Unmanned aerial vehicle (UAV) swarms are essential for mission-critical aerial Internet of Things (IoT) applications. However, reliable multi-hop routing in these swarms is severely challenged by highly dynamic topologies and partial, asynchronous observations. Furthermore, conventional training data poorly represent rare but decisive disruptions, such as terrain occlusion, no-fly-zone detours, and congestion bursts. To address these issues, this paper proposes a deployment-aligned robust learning framework organized into three functional layers. At the policy layer, we propose the Multi-Agent Opportunistic (MAO) routing method, learned via a Belief Graph-based MAPPO (BG-MAPPO) algorithm. To overcome partial and stale observations, BG-MAPPO constructs a local belief graph encoding the dynamic neighborhood state, which is then used to jointly determine the optimal forwarder-set size and a diversity-aware routing distribution. At the training layer, the policy is optimized inside a terrain-aware, physics-calibrated Digital Twin Network (DTN). To prevent overfitting to limited training distributions, a diffusion-based generator (FD3M) enriches the training data with trajectory-and-flow samples covering critical corner cases. At the validation layer, large-scale simulations show that MAO reduces end-to-end delay by 27–34% compared to representative baselines. The policy also incurs modest operational overhead, maintaining millisecond-level inference and bounded signaling. Finally, hardware-in-the-loop (HIL) experiments confirm that the DTN accurately predicts physical execution, with relative gaps of only 4% in packet delivery ratio and 7% in delay, effectively bridging the sim-to-real gap for robust UAV-swarm networking.

Path planning is a fundamental application of an unmanned aerial vehicle (UAV) swarm. Performing such a task in a complex mountain environment with a wind field would encounter challenges such as the sim-to-real (simulation-to-reality) gap. In this paper, we present a digital twin (a virtual replica of the physical system)-assisted path-planning framework for a UAV swarm with two phases: global path planning and real-time trajectory planning. For global path planning, we develop an optimization model that combines the constraints of a single UAV and the swarming rules, while also accounting for wind effects. To solve the optimization model, we improve the polar lights optimization (PLO) algorithm via multiple strategies (named PLOM), enhancing the initialization, exploitation, exploration, and equilibration processes. The major improvement strategies consist of opposition-based learning with refraction and elite, the logarithmic spiral motion, the Cauchy-Gaussian operator, and sine cosine perturbation. We construct a realistic geographical simulation environment based on a digital elevation model (DEM) and dominant wind, and design controlled experiments under different conditions of UAVs, threats, waypoints, and wind speeds. The simulation results demonstrate that the PLOM algorithm always achieves the best solution in swarm path planning scenarios with different complexities. Meanwhile, the PLOM algorithm has the greatest robustness with nearly the shortest runtime.

With the rapid development of low-altitude economies, unmanned aerial vehicle (UAV) swarm has attracted growing interest for cooperative target search. However, most existing studies focus on static targets and assume UAVs operate at a single horizontal altitude, limiting their practical applicability. This paper proposes a novel multi-UAV cooperative search framework for moving targets based on multi-agent deep reinforcement learning (MADRL). By coordinating UAVs across high, medium, and low-altitude layers, the system achieves improved search efficiency through altitude-adaptive operations. We further introduce a revisit-time compensation mechanism to enhance detection performance for moving targets in a multi-layer UAV swarm. To address the challenges of slow convergence and sparse feedback in MADRL, we propose hybrid-reward-based value decomposition networks (HRVDN) algorithm that integrates dense local rewards with sparse global rewards, accelerating learning while encouraging agents to collect high-value information. Simulation results demonstrate that the proposed approach outperforms existing methods in terms of target search rate and area coverage.

Digital twin network (DTN) technology provides significant support for intelligent applications of unmanned aerial vehicle (UAV) swarms. However, related research focuses on DTN applications and lacks attention to the construction and maintenance of high-fidelity digital twin (DT) models. In this paper, we first develop a DT simulation platform for UAV swarms. Then, a dynamic data-driven DT model calibration scheme is proposed on the example of the most fundamental flight state of a UAV. The scheme utilizes parameter identification to estimate offline the key parameters of the measurement model and system deviations. Furthermore, the flight state is corrected online utilizing data assimilation actuated on the actual and virtual data. Simulation experiments on the DT simulation platform are conducted, and the effects of data sampling rate on calibration accuracy and computational load are analyzed. The results demonstrate that parameter identification and data assimilation significantly improve the fidelity of the DT model in terms of the optimal sub-pattern assignment (OSPA) metric to different degrees.

