Beamforming

Intelligent Reflecting Surfaces (IRSs) are a promising technology for enhancing the spectral and energy efficiency of millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. In these systems, accurate channel estimation remains challenging due to the passive nature of IRS elements and the high pilot overhead in large-scale deployments. This paper presents a deep learning-based Multi-Block Attention (MBA) framework for efficient cascaded channel estimation in IRS-assisted mmWave MIMO systems that utilize orthogonal frequency division multiplexing (OFDM). First, we show the optimality of the discrete Fourier transform (DFT) and Hadamard matrices as phase configurations for least squares (LS) estimation. To reduce training overhead, we selectively deactivate IRS elements and compensate for induced feature loss using a two-stage architecture: (i) a Convolutional Attention Network (CAN) for spatial correlation recovery and (ii) a Complex Multi-Convolutional Network (CMN) for noise suppression. The MBA architecture mitigates error propagation through attention-guided feature refinement and denoising. Simulation results indicate that the MBA method reduces pilot overhead by up to 87% compared to the LS estimator. Additionally, at signal-to-noise ratios of 10 dB, our proposed method achieves approximately 51% lower normalized mean squared error (NMSE) than leading methods. It also maintains low computational complexity and adapts effectively to various propagation environments.

Target speech extraction remains difficult for compact devices because monaural neural models lack spatial evidence and classical beamformers lose resolving power when the microphone aperture is only a few centimetres. We present IsoNet, a user-selectable audio-visual target speech extraction system for a compact 4-microphone array. IsoNet combines complex multi-channel STFT features, GCC-PHAT spatial cues, face-conditioned visual embeddings, and auxiliary direction-of-arrival supervision inside a U-Net mask estimation network. Three curriculum variants were trained on 25,000 simulated VoxCeleb mixtures with progressively difficult SNR regimes. On a hard test set spanning -1 to 10 dB SNR, IsoNet-CL1 achieves 9.31 dB SI-SDR, a 4.85 dB improvement over the mixture, with PESQ 2.13 and STOI 0.84. Oracle delay-and-sum and MVDR beamformers degrade the same mixtures by 4.82 dB and 6.08 dB SI-SDRi, respectively, showing that the proposed learned multimodal conditioning solves a regime where conventional spatial filtering is ineffective. Ablation studies show consistent gains from visual conditioning, GCC-PHAT features, and extended delay-bin encoding. The results establish a compact-array, face-selectable speech extraction baseline under controlled simulation and identify the remaining barriers to real deployment, especially phase reconstruction, multi-interferer mixtures, and simulation-to-real transfer.

Modern edge devices increasingly rely on neural networks for intelligent applications. However, conventional digital computing-based edge inference requires substantial memory and energy consumption. In analog radio frequency (RF) computing, a base station (BS) encodes the weights of the neural networks and broadcasts the RF waveforms to the clients. Each client reuses its passive mixer to multiply the received weight-encoded waveform with a locally generated input-encoded waveform. This enables wireless receivers to perform the matrix-vector multiplications (MVMs) that account for most of the computation burden in edge inference with ultra-low energy consumption. Unlike conventional downlink transmissions which are optimized for communications, analog RF computing requires a computing-centric physical layer that controls both the analog MVM accuracy and the energy consumption for inference. Motivated by this, in this paper, we propose a physical layer design framework for analog RF computing in MU-MIMO wireless systems. We derive tractable models for computing accuracy and energy consumption for inference, formulate a joint BS beamforming and client-side scaling problem subject to computing accuracy, transmit power, and hardware constraints, and develop a low-complexity algorithm to solve the non-convex problem. The proposed design provides client- and layer-specific accuracy control for both uniform- and mixed-precision inference. Simulations under 3GPP specifications show that analog RF computing can significantly reduce client-side energy consumption by nearly two orders of magnitude compared to digital computing, while mixed-precision inference requires even lower energy consumption than uniform-precision inference. Overall, these results establish analog RF computing over wireless networks as a promising paradigm for energy-efficient edge inference.

