Hatem Abou-Zeid

NI
h-index21
19papers
287citations
Novelty47%
AI Score50

19 Papers

SPJun 4
LatentWave: JEPA Pretraining for Wireless Foundation Models

Ahmed Mohamed, Ahmed Aboulfotouh, Hatem Abou-Zeid

Wireless foundation models have emerged as a promising alternative to building separate models for each wireless task. However, existing approaches rely on masked input reconstruction, which can bias representations toward low-level signal details. In this paper, we propose LatentWave, a wireless foundation model pretrained using a Joint-Embedding Predictive Architecture (JEPA) on diverse wireless spectrograms and channel state information (CSI). By predicting masked regions in latent space, LatentWave learns representations that are more transferable out of the box across diverse downstream tasks. The proposed architecture employs per-channel patch embeddings with stochastic channel sampling during pretraining, allowing it to process variable antenna counts and improving usability across heterogeneous wireless configurations. We evaluate LatentWave on four downstream tasks: RF signal classification, 5G NR positioning, beam prediction, and LoS/NLoS classification, comparing against a masked-modeling baseline (WavesFM) pretrained on the same data. Additionally, we show that the masking geometry introduces a task-dependent inductive bias: frequency masking strongly favors channel-related tasks such as positioning and beam prediction, while region masking better preserves discriminability for signal classification.

AIDec 21, 2022
The Internet of Senses: Building on Semantic Communications and Edge Intelligence

Roghayeh Joda, Medhat Elsayed, Hatem Abou-zeid et al.

The Internet of Senses (IoS) holds the promise of flawless telepresence-style communication for all human `receptors' and therefore blurs the difference of virtual and real environments. We commence by highlighting the compelling use cases empowered by the IoS and also the key network requirements. We then elaborate on how the emerging semantic communications and Artificial Intelligence (AI)/Machine Learning (ML) paradigms along with 6G technologies may satisfy the requirements of IoS use cases. On one hand, semantic communications can be applied for extracting meaningful and significant information and hence efficiently exploit the resources and for harnessing a priori information at the receiver to satisfy IoS requirements. On the other hand, AI/ML facilitates frugal network resource management by making use of the enormous amount of data generated in IoS edge nodes and devices, as well as by optimizing the IoS performance via intelligent agents. However, the intelligent agents deployed at the edge are not completely aware of each others' decisions and the environments of each other, hence they operate in a partially rather than fully observable environment. Therefore, we present a case study of Partially Observable Markov Decision Processes (POMDP) for improving the User Equipment (UE) throughput and energy consumption, as they are imperative for IoS use cases, using Reinforcement Learning for astutely activating and deactivating the component carriers in carrier aggregation. Finally, we outline the challenges and open issues of IoS implementations and employing semantic communications, edge intelligence as well as learning under partial observability in the IoS context.

NISep 16, 2022
Toward Safe and Accelerated Deep Reinforcement Learning for Next-Generation Wireless Networks

Ahmad M. Nagib, Hatem Abou-zeid, Hossam S. Hassanein

Deep reinforcement learning (DRL) algorithms have recently gained wide attention in the wireless networks domain. They are considered promising approaches for solving dynamic radio resource management (RRM) problems in next-generation networks. Given their capabilities to build an approximate and continuously updated model of the wireless network environments, DRL algorithms can deal with the multifaceted complexity of such environments. Nevertheless, several challenges hinder the practical adoption of DRL in commercial networks. In this article, we first discuss two key practical challenges that are faced but rarely tackled when developing DRL-based RRM solutions. We argue that it is inevitable to address these DRL-related challenges for DRL to find its way to RRM commercial solutions. In particular, we discuss the need to have safe and accelerated DRL-based RRM solutions that mitigate the slow convergence and performance instability exhibited by DRL algorithms. We then review and categorize the main approaches used in the RRM domain to develop safe and accelerated DRL-based solutions. Finally, a case study is conducted to demonstrate the importance of having safe and accelerated DRL-based RRM solutions. We employ multiple variants of transfer learning (TL) techniques to accelerate the convergence of intelligent radio access network (RAN) slicing DRL-based controllers. We also propose a hybrid TL-based approach and sigmoid function-based rewards as examples of safe exploration in DRL-based RAN slicing.