Digital Twin (DT) technology represents a cutting-edge methodology that digitally maps physical entities with high fidelity, leading to the Digital Twin Network (DTN) through its integration with network technologies. DTN establishes bidirectional communication between virtual and physical spaces, enabling real-time monitoring, dynamic optimization, and precise control of physical networks. This addresses challenges posed by network expansion and service diversification, revolutionizing the management and optimization of complex network systems. Despite its potential, DTN implementation remains challenging, with research still nascent and lacking detailed guidelines. This paper aims to bridge this gap by presenting a comprehensive survey of the reference architecture for real-world DTN implementation and its key enabling technologies. It begins by defining the conceptual foundation of DTN and reviewing related architectural studies. This is followed by the proposal of a universal and scalable modular DTN architecture, encompassing the physical layer, data layer, DT model layer, and service layer. We then explore the critical enabling technologies required for implementing this architecture and analyze applications enhanced by DTN. Notably, We propose a five-level digital twin model evolution taxonomy framework that systematically reveals the evolution path from basic mapping to ultra-high-fidelity autonomous inference. This framework provides a structured evaluation benchmark for optimizing and advancing digital twin models. Finally, we discuss the primary open issues in DTN, offering theoretical and practical guidance for future research in this field.

Cooperative target search (CTS) technology is highly desirable in various multi-autonomous aerial vehicle (AAV) applications. However, searching for unknown targets in a dynamic threatening environment is a challenging problem, especially for AAVs with limited sensing range and communication capabilities. Besides, traditional searching methods lack scalability and efficient collaboration among the AAV swarm in dynamic environments. In this work, a digital twin (DT)-enabled distributed CTS approach was presented for AAV swarms and achieving sim-to-real transfer. Specifically, a new scalable multi-agent reinforcement learning (MARL) based algorithm called SAMARL is adopted to improve effectiveness and adaptability, combining a multi-head attention mechanism. In SAMARL, a scalable observation space with graph representation and an environmental cognition map is designed to thoroughly consider the target search rate, area coverage, and safety assurance. Then, a DT-driven training framework is proposed to facilitate the continuous evolution of MARL models and address the tradeoff between training speed and environment fidelity. Furthermore, we innovatively develop a distributed AAV swarm digital twin cooperative target search validation system, including real flight control, communication simulation tools, and a 3D physics engine. Extensive simulations validate its superiority compared to state-of-the-art strategies. More importantly, we also conduct real-world flight experiments on different scale mission areas and AAV swarms, further demonstrating the generalization and scalability of trained models.

The wide use of drones is playing a vital role in the era of low-altitude economy, but meanwhile its misuse could also presents a threat to the privacy, property damage, health and public safety. Therefore, there is a timely need to enhance the capability to detect and recognize the flying drones, which however is challenging owing to the small size, slow speed and low altitude of small drones. In the 5G and beyond, the widely deployed base stations are becoming more and more advanced, especially with the large spectrum like the millimetre wave (mmWave) frequency band. This provides a great potential to turn the network of base stations into a network of mmWave radars for the drones’ detection by leveraging the integrated sensing and communication (ISAC) techniques. This work aims to classify the drones based on their mmWave radar cross section (RCS) real data that will be converted to two-dimensional (2D) RCS images. Thus, 2D Convolutional Neural Network (CNN) is applied to the image sets to achieve the drone classification. The satisfactory testing results verify the proposed drone classification method.

This paper studies the secrecy energy efficiency (SEE) of a simultaneous wireless information and power transfer (SWIPT) network aided by multiple reconfigurable intelligent surfaces (RIS). The SWIPT network comprises several information decoding receivers (IDRs) and energy harvesting receivers (EHR) served by an access point (AP) supported by several distributed RIS. To effectively define the trade-off between the secrecy rate and energy efficiency of the multi-RIS SWIPT system, an optimization problem is formulated to maximize the SEE by optimizing the transmit beamforming at the AP and the phase shift at each RIS while dynamically controlling each RIS's ON/OFF status. The resultant non-convex optimization problem is solved using a deep reinforcement learning (DRL) framework to design the beamforming policy and a control mechanism for the RISs. Simulation results show that the proposed algorithm enhances the SEE compared to other benchmark schemes.

