online algorithms. The joint problem can be solved exactly offline for small to medium size settings using branch-reduce-and-bound. For larger settings, we note that, given a choice of user selection, the problem reduces to a power distribution problem that can be solved exactly. Thus, the joint problem reduces to a search over user-sets where for each considered user-set, a power distribution problem is solved. We propose various search methods and evaluate their performance. For online operation, we leverage the problem structure to propose an algorithm based on three ideas: i) grouping, 2) MCS-aware power distribution, and 3) an iterative process to remove users that see a zero rate. The algorithm achieves 94% of the performance target set by the offline study results.

This article introduces a novel method for generating ultrawideband (UWB) modulated signals at millimeter-wave (mmW) and sub-THz frequency bands using readily available high-resolution digital-to-analog converters (DACs) with sampling rates lower than twice the target bandwidth. The method exploits the periodicity of test signals to divide them into frequency subbands, with each subband generated by a dedicated channel consisting of an IQ-DAC followed by an IQ mixer. Phase coherent local oscillators (LOs) drive the IQ mixers, and the final UWB signal is synthesized by combining the outputs of all channels. To address inherent nonidealities in the proposed UWB signal generation method, a novel calibration technique is introduced. This technique uses nonuniformly interleaved tones to correct IQ imbalances, phase and magnitude offsets across channels, and linear distortions in each RF chain. The calibration formulation ensures continuity in the phase and magnitude frequency responses across different channels. For experimental validation, the proposed method was used to generate a 256-QAM orthogonal frequency-division multiplexing (OFDM) signal at D band (149 GHz) with an instantaneous bandwidth of up to 12 GHz, achieving a peak data rate of 96 Gbps. The calibration technique effectively compensates for the nonidealities in the proposed signal generator, improving the measured error vector magnitude (EVM) and normalized mean square error (NMSE) from 82.6% and 23.8% to less than 2% and 1%, respectively, when tested with a 12-GHz bandwidth 256-QAM OFDM UWB signal. Furthermore, the method was applied to linearize a D band power amplifier driven by a 256-QAM OFDM signal with a 4-GHz modulation bandwidth. The adjacent channel power ratio (ACPR) and EVM improved from $-$ 27.8/ $-$ 26 dBc and 8.5% before linearization to $-$ 42.8/ $-$ 43.1 dBc and 1.2% after linearization, ensuring a linearization bandwidth over 12 GHz. These results underscore the suitability of the proposed method for generating high-quality UWB modulated signals for component testing at mmW and sub-THz frequency bands.

This letter presents an innovative frequency extender based measurement system designed for the comprehensive characterization of millimeter-wave devices under both continuous-wave (CW) and modulated signal excitation. In addition to traditional CW-based measurement systems consisting of Vector Network Analyzers (VNAs) and VNA frequency extenders, the proposed system integrates an Intermediate Frequency (IF) Vector Signal Generator (VSG) and IF Vector Signal Analyzers (VSAs). During modulated signal testing, the IF VSG feeds the VNA frequency extender, enabling the generation of RF-modulated signals at the device-under-test (DUT) reference plane without the need for a mixer. Concurrently, the IF VSAs are connected to the VNA frequency extenders, facilitating the capture of wideband modulated signals at the DUT input and output reference planes. Additionally, the proposed system incorporates a novel Iterative Learning Control (ILC) algorithm formulated to linearize frequency multipliers (FMs) within VNA frequency extenders ensuring error-free RF modulated signal generation at the DUT input reference plane. To validate the proposed measurement system, proof-of-concept experiments were conducted at V-band (around 57.6 GHz) using an Oleson Microwave Labs (OML) VNA frequency extender. The novel ILC algorithm was employed to linearize the FM within the OML frequency extender, enabling the mixer-less generation of 256 QAM orthogonal frequency division multiplexing signals with modulation bandwidths up to 800 MHz. The measurement results showcase exceptional signal integrity achieved by the proposed system and enabled by the proposed ILC algorithm, achieving an adjacent channel power ratio and error vector magnitude at the DUT input reference plane of 51.6/48.7 dBc and 1.2%, respectively, when using an 800 MHz test signal case.