The integration of terahertz communications and ultra-massive multiple-input multiple-output (UM-MIMO) systems in 6G networks is motivated by their ability to enable unprecedented data rates, mitigate spectrum congestion, and enhance overall network performance. However, the enlarged antenna apertures and higher carrier frequencies in these systems increase the Rayleigh distance, causing users to span both the near-field and conventional far-field regions. Accurate spatial precoding thus requires exact channel estimation at the base station - a task made more challenging by the hybrid coexistence of near- and far-field effects and the limited number of digital chains available in hybrid beamforming architectures. In this paper, we propose a block recurrent transformer model to address this challenge. We demonstrate that a single transformer block equipped with state memory can be trained once and then iteratively applied for hybrid-field channel estimation. Furthermore, we train the model such that it generalizes to wireless channels with varying scatterer distances, different numbers of propagation paths, and wideband operation. Simulation results show that the proposed method achieves performance gains of approximately 5 dB and 7.5 dB in normalized mean squared error (NMSE) over state-of-the-art solutions in narrowband and wideband scenarios, respectively.

Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the spatial correlation matrix is often snapshot-deficient. This deficiency degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To ensure stable and robust beamforming, we previously proposed an adaptive diagonal loading method that leverages the Kantorovich inequality to guarantee the WNG remains strictly within specified bounds. However, accurately determining the smallest necessary loading level requires calculating the extreme eigenvalues of the spatial correlation matrix, a computationally expensive $\mathcal{O}(M^3)$ operation for large arrays. In this paper, we introduce a highly efficient $\mathcal{O}(kM^2)$ estimation technique using Lanczos iterations to build a small Krylov subspace. By projecting the correlation matrix onto a tridiagonal matrix of dimension $k \ll M$, we extract Ritz values that rapidly converge to the exact extreme eigenvalues. Our evaluations demonstrate that this Lanczos-accelerated approach achieves performance identical to exact Eigenvalue Decomposition (EVD), ensuring optimal interference suppression and strict WNG adherence at a fraction of the computational cost.

In dynamic acoustic environments characterized by time-varying interferers and moving sources, effective beamforming requires accurately identifying stationary regions over time. Traditional Capon beamformers rely on the instantaneous ensemble covariance matrix, which is inaccessible in practice. Practical implementations overcome this by estimating the sample covariance matrix (SCM) through averaging over a block of temporal samples. However, in non-stationary settings, a naive batch approach fails. Moving interferers smear the SCM, causing the beamformer to place nulls in outdated locations while failing to track newly active interferers, thereby degrading its nulling capabilities. To address this fundamental limitation, an Online Segmented Beamformer is proposed. This algorithm incorporates data-driven temporal segmentation to causally minimize output power while dynamically adapting the SCM estimation windows to local stationarity. By framing the problem through the lens of dynamic programming, the proposed method tracks abrupt environmental changes and resets covariance estimates in real-time. We validate the performance of this framework in a complex, reverberant simulated acoustic environment and in highly reverberant real world experiments, demonstrating its superiority over fixed-window adaptive methods.

Precoding is a key technique for interference management and performance improvement in multi-antenna wireless systems. However, existing precoding methods are typically developed for specific system models, objectives, and constraint sets, which limits their adaptability to the heterogeneous and evolving scenarios expected in future 6G networks. To address this limitation, we propose AgenticPrecoding, a universal multi-agent framework that automates end-to-end precoding derivation directly from user-level communication requirements. Specifically, AgenticPrecoding decomposes the derivation process into four coordinated stages: problem formulation, solver selection, prompt upsampling, and code generation, assigning each stage to a specialized agent tailored to its specific reasoning demands. We employ two LoRA-adapted reasoning agents to inject precoding-specific domain knowledge for problem formulation and solver selection, while two general-purpose Large Language Models (LLMs) handle prompt refinement and executable code generation. Furthermore, a feedback-driven refinement mechanism is incorporated to enhance code executability, constraint feasibility, and solution quality. Extensive experiments across 10 representative precoding scenarios demonstrate that AgenticPrecoding achieves superior cross-scenario adaptability compared to conventional optimization-based and LLM-based baselines.