NISep 13, 2023
Safe and Accelerated Deep Reinforcement Learning-based O-RAN Slicing: A Hybrid Transfer Learning Approach

Ahmad M. Nagib, Hatem Abou-Zeid, Hossam S. Hassanein

The open radio access network (O-RAN) architecture supports intelligent network control algorithms as one of its core capabilities. Data-driven applications incorporate such algorithms to optimize radio access network (RAN) functions via RAN intelligent controllers (RICs). Deep reinforcement learning (DRL) algorithms are among the main approaches adopted in the O-RAN literature to solve dynamic radio resource management problems. However, despite the benefits introduced by the O-RAN RICs, the practical adoption of DRL algorithms in real network deployments falls behind. This is primarily due to the slow convergence and unstable performance exhibited by DRL agents upon deployment and when encountering previously unseen network conditions. In this paper, we address these challenges by proposing transfer learning (TL) as a core component of the training and deployment workflows for the DRL-based closed-loop control of O-RAN functionalities. To this end, we propose and design a hybrid TL-aided approach that leverages the advantages of both policy reuse and distillation TL methods to provide safe and accelerated convergence in DRL-based O-RAN slicing. We conduct a thorough experiment that accommodates multiple services, including real VR gaming traffic to reflect practical scenarios of O-RAN slicing. We also propose and implement policy reuse and distillation-aided DRL and non-TL-aided DRL as three separate baselines. The proposed hybrid approach shows at least: 7.7% and 20.7% improvements in the average initial reward value and the percentage of converged scenarios, and a 64.6% decrease in reward variance while maintaining fast convergence and enhancing the generalizability compared with the baselines.

NIJan 20, 2023
Accelerating and Compressing Deep Neural Networks for Massive MIMO CSI Feedback

Omar Erak, Hatem Abou-Zeid

The recent advances in machine learning and deep neural networks have made them attractive candidates for wireless communications functions such as channel estimation, decoding, and downlink channel state information (CSI) compression. However, most of these neural networks are large and inefficient making it a barrier for deployment in practical wireless systems that require low-latency and low memory footprints for individual network functions. To mitigate these limitations, we propose accelerated and compressed efficient neural networks for massive MIMO CSI feedback. Specifically, we have thoroughly investigated the adoption of network pruning, post-training dynamic range quantization, and weight clustering to optimize CSI feedback compression for massive MIMO systems. Furthermore, we have deployed the proposed model compression techniques on commodity hardware and demonstrated that in order to achieve inference gains, specialized libraries that accelerate computations for sparse neural networks are required. Our findings indicate that there is remarkable value in applying these model compression techniques and the proposed joint pruning and quantization approach reduced model size by 86.5% and inference time by 76.2% with minimal impact to model accuracy. These compression methods are crucial to pave the way for practical adoption and deployments of deep learning-based techniques in commercial wireless systems.

NIAug 22, 2023
Using Early Exits for Fast Inference in Automatic Modulation Classification

Elsayed Mohammed, Omar Mashaal, Hatem Abou-Zeid

Automatic modulation classification (AMC) plays a critical role in wireless communications by autonomously classifying signals transmitted over the radio spectrum. Deep learning (DL) techniques are increasingly being used for AMC due to their ability to extract complex wireless signal features. However, DL models are computationally intensive and incur high inference latencies. This paper proposes the application of early exiting (EE) techniques for DL models used for AMC to accelerate inference. We present and analyze four early exiting architectures and a customized multi-branch training algorithm for this problem. Through extensive experimentation, we show that signals with moderate to high signal-to-noise ratios (SNRs) are easier to classify, do not require deep architectures, and can therefore leverage the proposed EE architectures. Our experimental results demonstrate that EE techniques can significantly reduce the inference speed of deep neural networks without sacrificing classification accuracy. We also thoroughly study the trade-off between classification accuracy and inference time when using these architectures. To the best of our knowledge, this work represents the first attempt to apply early exiting methods to AMC, providing a foundation for future research in this area.