This paper investigates the linearizability of a custom-built 16-chain fully digital MIMO transmitter system. The transmitter front-end consists of multistage, Class-AB power amplifiers (PAs) and a stacked patch antenna array. To assess the linearizability of the RF front end, an iterative learning control (ILC) solution is proposed to identify the predistorted signal that results in the desired modulated signal with the least distortion at the output. ILC is then applied to the 16-chain transmitter front-end for orthogonal frequency-division multiplexing (OFDM) signals of 8 dB peak-to-average ratio (PAPR) and instantaneous modulation bandwidths of 60, 80, 100, and 120 MHz. The experimental results show that the average root normalized mean square error (RNMSE) of all 16 chains can be reduced from values up to 28% to values below 2% across all 16 chains for all bandwidths, while the average adjacent channel power ratio (ACPR) is improved from -36 dB to -54,-52,-51,-48 dB for 60, 80, 100, and 120 MHz, respectively. The performance of pruned Volterra-based single-input single-output (SISO) and multiple-input single-output (MISO) digital predistortion (DPD) is compared against the ILC benchmark. Compared to the ILC benchmark, pruned-Volterra SISO and MIMO DPD exhibited significantly degraded performance. These results suggest that current DPD modeling approaches, potentially formulated based on smaller MIMO systems, need to be revisited to account for non-idealities impacting linearizability in larger-scale massive MIMO transmitters. The proposed linearizability assessment methodology can support the development of future massive MIMO RF front-end designs and DPD linearization techniques for improved system-level performance.

We consider configuring discrete reconfigurable intelligent surfaces (RIS) with phase-dependent amplitude responses. The problem is formulated as a constrained virtual-channel selection problem. When considered over subsets with maximum phase-variation theta(max )< pi , the solution is shown to be bounded between two matroid-constrained problems. We illustrate configuration problems whose optimal solution lies within such subsets and show that a greedy framework guarantees a worst-case |2 log(2 )cos(theta(max)/2)| optimality gap uniformly over all system parameters. Subsequently, a low-complexity framework is proposed for general discrete configuration problems. Numerical experiments show that the framework performs within 4% of the optimal binary-RIS configuration and achieves at least 90% of the continuous phase-shift performance using a 3-bit configuration.

This article proposes a novel digital predistortion (DPD) scheme to linearize frequency multiplier (FX)-based vector signal sources that are subject to constrained transmitter and observation receiver bandwidth. Specifically, the proposed technique aims to reduce the digital-to-analog converter (DAC) sampling speed and the bandwidth of the transmitter RF front-end required by conventional DPD schemes for FX-based signal generation while maintaining excellent linearized output signal quality. This article starts by formulating an additive error model for an FX driven by a $D$ th root function subject to bandwidth constraint. This model is then utilized to derive the expression of the proposed DPD model and underlying DPD training algorithm while allowing for the reduction of the required transmitter observation receiver (TOR) bandwidth. The extent of the TOR bandwidth relaxation is determined based on the bandwidth of the $D$ th root function output. Using the proposed DPD scheme, extensive simulations and measurements carried out on two different FXs revealed a 22–25-dB improvement in adjacent channel power ratio (ACPR), when the transmitter and receiver bandwidths are limited to 4 $\times$ and 3 $\times$ the signal bandwidth, respectively. Moreover, the error vector magnitude (EVM) after DPD is reduced from 13.6%–21.1% to 1%–1.6% when the transmitter and receiver bandwidths are reduced down to 2 $\times$ and 1 $\times$ the signal bandwidth, respectively.

This paper proposes a far-field (FF) -based digital predistortion (DPD) training method for linearizing dual-polarized (dual-pol) beamforming arrays in the presence of cross-polarization channel (XPC) interference experienced in the DPD FF-based observation receiver (OR). The cross-polarization interference (XPI) in the XPC can be attributed to the transmitter’s (TX’s) antennas, the probe used in the DPD FF OR, the OR’s over-the-air channel, as well as the mechanical misalignment between the TX antenna and the FF-based OR probe. Specifically, an XPC estimation and de-embedding technique using interleaved multi-tone test signals is proposed. Experiments conducted using a 4x4 dual-pol RF beamforming array operated at 38 GHz and excited by a 5G NR 200 MHz 256-QAM orthogonal frequency division multiplexing test signal are presented. The measurement revealed the capacity of the proposed technique to correct for the nonidealities in the XPC where the XPI was reduced from -10 dB to -40 dB. Furthermore, using the proposed DPD training method, the adjacent channel power ratio (ACPR) and error vector magnitude (EVM) improved from 26.7 dB and 10.96% to 36.38 dB and 3.3%, respectively, when a single-input-single-output DPD function was used. The ACPR and EVM were further improved by 3 dB and 1.1% when a dual-input-single-output DPD function was used.