A better understanding of the mmWave channel coherence time will play a significant role in both communication and sensing. Traditional literatures consider that the channel coherence time in mmWave communication will be very short due to high frequency, which makes the channel estimation more difficult. However, we believe that the propagation characteristics of the mmWave channel will affect its coherence time, i.e., channel sparsity may limit its time variability. In this paper, we investigate the time-varying nature of mmWave channel by analyzing its Doppler spread based on the clustered sparsity model. After the derivation of Doppler spectrum DPS and the simulation analysis based on the two-cluster channel, we found that the maximum angle between clusters and the power distribution between clusters are two main factors limiting the Doppler spread. Finally, the realistic mmWave NYUSIM model is used for Doppler spread comparative analysis with Clarke’s model and find that Doppler spread of NYUSIM channel is far less than that estimated based on Clarke’s model. Thus, it is demonstrated that even if the mmWave frequency is high, the clustered sparsity characteristics makes its channel coherence time not as short as thought intuitively, which is meaningful for mmWave vehicular sensing and communication.

Over the past decades, unmanned aerial vehicles (UAVs) have been widely used in both military and civilian fields. In these applications, flocking motion is a fundamental but crucial operation of multi-UAV systems. Traditional flocking motion methods usually designed for a specific environment. However, the real environment is mostly unknown and stochastic, which greatly reduces the practicality of these methods. In this article, deep reinforcement learning (DRL) is used to realize the flocking motion of multi-UAV systems. Considering that the sim-to-real problem restricts the application of DRL to the flocking motion scenario, a digital twin (DT)-enabled DRL training framework is proposed to solve this problem. The DRL model can learn from DT and be quickly deployed on the real-world UAV with the help of DT. Under this training framework, this article proposes an actor–critic DRL algorithm, named behavior-coupling deep deterministic policy gradient (BCDDPG), for the flocking motion problem, which is inspired by the flocking behavior of animals. Extensive simulations are conducted to evaluate the performance of BCDDPG. Simulation results show that BCDDPG achieves a higher average reward and performs better in terms of arrival rate and collision rate compared with the existing methods.

In this paper, we propose a deep neural network (DNN) based beamforming scheme for frequency-division-duplex (FDD) millimeter-Wave (mmWave) massive multipleinput multiple-output (MIMO) systems. Different from the time-division-duplex (TDD) systems, for FDD systems the channel reciprocity between the down-link (DL) and up-link (UL) channels does not hold in general, requiring an extra channel state information (CSI) feedback stage. Based on the previous theoretical analysis and measurements, however, partial reciprocities, including the spatial directional angles and number of propagation paths, do exist for FDD mmWave systems. With this partial reciprocity, we propose a multi-path beamforming scheme with a predefined codebook. Different from most previous works that only focus on one dominant path of each mobile station (MS), this work considers a multi-path scenario where the proposed scheme identifies all the propagation paths of all MSs, and selects the optimal combination of codewords with the help of a DNN that not only overcomes angle ambiguity but also significantly reduces computational complexity.

In this paper, a hybrid multi-user massive MIMO system operating on the mmWave frequency is considered. To reduce the heavy beam training overhead for such a massive MIMO system, we propose a 3D beam training algorithm, which estimates the azimuth and elevation of the angle of arrival (AoA) and departure (AoD) between the base station (BS) and the mobile stations (MSs). The proposed algorithm first executes a hierarchical search to acquire the range of azimuth and elevation, then applies an exhaustive search within this range for a more precise matching. Through this two-stage approach, the beam training overhead can be substantially reduced.

Adaptive observer based grid synchronization technique has received wide attention recently. This technique has fast convergence property. However, adaptive observer is sensitive to unmodeled dynamics e.g. harmonics. Moreover, no small-signal models are available which can be useful for gain tuning purpose. To solve these issues, in this work, a harmonic robust adaptive observer is presented using the concept of in-loop filter. This improves the existing literature on adaptive observer based grid synchronization technique, which is the main novelty of this paper. To analyze the stability of the proposed technique, small-signal model of the adaptive observer with and without in-loop filter are presented. Finally, simulation study is presented to show the effectiveness of the proposed technique over two other advanced techniques from the literature.