SPNov 15, 2024
Building 6G Radio Foundation Models with Transformer Architectures

Ahmed Aboulfotouh, Ashkan Eshaghbeigi, Hatem Abou-Zeid

Foundation deep learning (DL) models are general models, designed to learn general, robust and adaptable representations of their target modality, enabling finetuning across a range of downstream tasks. These models are pretrained on large, unlabeled datasets using self-supervised learning (SSL). Foundation models have demonstrated better generalization than traditional supervised approaches, a critical requirement for wireless communications where the dynamic environment demands model adaptability. In this work, we propose and demonstrate the effectiveness of a Vision Transformer (ViT) as a radio foundation model for spectrogram learning. We introduce a Masked Spectrogram Modeling (MSM) approach to pretrain the ViT in a self-supervised fashion. We evaluate the ViT-based foundation model on two downstream tasks: Channel State Information (CSI)-based Human Activity sensing and Spectrogram Segmentation. Experimental results demonstrate competitive performance to supervised training while generalizing across diverse domains. Notably, the pretrained ViT model outperforms a four-times larger model that is trained from scratch on the spectrogram segmentation task, while requiring significantly less training time, and achieves competitive performance on the CSI-based human activity sensing task. This work demonstrates the effectiveness of ViT with MSM for pretraining as a promising technique for scalable foundation model development in future 6G networks.

SPApr 18, 2025
6G WavesFM: A Foundation Model for Sensing, Communication, and Localization

Ahmed Aboulfotouh, Elsayed Mohammed, Hatem Abou-Zeid

This paper introduces WavesFM, a novel Wireless Foundation Model (WFM) framework, capable of supporting a wide array of communication, sensing, and localization tasks. Our proposed architecture combines a shared Vision Transformer (ViT) backbone with task-specific multi-layer perceptron (MLP) heads and incorporates Low-Rank Adaptation (LoRA) for parameter-efficient fine-tuning. This design promotes full parameter sharing across tasks, significantly reducing the computational and memory footprint without sacrificing performance. The model processes both image-like wireless modalities, such as spectrograms and channel state information (CSI), and in-phase and quadrature (IQ) signals arranged as orthogonal frequency-division multiplexing (OFDM) resource grids. We demonstrate the strong generalization capabilities of WavesFM through extensive experiments on four downstream tasks: Fifth Generation New Radio (5G NR) positioning; multiple-input multiple-output OFDM (MIMO-OFDM) channel estimation; human activity sensing; and radio-frequency (RF) signal classification. Compared to supervised baselines trained individually, our approach achieves superior performance while sharing 80% of its parameters across tasks. Furthermore, we show that pretraining on domain-relevant data not only boosts performance but also accelerates convergence, reducing training time by up to 5x. These results demonstrate that our unified WFM can support diverse tasks and deliver significant gains in both performance and efficiency, highlighting the transformative potential of foundation models to drive AI-native paradigms in future sixth-generation (6G) networks.

SPNov 14, 2024
Self-Supervised Radio Pre-training: Toward Foundational Models for Spectrogram Learning

Ahmed Aboulfotouh, Ashkan Eshaghbeigi, Dimitrios Karslidis et al.

Foundational deep learning (DL) models are general models, trained on large, diverse, and unlabelled datasets, typically using self-supervised learning techniques have led to significant advancements especially in natural language processing. These pretrained models can be fine-tuned for related downstream tasks, offering faster development and reduced training costs, while often achieving improved performance. In this work, we introduce Masked Spectrogram Modeling, a novel self-supervised learning approach for pretraining foundational DL models on radio signals. Adopting a Convolutional LSTM architecture for efficient spatio-temporal processing, we pretrain the model with an unlabelled radio dataset collected from over-the-air measurements. Subsequently, the pretrained model is fine-tuned for two downstream tasks: spectrum forecasting and segmentation. Experimental results demonstrate that our methodology achieves competitive performance in both forecasting accuracy and segmentation, validating its effectiveness for developing foundational radio models.

LGSep 12, 2025
Adaptive Token Merging for Efficient Transformer Semantic Communication at the Edge

Omar Erak, Omar Alhussein, Hatem Abou-Zeid et al.