This article proposes an algorithm to synthesize a tapering profile that reduces the extent of the variation of the active reflection coefficients seen by the power amplifiers (PAs) in a radio frequency (RF) beamforming array, and accordingly reduces the variation in the array nonlinearity versus steering angle. Specifically, it starts by theoretically analyzing the following: 1) the dependence of the RF beamforming array nonlinearity on the antenna active reflection coefficients as well as the PA output reflection coefficients and 2) the dependence of the antenna active reflection coefficients on the tapering profile. A novel algorithm that uses the antenna array scattering parameters is then devised to synthesize a tapering profile that both hold the following: 1) reduces the extent of the variation of the active reflection coefficients seen by the PAs and 2) constrains the maximum reduction in the antenna array factor compared with uniform tapering. The performance of the proposed algorithm is validated in simulation and experimentally using an $8\times $ 8 RF beamforming array. The simulation revealed that applying the tapering profile obtained from the proposed algorithm reduced the variation in the antenna active reflection coefficients by 6 dB or more for 25% of the antenna elements (3.9-dB median) compared with when a uniform tapering profile is applied. Furthermore, experimental results showed that the application of the synthesized tapering profile enhanced the capacity of digital predistortion (DPD) with a single set of coefficients to linearize the RF beamforming array over a wide steering range. Specifically, when the elevation angle $\theta $ is steered between −50° and 50°, the variations in the adjacent channel power ratio (ACPR) and error vector magnitude (EVM) after DPD are $\leq 0.5$ and $\leq 0.3$ dB for the designed taper compared with 6 and 4 dB, respectively, for a uniform taper.

This paper presents the hardware implementation of a real-time digital predistorter (DPD) for fully digital multiple-input multiple-output (MIMO) transmitters. The predistorter is comprised of a dual-input single-output (DISO) DPD module for each chain and a shared crosstalk and mismatch (CTMM) module that estimates the reflected wave back into each PA. The proposed real-time DPD is a DISO piece-wise linear (PWL) model implemented on a field-programmable gate array (FPGA) and achieves a linearization bandwidth up to 1.2 GHz at a clock rate of 300 MHz. The real-time DPD engine is demonstrated on a four-chain MIMO testbed and validated against a PC-based DPD engine. The FPGA-based DISO DPD performs within 1 dB ACPR of the PC-based implementation and achieves a similar root-normalized-mean-square error (RNMSE) of 1.59%.

We investigate the support of a capacity-achieving input to a vector-valued Gaussian noise channel. The input is subjected to a radial even-moment constraint and is either allowed to take any value in Rn or is restricted to a given compact subset of Rn. It is shown that the support of the capacity-achieving distribution is composed of a countable union of submanifolds, each with a dimension of n−1 or less. When the input is restricted to a compact subset of Rn, this union is finite. Finally, the support of the capacity-achieving distribution is shown to have Lebesgue measure 0 and to be nowhere dense in Rn.

This letter proposes a new technique to calibrate the frequency response of the upconverter in frequency-multiplier-based transmitters. The proposed technique only requires capturing the multiplier output, using the same feedback path needed to train the digital predistortion (DPD) module. In addition, this letter proposes a low-complexity piecewise-based DPD model to compensate for the multiplier nonlinearity. Experiments carried out on a millimeter-wave (mm-wave) frequency doubler showed excellent output signal quality with a 400-MHz modulation bandwidth.

This letter lays the foundation for reducing the required number of transmitter-observation receivers (TORs) for training digital predistortion (DPD) in fully digital massive multiple-input, multiple-output (MIMO) transmitters. Specifically, it investigates the viability of applying the same, common set of DPD coefficients to linearize all RF chains in fully digital massive MIMO transmitters. First, it is shown that if all RF chains are operated at the same output power, the common set of DPD coefficients can be found by simply averaging the coefficients obtained by training each RF chain on its own. This suggests that only a few chains may be needed for training provided the chains are a representative sample. Experimental results are then conducted where one and three chains are used for training. It is found that when training for one chain, significant variations in normalized mean square error (NMSE) and adjacent channel power ratio (ACPR) of up to 9 dB across the chains are realized. For training with three chains, the common set of DPD coefficients can reduce the variation to 1–2 dB. Finally, after over-the-air (OTA) combining, excellent linearization performance is found for three chains.