Millimeter-wave (mmWave) frequencies promise multi-gigabit connectivity for vehicle-to-everything (V2X) networks, but face challenges in terms of severe path loss and mobility-related beam misalignment. Reliable V2X connectivity requires fast, double-directional beam alignment. However, existing methods suffer from high training overhead and limited generalization to unseen scenarios. This paper presents VIsion-based BEamforming(VIBE), a hybrid model-based, closed-loop, learning architecture for real-time double-directional mmWave beam management primed by camera sensing. VIBE fuses machine learning, model-based reasoning, and closed-loop RF feedback to balance beam-pair establishment latency with link quality. VIBE bypasses exhaustive training overhead and accelerates link establishment by leveraging camera observations to reduce the beam-search space. Lightweight beam refinement and offset tracking mechanisms adaptively refine beams in response to dynamic application requirements. VIBE is implemented and evaluated across online indoor/outdoor testbeds, public datasets, and real-time vehicular experiments, demonstrating strong generalization capabilities, making it suitable for real-time V2X communication. Comparisons with 5G NR hierarchical beamforming show that VIBE consistently maintains lower outage rates. Furthermore, VIBE outperforms state-of-the-art end-to-end ML models for beam selection when evaluated on public datasets and achieves outage rates as low as 1.1-1.4 %. The results show that a hybrid model-based, closed-loop learning architecture is better suited for real-world mmWave vehicular connectivity than end-to-end trained ML models. For reproducibility, we publish our code to https://github.com/UNL-CPN-Lab/Look-Once-Beam-Twice.

Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the spatial correlation matrix is often snapshot-deficient. This deficiency, coupled with array imperfections, degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To ensure stable and robust beamforming, we propose a novel adaptive diagonal loading method that guarantees the WNG remains strictly within specified bounds. By leveraging the Kantorovich inequality, we map the desired WNG to a strict upper bound on the condition number of the correlation matrix. Furthermore, we present three estimation techniques for the adaptive loading level, ranging from trace-based bounding to exact eigenvalue decomposition, offering scalable computational complexities of $\mathcal{O}(M)$, $\mathcal{O}(M^2)$, and $\mathcal{O}(M^3)$. Our approach demonstrates highly stable beamforming under fast-changing interference.

Maintaining robust millimeter-wave (mmWave) connectivity in vehicular networks requires real-time adaptation to environmental dynamics, sensor degradation, and link variability. This paper presents Enwar 3.0, an environment-aware reasoning framework that unifies multi-modal sensing, agentic large language models (LLMs), and context-driven model selection for predictive beamforming, blockage detection, and handover management. Building upon prior iterations of Enwar, the proposed architecture integrates a classifier-driven assessment of sensor health with a primed LLM that orchestrates multiple specialized agents through structured, task-aware prompting. A novel synthetic degradation pipeline enables the training of a sensor degradation classifier that detects real-time impairments across camera, radar, LiDAR, and GPS inputs, achieving over 99% accuracy. The LLM, trained via chain-of-thought (CoT) priming and human-in-the-loop feedback, coordinates agent calls for beam selection, blockage forecasting, and environment perception while dynamically loading sensor-specific models based on environmental context. Extensive evaluations across 15 sensor combinations demonstrate that Enwar 3.0 delivers state-of-the-art performance in both predictive accuracy and interpretability, with beam selection accuracy exceeding 88%, blockage F1-scores surpassing 98%, and reasoning correctness reaching 87% on complex decision prompts. This work establishes a scalable foundation for LLM-integrated wireless systems that reason, perceive, and adapt in real-time.

An evolution of Wireless Communications towards 5G and beyond provides improved user experience in terms of quality of services. Understanding and estimating Channel information plays crucial role in providing better user experience. Traditional methods of channel estimation involves periodically sending pilots (known signals), estimating channel and send back estimated channel information to the BS which increases computational complexity and communication complexity. Hence, we focus on data driven approach for channel estimation. In this work, we explore a channel estimation mechanism at 7GHz frequency band for a given user location. This work involves data generation using Ray tracing mechanism and Machine learning model training that contains feature variables such as transmitter location, user location and target variable as channel coefficient . We explored Support Vector Regression, K-nearest neighbor (KNN), Random Forest, XGBoost and MLP. We found via simulations that XG Boost and proposed MLP performs better than Support Vector Regression, KNN and Random forest regression.