Large-scale transformers are central to modern semantic communication, yet their high computational and communication costs hinder deployment on resource-constrained edge devices. This paper introduces a training-free framework for adaptive token merging, a novel mechanism that compresses transformer representations at runtime by selectively merging semantically redundant tokens under per-layer similarity thresholds. Unlike prior fixed-ratio reduction, our approach couples merging directly to input redundancy, enabling data-dependent adaptation that balances efficiency and task relevance without retraining. We cast the discovery of merging strategies as a multi-objective optimization problem and leverage Bayesian optimization to obtain Pareto-optimal trade-offs between accuracy, inference cost, and communication cost. On ImageNet classification, we match the accuracy of the unmodified transformer with 30\% fewer floating-point operations per second and under 20\% of the original communication cost, while for visual question answering our method achieves performance competitive with the full LLaVA model at less than one-third of the compute and one-tenth of the bandwidth. Finally, we show that our adaptive merging is robust across varying channel conditions and provides inherent privacy benefits, substantially degrading the efficacy of model inversion attacks. Our framework provides a practical and versatile solution for deploying powerful transformer models in resource-limited edge intelligence scenarios.

LGMar 21, 2024
Advancing IIoT with Over-the-Air Federated Learning: The Role of Iterative Magnitude Pruning

Fazal Muhammad Ali Khan, Hatem Abou-Zeid, Aryan Kaushik et al.

The industrial Internet of Things (IIoT) under Industry 4.0 heralds an era of interconnected smart devices where data-driven insights and machine learning (ML) fuse to revolutionize manufacturing. A noteworthy development in IIoT is the integration of federated learning (FL), which addresses data privacy and security among devices. FL enables edge sensors, also known as peripheral intelligence units (PIUs) to learn and adapt using their data locally, without explicit sharing of confidential data, to facilitate a collaborative yet confidential learning process. However, the lower memory footprint and computational power of PIUs inherently require deep neural network (DNN) models that have a very compact size. Model compression techniques such as pruning can be used to reduce the size of DNN models by removing unnecessary connections that have little impact on the model's performance, thus making the models more suitable for the limited resources of PIUs. Targeting the notion of compact yet robust DNN models, we propose the integration of iterative magnitude pruning (IMP) of the DNN model being trained in an over-the-air FL (OTA-FL) environment for IIoT. We provide a tutorial overview and also present a case study of the effectiveness of IMP in OTA-FL for an IIoT environment. Finally, we present future directions for enhancing and optimizing these deep compression techniques further, aiming to push the boundaries of IIoT capabilities in acquiring compact yet robust and high-performing DNN models.

LGSep 11, 2025
Adaptive Pareto-Optimal Token Merging for Edge Transformer Models in Semantic Communication

Omar Erak, Omar Alhussein, Hatem Abou-Zeid et al.

Large-scale transformer models have emerged as a powerful tool for semantic communication systems, enabling edge devices to extract rich representations for robust inference across noisy wireless channels. However, their substantial computational demands remain a major barrier to practical deployment in resource-constrained 6G networks. In this paper, we present a training-free framework for adaptive token merging in pretrained vision transformers to jointly reduce inference time and transmission resource usage. We formulate the selection of per-layer merging proportions as a multi-objective optimization problem to balance accuracy and computational cost. We employ Gaussian process-based Bayesian optimization to construct a Pareto frontier of optimal configurations, enabling flexible runtime adaptation to dynamic application requirements and channel conditions. Extensive experiments demonstrate that our method consistently outperforms other baselines and achieves significant reductions in floating-point operations while maintaining competitive accuracy across a wide range of signal-to-noise ratio (SNR) conditions. Additional results highlight the effectiveness of adaptive policies that adjust merging aggressiveness in response to channel quality, providing a practical mechanism to trade off latency and semantic fidelity on demand. These findings establish a scalable and efficient approach for deploying transformer-based semantic communication in future edge intelligence systems.

SPNov 19, 2025
Multimodal Wireless Foundation Models

Ahmed Aboulfotouh, Hatem Abou-Zeid

Wireless foundation models (WFMs) have recently demonstrated promising capabilities, jointly performing multiple wireless functions and adapting effectively to new environments. However, while current WFMs process only one modality, depending on the task and operating conditions, the most informative modality changes and no single modality is best for all tasks. WFMs should therefore be designed to accept multiple modalities to enable a broader and more diverse range of tasks and scenarios. In this work, we propose and build the first multimodal wireless foundation model capable of processing both raw IQ streams and image-like wireless modalities (e.g., spectrograms and CSI) and performing multiple tasks across both. We introduce masked wireless modeling for the multimodal setting, a self-supervised objective and pretraining recipe that learns a joint representation from IQ streams and image-like wireless modalities. We evaluate the model on five tasks across both modality families: image-based (human activity sensing, RF signal classification, 5G NR positioning) and IQ-based (RF device fingerprinting, interference detection/classification). The multimodal WFM is competitive with single-modality WFMs, and in several cases surpasses their performance. Our results demonstrates the strong potential of developing multimodal WFMs that support diverse wireless tasks across different modalities. We believe this provides a concrete step toward both AI-native 6G and the vision of joint sensing, communication, and localization.