For a mmWave multiple input multiple output (MIMO) system, the hybrid precoding scheme is of great interest due to its lower power consumption and hardware cost, where a smaller number of RF chains are used to feed a larger scale of antenna array. In this paper we consider a flexible architecture where RF chains and antennae can be dynamically connected, and propose a greedy algorithm to achieve dynamic subarray configuration. The greedy algorithm can select the best subarrays from all the possible candidates in each search process, while the Lanczos algorithm is applied to further reduce the computation complexity. Simulation results demonstrate the superior performance of the proposed algorithm to existing works yet with a lower complexity.

The hybrid beamforming strategy that applies a combination of analog and digital precoders has attracted much attention recently for its ability to reduce both hardware complexity and energy consumption. However due to the large number of antennae, the determination of hybrid precoders usually involves a large amount of computation, which may take much time and potentially risk the low-latency demand. In this paper we propose a novel divide-and-conquer precoding scheme where the precoding problem for the sub-connected architecture is divided into a series of independent subproblems. These subproblems can be solved simultaneously to save time. To deal with the subproblems, we propose a semidefinite relaxation based approach. By dividing the precoding problem, computational complexity can be reduced, and simulation results show its comparable performance with existing works, and robustness against potential saddle points with poor performance.

How to provide a low-cost but accurate localization solution for the indoor mobile robots are essential in many Internet of Things applications, such as smart home and asset tracking. To achieve this goal, this paper originally proposes a modified two-filter smoother based on ensemble Kalman filter (KF) (denoted as EnKS) for the localization of indoor mobile robots. The proposed EnKS algorithm consists of both a forward part of an ensemble KF (EnKF) with statistical linear regression and a backward part of a modified information KF with state error vector. The EnKS based on stochastic sampling with ensemble members can achieve better positioning accuracy than other Kalman smoothers. When compared to EnKF, the proposed EnKS combines a backward filter to compensate for the estimation error of EnKF and further improves the accuracy. Furthermore, the implementation of the proposed EnKS is conducted in the real world visible light positioning (VLP) system using pre-existing LED lights for low-cost robot localization. To make a performance comparison, this paper also uses baseline smoothers based on extended KF and central difference KF in the VLP system. Preliminary experimental results imply that the proposed EnKS is able to achieve the best positioning accuracy, as high as 11.18 cm on average, but with a comparable computational complexity, which enables to meet the demands of many robot applications.

This paper focuses on the issues of cooperative spectrum sensing (CSS) in a large cognitive radio network (CRN) where cognitive radio (CR) nodes can cooperative with neighboring nodes using spatial cooperation. A novel optimal global primary user (PU) detection framework with geographical cooperation using a deflection coefficient metric measure to characterize detection performance is proposed. It is assumed that only a small fraction of CR nodes communicate with the fusion center (FC). Optimal cooperative techniques which are global for class deterministic PU signals are proposed. By establishing the relationship between the CSS technique design issues and Kosambi-Karhunen-Loève transform (KLT) the problem is solved efficiently and the impact on detection performance is evaluated using simulation.

Light fidelity (LiFi), using light emitting devices such as light emitting diodes (LEDs) which are operating in the visible light spectrum between 400 and 800 THz, provides a new layer of wireless connectivity within existing heterogeneous radio frequency wireless networks. Link data rates of 10 Gbps from a single transmitter have been demonstrated under ideal laboratory conditions. Synchronization is one of these issues usually assumed to be ideal. However, in a practical deployment, this is no longer a valid assumption. Therefore, we propose for the first time a low-complexity maximum likelihood-based timing synchronization process that includes frame detection and sampling clock synchronization for direct current-biased optical orthogonal frequency division multiplexing LiFi systems. The proposed timing synchronization structure can reduce the high-complexity two-dimensional search to two low-complexity one-dimensional searches for frame detection and sampling clock synchronization. By employing a single training block, frame detection can be realized, and then sampling clock offset (SCO) and channels can be estimated jointly. We propose three frame detection approaches, which are robust against the combined effects of both SCO and the low-pass characteristic of LEDs. Furthermore, we derive the Cramér–Rao lower bounds (CRBs) of SCO and channel estimations, respectively. In order to minimize the CRBs and improve synchronization performance, a single training block is designed based on the optimization of training sequences, the selection of training length, and the selection of direct current (DC) bias. Therefore, the designed training block allows us to analyze the trade-offs between estimation accuracy, spectral efficiency, energy efficiency, and complexity. The proposed timing synchronization mechanism demonstrates low complexity and robustness benefits and provides performance significantly better than achieved with existing methods.