This paper investigates coordinated downlink transmission in a multi-base station (multi-BS) multi-reconfigurable intelligent surface (multi-RIS)-assisted pinching-antenna (PA) system, where each user equipment (UE) is associated with a single BS and each BS is equipped with movable PAs deployed on parallel waveguides. We formulate sum rate (SR) and energy efficiency (EE) maximization problems by jointly optimizing PA placement, RIS phase shifts, transmit beamforming, and BS-UE association under constraints of inter-PA spacing, power budget, and unit-modulus phase shift. To address the resulting highly coupled mixed-variable problem, we propose a three-stage graph neural network (GNN) that integrates heterogeneous and homogeneous graph representations and is trained end-to-end in an unsupervised manner. Extensive numerical results demonstrate that the proposed three-stage GNN consistently outperforms representative system and learning baselines, generalizes well to unseen numbers of UEs, RISs, and BSs, and maintains millisecond-level inference time. Besides, the results validate the effectiveness of the proposed design from both system and architectural perspectives. Moreover, PAs are shown to enhance SR and EE, and the performance gain is enlarged with increasing number of PAs.

Animals hear and vocalize across frequency ranges that differ substantially from humans, often extending into the ultrasonic domain. Yet most computational bioacoustics systems rely on audio models pre-trained at 16 kHz, restricting their usable bandwidth to the 0-8 kHz baseband and discarding higher-frequency information present in many bioacoustic recordings. We investigate a multi-band encoding framework that decomposes the full spectrum of animal calls into band features and fuses them into a unified representation. Similarity analyses on models show that certain encoders produce decorrelated band embeddings that improve class separation after fusion. Classification experiments on three bioacoustic datasets using eight pre-trained models and five fusion strategies show that fused representations consistently outperform the baseband and time-expansion baselines on two datasets, showing the potential of multi-band methods for full-spectrum encoding of animal calls.

This paper provides a concise yet comprehensive review of recent advancements in millimeter-wave (mm-wave) oscillators below 100 GHz and sub-terahertz (sub-THz/THz) oscillators above 100 GHz for next-generation computing and communication systems, including 5G, 6G, and beyond. Various design approaches, including CMOS, SiGe, and III-V semiconductor technologies, are explored in terms of performance metrics such as phase noise, output power, efficiency, frequency tunability, and stability. The review highlights key challenges in achieving high-performance and reliable oscillator designs while discussing emerging techniques for performance enhancement. By evaluating recent design trends, this work aims to offer valuable insights and design guidelines that facilitate the development of robust mm-wave and sub-THz/THz oscillators for future communication, computing, and sensing applications.

This paper addresses velocity estimation within robot-aided integrated sensing and communications (ISAC), where mobile robots act as sensing nodes but can only opportunistically reuse irregular 5G/6G reference signals (RSs). We show that the velocity profile induced by such irregular time-domain patterns can be decomposed into a periodic-peak component and an amplitude-shaping (weighting) component. Leveraging this structure, we propose a multi-periodogram velocity estimation algorithm that is standard-compliant and does not require new sensing-dedicated RSs or 3GPP modifications. Simulation results demonstrate that, compared with conventional periodogram processing, the proposed method improves low-SNR robustness by achieving a 3 dB SNR gain at the 10% missed-detection rate and reducing false alarms by 51%.

Multi-antenna receiving systems have become a prevalent technical solution in communication systems. Meanwhile, deep learning has achieved significant progress in automatic modulation recognition tasks in single-antenna systems. However, the application of deep learning in multi-antenna modulation recognition (MAMR) tasks is still limited. In this paper, we propose an MAMR method namely MAMR-IQ to fully explore the diversity gain of a multi-antenna receiving system, which concatenates the raw received in-phase and quadrature (IQ) signals of multiple antennas and feeds them into a convolutional neural network. Simulation results show that the proposed MAMR-IQ method outperforms two existing deep learning-based MAMR methods which are based on direct voting (DV) and weight average (WA) in terms of both recognition accuracy and computational complexity. To address the problem of limited training data in few-shot scenarios, we further propose a data augmentation method that involves exchanging IQ sequences received by any two antennas to generate augmented samples. Simulation results show that with the proposed augmentation method, the recognition accuracy can be further improved.

Reconfigurable intelligent surfaces (RISs) modify signal reflections to enhance wireless communication capabilities. Classical RIS phase optimization is highly non convex and challenging in dynamic environments due to high interference and user mobility. Here we propose a hierarchical multi-objective quantum metalearning algorithm that switches among specific quantum paths based on historical success, energy cost, and current data rate. Candidate RIS control directions are arranged as switch paths between quantum neural network layers to minimize inference, and a scoring mechanism selects the top performing paths per layer. Instead of merely storing past successful settings of the RIS and picking the closest match when a new problem is encountered, the algorithm learns how to select and recombine the best parts of different solutions to solve new scenarios. In our model, high-dimensional RIS scenario features are compressed into a quantum state using the tensor product, then superimposed during quantum path selection, significantly improving quantum computational advantage. Results demonstrate efficient performance with enhanced spectral efficiency, convergence rate, and adaptability.