NIMar 17, 2025
SafeSlice: Enabling SLA-Compliant O-RAN Slicing via Safe Deep Reinforcement Learning

Ahmad M. Nagib, Hatem Abou-Zeid, Hossam S. Hassanein

Deep reinforcement learning (DRL)-based slicing policies have shown significant success in simulated environments but face challenges in physical systems such as open radio access networks (O-RANs) due to simulation-to-reality gaps. These policies often lack safety guarantees to ensure compliance with service level agreements (SLAs), such as the strict latency requirements of immersive applications. As a result, a deployed DRL slicing agent may make resource allocation (RA) decisions that degrade system performance, particularly in previously unseen scenarios. Real-world immersive applications require maintaining SLA constraints throughout deployment to prevent risky DRL exploration. In this paper, we propose SafeSlice to address both the cumulative (trajectory-wise) and instantaneous (state-wise) latency constraints of O-RAN slices. We incorporate the cumulative constraints by designing a sigmoid-based risk-sensitive reward function that reflects the slices' latency requirements. Moreover, we build a supervised learning cost model as part of a safety layer that projects the slicing agent's RA actions to the nearest safe actions, fulfilling instantaneous constraints. We conduct an exhaustive experiment that supports multiple services, including real virtual reality (VR) gaming traffic, to investigate the performance of SafeSlice under extreme and changing deployment conditions. SafeSlice achieves reductions of up to 83.23% in average cumulative latency, 93.24% in instantaneous latency violations, and 22.13% in resource consumption compared to the baselines. The results also indicate SafeSlice's robustness to changing the threshold configurations of latency constraints, a vital deployment scenario that will be realized by the O-RAN paradigm to empower mobile network operators (MNOs).

NISep 1, 2023
How Does Forecasting Affect the Convergence of DRL Techniques in O-RAN Slicing?

Ahmad M. Nagib, Hatem Abou-Zeid, Hossam S. Hassanein

The success of immersive applications such as virtual reality (VR) gaming and metaverse services depends on low latency and reliable connectivity. To provide seamless user experiences, the open radio access network (O-RAN) architecture and 6G networks are expected to play a crucial role. RAN slicing, a critical component of the O-RAN paradigm, enables network resources to be allocated based on the needs of immersive services, creating multiple virtual networks on a single physical infrastructure. In the O-RAN literature, deep reinforcement learning (DRL) algorithms are commonly used to optimize resource allocation. However, the practical adoption of DRL in live deployments has been sluggish. This is primarily due to the slow convergence and performance instabilities suffered by the DRL agents both upon initial deployment and when there are significant changes in network conditions. In this paper, we investigate the impact of time series forecasting of traffic demands on the convergence of the DRL-based slicing agents. For that, we conduct an exhaustive experiment that supports multiple services including real VR gaming traffic. We then propose a novel forecasting-aided DRL approach and its respective O-RAN practical deployment workflow to enhance DRL convergence. Our approach shows up to 22.8%, 86.3%, and 300% improvements in the average initial reward value, convergence rate, and number of converged scenarios respectively, enhancing the generalizability of the DRL agents compared with the implemented baselines. The results also indicate that our approach is robust against forecasting errors and that forecasting models do not have to be ideal.

NIJun 29, 2021
Structure-aware reinforcement learning for node-overload protection in mobile edge computing

Anirudha Jitani, Aditya Mahajan, Zhongwen Zhu et al.