Channel asymmetry and channel correlation are frequently encountered in wireless communication systems. Orthogonal transmission schemes are usually inefficient in dealing with these problems. In this paper, in order to boost the throughput performance for multiple-input multiple-output broadcast communications in the presence of channel asymmetry and/or channel correlation, we study optimization algorithms for multi-user superposition coding beamforming (SCBF). Starting with solving the minimum power optimization problem for the two-user case, we derive the optimal solution structure of the problem and two types of dedicated algorithms that could efficiently find the optimal solutions with all parameter setups. Extensions are then made to the same problem with the signals of more than two users multiplexed in the power domain as well as to the rate region computation problem. Finally, to adapt our algorithms to more general cases, novel hybrid precoding schemes are proposed, where certain user grouping strategy is used to combine zero-forcing beamforming and SCBF. Numerical simulations are provided to show that with our algorithms, a considerable performance gain is achieved by SCBF compared to the other orthogonal transmission methods.

Millimeter wave (mm-wave) system performance may be degraded if the operation mechanism is not properly designed, because mm-wave systems suffer severe path loss and very short coherence time. Thanks to the sparse channel model and directional transmission property, it is usually sufficient to use analog beam codebooks in beam training to estimate dominant channel components instead of complete instantaneous channel matrices. With this viewpoint, we first characterize the achievable beam gain by the number of antennas and beamwidth, and then propose a low complexity mechanism that employs the offline designed analog beam codebooks for both beam training and data transmission. This mechanism not only avoids high overhead and delay caused by the online beamforming design based on instantaneous channels but also enables a much longer quasi coherence time, which is the new concept proposed in this work. In addition, it can realize a theoretical analysis of the role of system parameters in energy efficiency. We consider a phase-controlled point-to-point (P2P) mm-wave system example to illustrate the proposed concepts and mechanism. Numerical simulations also verify the effectiveness of the theoretical analysis result and also provide a suggestion for system design.

This paper addresses an energy-saving problem for the downlink of a cloud-assisted heterogeneous network (HetNet) using a time-division duplex (TDD) model, which aims to minimize the base stations (BSs) sum power consumption while meeting the rate requirement of each user equipment (UE). The basic idea of this work is to make use of the scalability of system configurations such that green resource management can be employed by flexibly switching off some unnecessary hardware components, especially for off-peak traffic scenarios. This motivates us to utilize a flexible BS power consumption formulation to jointly model its signal processing and circuit power, transmit power, and backhaul transmission power. Instead of using the integer variables [1,0] to control the “on/off” two status of a BS in most previous work, we employ the group sparsity of a transmit power vector to denote the activity of each frequency carrier (FC) such that the signal processing and circuit power can be scaled with the effective bandwidth, thereby leading to multiple sleep modes for a BS in multi-FC systems. Based on this BS power model and the group sparsity concept, a simplified resource allocation scheme for joint BS-UE association, FC assignment, downlink power allocation, and BS sleep modes determination is presented, which is based on the average channel statistics computed over the coherence time of the large scale fading (LSF). This semidynamic green resource management mechanism can be formulated as a NP-hard optimization problem. In order to make it tractable, the successive convex approximation (SCA)-based algorithm is applied to efficiently find a stationary solution using a cloud-based centralized optimization. Simulation results also verify the effectiveness of the proposed mechanism under the developed BS power consumption model.

We consider a multi-cell interfering MIMO-MAC system, where each user transmits a single data stream to its desired base station (BS). First, we study the multiplexing gain of the system using two interference cancellation (IC) schemes: the coordinated zero-forcing receiver (CZFR) and the extended grouping method based IA (EGM-IA) with the perfect channel state information at transmitters (CSIT). Then, we propose two algorithms to find the IC transceivers maximizing the rate of each user. Under limited feedback, we additionally propose an algorithm to maximize the minimum worst-case rate of the users by adaptively allocating the feedback bits. Numerical results illustrate the performance of the proposed algorithms.