Visual-inertial odometry (VIO) is widely used for mobile robot localization, but its long-term accuracy degrades without global constraints. Incorporating ranging sensors such as ultra-wideband (UWB) can mitigate drift; however, high-accuracy ranging usually requires well-deployed anchors, which is difficult to ensure in narrow or low-power environments. Moreover, most existing visual-inertial-ranging (VIR) fusion methods rely on discrete time-based filtering or optimization, making it difficult to balance positioning accuracy, trajectory consistency, and fusion efficiency under asynchronous multi-sensor sampling. To address these issues, we propose a spline-based continuous-time state estimation method for VIR fusion localization. In the preprocessing stage, VIO motion priors and UWB ranging measurements are used to construct virtual anchors and reject outliers, thereby alleviating geometric degeneration and improving range reliability. In the estimation stage, the pose trajectory is parameterized in continuous time using a B-spline, while inertial, visual, and ranging constraints are formulated as factors in a sliding-window graph. The spline control points, together with a small set of auxiliary parameters, are then jointly optimized to obtain a continuous-time trajectory estimate. Evaluations on public datasets and real-world experiments demonstrate the effectiveness and practical potential of the proposed approach.

Reconfigurable Intelligent Surfaces (RIS) have the potential to engineer smart radio environments for next-generation millimeter-wave (mmWave) networks. However, the prohibitive computational overhead of Channel State Information (CSI) estimation and the dimensionality explosion inherent in centralized optimization severely hinder practical large-scale deployments. To overcome these bottlenecks, we introduce a per-element CSI-free paradigm powered by a Hierarchical Multi-Agent Reinforcement Learning (HMARL) architecture to control mechanically reconfigurable reflective surfaces. By substituting pilot-based channel estimation for each element of the device with accessible user localization data, our framework leverages spatial intelligence for macro-scale wave propagation management. The control problem is decomposed into a two-tier neural architecture: a high-level controller executes temporally extended, discrete user-to-reflector allocations, while low-level controllers autonomously optimize continuous focal points using Multi-Agent Proximal Policy Optimization (MAPPO) under a Centralized Training with Decentralized Execution (CTDE) scheme. Comprehensive deterministic ray-tracing evaluations in an indoor mmWave scenario demonstrate that this hierarchical framework achieves received signal strength indicator (RSSI) improvements of up to 7.79 dB over centralized Proximal Policy Optimization (PPO) baselines. Furthermore, the system maintains resilient beam-focusing performance under practical sub-meter localization tracking errors for up to four users and two reflector arrays. By eliminating execution-time CSI overhead while preserving high-fidelity signal redirection, this work provides a scalable and cost-effective step toward intelligent indoor wireless environments.

We establish that temporal averaging over multiple observations is the degenerate case of algebraic group action with the trivial group $G=\{e\}$. A General Replacement Theorem proves that a group-averaged estimator from one snapshot achieves equivalent subspace decomposition to multi-snapshot covariance estimation. The Trivial Group Embedding Theorem proves that the sample covariance is the accumulation of trivial-group estimates, with variance governed by a $(G,L)$ continuum as $1/(|G|\cdot L)$. The processing gain $10\log_{10}(M)$ dB equals the classical beamforming gain, establishing that this gain is a property of group order, not sensor count. The DFT, DCT, and KLT are unified as group-matched special cases. We conjecture a General Algebraic Averaging Theorem extending these results to arbitrary statistics, with variance governed by the effective group order $d_{\mathrm{eff}}$. Monte Carlo experiments on the first four sample moments across five group types confirm the conjecture to four-digit precision. The framework exploits the $structure$ of information (representation-theoretic symmetry of the data object) rather than the content, complementing Shannon's theory. Five applications are demonstrated: single-snapshot MUSIC, massive MIMO, single-pulse waveform classification, graph signal processing, and analysis of transformer LLMs. Techniques for blind group matching are described.