Mobile Edge Computing (MEC) refers to the concept of placing computational capability and applications at the edge of the network, providing benefits such as reduced latency in handling client requests, reduced network congestion, and improved performance of applications. The performance and reliability of MEC are degraded significantly when one or several edge servers in the cluster are overloaded. Especially when a server crashes due to the overload, it causes service failures in MEC. In this work, an adaptive admission control policy to prevent edge node from getting overloaded is presented. This approach is based on a recently-proposed low complexity RL (Reinforcement Learning) algorithm called SALMUT (Structure-Aware Learning for Multiple Thresholds), which exploits the structure of the optimal admission control policy in multi-class queues for an average-cost setting. We extend the framework to work for node overload-protection problem in a discounted-cost setting. The proposed solution is validated using several scenarios mimicking real-world deployments in two different settings - computer simulations and a docker testbed. Our empirical evaluations show that the total discounted cost incurred by SALMUT is similar to state-of-the-art deep RL algorithms such as PPO (Proximal Policy Optimization) and A2C (Advantage Actor Critic) but requires an order of magnitude less time to train, outputs easily interpretable policy, and can be deployed in an online manner.

ITMay 9, 2021
Delay-Tolerant Constrained OCO with Application to Network Resource Allocation

Juncheng Wang, Ben Liang, Min Dong et al.

We consider online convex optimization (OCO) with multi-slot feedback delay, where an agent makes a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that are possibly time-varying. The current convex loss function and the long-term constraint function are revealed to the agent only after the decision is made, and they may be delayed for multiple time slots. Existing work on OCO under this general setting has focused on the static regret, which measures the gap of losses between the online decision sequence and an offline benchmark that is fixed over time. In this work, we consider both the static regret and the more practically meaningful dynamic regret, where the benchmark is a time-varying sequence of per-slot optimizers. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel constraint penalty with double regularization to tackle the asynchrony between information feedback and decision updates. We derive upper bounds on its dynamic regret, static regret, and constraint violation, proving them to be sublinear under mild conditions. We further apply DTC-OCO to a general network resource allocation problem, which arises in many systems such as data networks and cloud computing. Simulation results demonstrate substantial performance gain of DTC-OCO over the known best alternative.

MMSep 3, 2014
Toward Green Media Delivery: Location-Aware Opportunities and Approaches

Hatem Abou-zeid, Hosssam S. Hassenein

Mobile media has undoubtedly become the predominant source of traffic in wireless networks. The result is not only congestion and poor Quality-of-Experience, but also an unprecedented energy drain at both the network and user devices. In order to sustain this continued growth, novel disruptive paradigms of media delivery are urgently needed. We envision that two key contemporary advancements can be leveraged to develop greener media delivery platforms: 1) the proliferation of navigation hardware and software in mobile devices has created an era of location-awareness, where both the current and future user locations can be predicted; and 2) the rise of context-aware network architectures and self-organizing functionalities is enabling context signaling and in-network adaptation. With these developments in mind, this article investigates the opportunities of exploiting location-awareness to enable green end-to-end media delivery. In particular, we discuss and propose approaches for location-based adaptive video quality planning, in-network caching, content prefetching, and long-term radio resource management. To provide insights on the energy savings, we then present a cross-layer framework that jointly optimizes resource allocation and multi-user video quality using location predictions. Finally, we highlight some of the future research directions for location-aware media delivery in the conclusion.

NIMar 31, 2014
Energy-Efficient Adaptive Video Transmission: Exploiting Rate Predictions in Wireless Networks

Hatem Abou-zeid, Hossam S. Hassanein, Stefan Valentin

The unprecedented growth of mobile video traffic is adding significant pressure to the energy drain at both the network and the end user. Energy efficient video transmission techniques are thus imperative to cope with the challenge of satisfying user demand at sustainable costs. In this paper, we investigate how predicted user rates can be exploited for energy efficient video streaming with the popular HTTP-based Adaptive Streaming (AS) protocols (e.g. DASH). To this end, we develop an energy-efficient Predictive Green Streaming (PGS) optimization framework that leverages predictions of wireless data rates to achieve the following objectives 1) minimize the required transmission airtime without causing streaming interruptions, 2) minimize total downlink Base Station (BS) power consumption for cases where BSs can be switched off in deep sleep, and 3) enable a trade-off between AS quality and energy consumption. Our framework is first formulated as a Mixed Integer Linear Program (MILP) where decisions on multi-user rate allocation, video segment quality, and BS transmit power are jointly optimized. Then, to provide an online solution, we present a polynomial-time heuristic algorithm that decouples the PGS problem into multiple stages. We provide a performance analysis of the proposed methods by simulations, and numerical results demonstrate that the PGS framework yields significant energy savings.