Green resource allocation in an amplify-and-forward (AF) relay-assisted MIMO system is considered, consisting of one source, one AF relay, and one destination, in which the relay-to-destination channel is only statistically known to the source and relay. The source covariance matrix and the relay AF matrix are optimized so as to maximize the system energy efficiency (EE), defined as the ratio of the system ergodic achievable rate over the total consumed power. The resulting optimization problem is a challenging non-convex problem, which is tackled employing fractional programming in conjunction with the alternating maximization algorithm. In addition, the regime of single-stream transmission is investigated and a sufficient condition for its optimality is derived.

In this paper, we study the problems of power allocation in a multi-user relay-assisted wireless network. From the perspective of game theory, we formulate and analyze this power allocation problem as a power trading game by considering users as bidders and the relay as an auctioneer. Aiming at solving this problem where each bidder has a private budget limit, we apply an adaptive clinching auction algorithm, which can maximize the utilities of users and the assisted relay. Additionally, simulations illustrate the performance of the proposed method.

The multiple-input multiple-output interference channel is considered with perfect channel information at the transmitters and single-user decoding receivers. With all transmissions restricted to single stream beamforming, we consider the problem of finding all Pareto optimal rate-tuples in the achievable rate region. The problem is cast as a rate profile optimization problem. Due to its nonconvexity, we resort to an alternating approach: For fixed receivers, optimal transmission is known. For fixed transmitters, we show that optimal receive beamforming is a solution to an inverse field of values problem. We prove the solution's stationarity and compare it with existing approaches.

Energy-efficient resource allocation in a single-user, amplify-and-forward (AF), relay-assisted, multiple-input-multiple-output (MIMO) system is considered in this paper. Previous results in this area assume that perfect CSI is available for at least one of the source-relay and relay-destination channels. Instead, the case in which statistical CSI is available for both the source-relay and relay-destination channel is tackled in this letter. Using fractional programming theory and the alternating maximization algorithm, low-complexity source and relay precoding is performed, subject to quality-of-service (QoS) and power constraints.

We consider a set of transmitter-receiver pairs operating concurrently in the same spectral band. The transmitters and receivers are equipped with multiple antennas and are restricted to apply single stream beamforming. This setting corresponds to the single stream multiple-input multiple-output (MIMO) interference channel. We assume perfect channel state information at the transmitters and the single-user decoding receivers. Efficient operating points in this setting correspond to points on the Pareto boundary of the achievable rate region. Characterizing all Pareto optimal points in the MIMO interference channel is still an unsolved problem. An approach to attain different Pareto optimal points in the MIMO interference channel is rate profile optimization. Given the nonconvexity of the problem, we propose an alternating approach based on successive optimization of the transmit and receive beamforming vectors. For fixed receive beamforming vectors, a solution for the rate profile optimization exists and is solved by a set of convex feasibility problems. For fixed transmit beamforming vectors, we show that the rate profile optimization can be solved by a set of feasibility problems each corresponding to an inverse field of values problem. The convergence of the alternating algorithm is guaranteed to a stationary point of the original problem.

Nowadays, the increasing demand for higher data rate and ubiquitous connectivity of a smart phone significantly conflicts with its limited battery lifetime. In order to prolong the battery lifetime, we desire to save the uplink transmit power of a mobile terminal with the aid of a cooperative relay with higher transmit power level (e.g., powered by electrical networks), since the battery power is much more limited. In this paper, we consider a relay-aided two-hop system consisting one source (e.g., a mobile terminal in uplink), one Amplify-and-Forward (AF) relay and one destination (e.g., a base station). For this scenario, the source transmit power is reduced on the expense of the relay power. More precisely, we jointly optimize the transceiver strategies to minimize the source transmit power subject to a rate requirement. The closed-form optimal transceiver strategies are obtained when the perfect instantaneous channel statement information (CSI) is known. Furthermore, for the Rayleigh fading channel, an exact form of source energy-saving probability of this AF relay-aided transmission compared with direct transmission (DT) is derived. Monte Carlo simulations are provided to verify the analytical results, from which we additionally find the source energy-saving region for a source when the relay location is fixed and that for a relay when the source location is fixed.

In this letter, a novel approach to autofocus for inverse synthetic aperture radar (ISAR) imaging called minimum entropy via subspace autofocus is presented. This scheme uses the weighted signal subspace to express the phase errors left in the echoes after range-bin alignment and estimates the optimal weights sequentially via an optimization algorithm based on an entropy minimization principle, and its robustness and convergence can be ensured by the optimization method. Both the theoretical analysis and processing results of the real ISAR data have confirmed the feasibility of this new scheme.