The paper presents an approach for learning antenna Radiation Patterns (RPs) of a pair of heterogeneous quadrotor Uncrewed Aerial Vehicles (UAVs) by calibration flight data. RPs are modeled either as a Spherical Harmonics series or as a weighted average over inducing samples. Linear regression of polynomial coefficients enables decoupling of independent UAVs' RPs from the observed joint gain. A synchronized calibration trajectory provides training and testing samples in an obstacle-free anechoic altitude. Evaluation on a real-world dataset demonstrates the feasibility of learning both radiation patterns, achieving 4.56 dB RMS extrapolation error. The proposed RP learning and decoupling can be exploited in rapid recalibration upon payload changes, thereby enabling precise autonomous path planning and swarm control in real-world applications where setup changes are expected.

This paper investigates secure communications in rate-splitting multiple access (RSMA) enabled heterogeneous UAV networks, where multiple UAVs collaboratively serve ground terminals in the presence of eavesdroppers. By jointly considering secrecy rate maximization and propulsion energy consumption minimization, we formulate a multi-objective optimization problem involving UAV trajectory design, service association, power allocation, and secrecy precoding under mobility, collision-avoidance, service-capacity, and communication constraints. The formulated problem is highly non-convex due to the coupling among UAV trajectories, RSMA transmission variables, and secrecy constraints. To address the resulting non-convex and highly coupled optimization problem, we propose a hierarchical optimization framework. The inner layer uses a semidefinite relaxation (SDR)-based S2DC algorithm combining penalty functions and difference-of-convex (D.C.) programming to solve the secrecy precoding problem with fixed UAV positions. The outer layer introduces a Large Language Model (LLM)-guided heuristic multi-agent reinforcement learning approach (LLM-HeMARL) for trajectory optimization. LLM-HeMARL efficiently incorporates LLM-generated expert heuristic policy, enabling UAVs to learn energy-aware, security-driven trajectories without the inference overhead of real-time LLM calls. The simulation results show that our method outperforms existing baselines in secrecy rate and energy efficiency, with consistent robustness across varying UAV swarm sizes and random seeds.

Efficient resource utilization is proposed for simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) to ensure fair and high data rates. We optimize the number of STAR-RIS elements to be allocated to each user and maximize the sum of the user rates. To promote fairness, we introduce a soft fairness mechanism that guarantees a minimum STAR-RIS element allocation to every user. Subject to this requirement, the phase shifts of the STAR-RIS elements and the remaining element assignments are jointly optimized by harnessing an appropriately tailored deep reinforcement learning (DRL) algorithm. The proposed DRL method is also compared to Dinkelbach's algorithm and to a bespoke hybrid DRL approach. A deactivation incentive is incorporated into the DRL model for enhancing resource utilization by intelligently deactivating some of the STAR-RIS elements when not required. The proposed DRL method achieves fair and high data rates for both stationary and mobile users, while ensuring efficient resource utilization. Using the proposed DRL method, up to 34% and 23% of STAR-RIS elements can be deactivated in static and mobile scenarios, respectively, with negligible degradation in the average DL data rate.

Conventional acoustic beamformers typically assume short-time stationarity and process frequency bins independently, ignoring inter-frequency correlations. This is suboptimal for almost-periodic noise sources such as engines, fans, and musical instruments: these signals are better modeled as (almost) cyclostationary (ACS) processes with statistically correlated spectral components. This paper introduces the cyclic minimum power distortionless response (cMPDR) beamformer, which extends the conventional MPDR to jointly exploit spatial and spectral correlations. Building on frequency-shifted (FRESH) filtering, it suppresses noise components that are coherent across harmonically related frequencies, reducing residual noise beyond what spatial filtering alone can achieve. To address inharmonicity, where partials deviate from exact integer multiples of a fundamental frequency, we estimate resonant frequencies from a periodogram and derive frequency shifts from their pairwise spacing. Theoretical analysis yields closed-form expressions for residual noise and proves that output power decreases monotonically with the number of cyclic components. Experiments on synthetic harmonic noise and real UAV motor recordings confirm these findings: in low-SNR scenarios, the cMPDR achieves up to 5 dB improvement in SI-SDR over the MPDR, yields consistent STOI gains, and remains effective with a single microphone. When spectral correlation is absent, the method reduces to conventional MPDR and does not degrade performance. These results suggest that cyclic processing is a viable direction for acoustic noise reduction that deserves further investigation. Code and audio samples are available at https://github.com/Screeen/cMPDR.