Decentralized Multi-Channel MANET Power Optimization Using Graph Neural Networks
arXiv:2605.12612v1 [cs.NI] 12 May 2026
Tomer Alter, Nir Shlezinger, and Michael Segal
Abstract—The increasing demand for mobile ad hoc networks (MANETs) calls for decentralized mechanisms that can allocate transmit power across nodes and channels under stringent resource constraints. Existing optimization-based approaches, however, do not account for expected settings where each link includes multiple channels (e.g., multi-band signaling). Motivated by recent advances in machine learning for distributed optimization, we propose MANETGNN, a graph neural network (GNN)-based algorithm for decentralized power allocation in multi-channel MANETs. MANET-GNN explicitly exploits the network topology, scales efficiently with the number of nodes and frequency bands, generalizes across topologies and channel conditions, and enables near-instantaneous inference suitable for real-time deployment. Our design builds on a constrained optimization formulation and employs a dedicated GNN architecture inspired by message passing, trained via an unsupervised procedure that is robust to noisy channel state information. Numerical evaluations demonstrate that MANET-GNN achieves high-throughput multi-channel communication across diverse MANET scenarios. Index Terms—GNNs, decentralized optimization, MANET.
I. I NTRODUCTION Mobile ad hoc network (MANET) is a popular framework for studying and developing flexible decentralized communication systems without fixed infrastructure [1]. Their ability to selforganize and adapt makes them attractive for a wide range of applications, including vehicular communications, industrial IoT, emergency response networks, and tactical operations. In these scenarios, devices must dynamically form multi-hop topologies and collaboratively manage shared wireless resources under strict latency and energy constraints [2]. In various MANET technologies, communication is enabled via multiple channels for each link, either due to heterogeneous communication technologies, spectrum partitioning, or the availability of orthogonal frequency bands [3]–[5]. While leveraging multiple channels can significantly improve throughput and reliability, it also introduces new challenges. Since MANET devices are often power-limited and operate in rapidly changing environments, efficient allocation of transmit power across both links and channels becomes critical for maintaining high spectral efficiency and reliable connectivity. However, the successful exploitation of multi-channel diversity requires dedicated mechanisms for distributed power allocation that can scale to large networks. The authors are with the ECE School, Ben-Gurion University of the Negev, Israel (e-mail: [email protected]; {nirshl; segal}@bgu.ac.il). The work of this paper has been partially funded by Israeli Science Foundation (Grant No. 465/22), US Army Research Office under Grant Number W911NF-22-1-0225, and the European Research Council (ERC) under the ERC starting grant nr. 101163973 (FLAIR).
A wide variety of optimization-based solutions have been proposed to address the problem of power allocation in MANETs [6]. These methods span multiple categories, including adaptations of radio state operational modes [7], [8], adaptive load balancing [9], location- and multicast-based routing [10], [11], and cross-layer optimization frameworks [12]. Despite their diversity, most of these works have been developed under the assumption of single-channel MANETs, where each link operates over a single communication resource. Consequently, they do not naturally extend to the multi-channel setting, where each link may exploit multiple subcarriers or physical channels. This limitation highlights the need for decentralized optimization frameworks that can effectively scale to the more demanding multi-channel MANET scenario. The growing success of deep learning has led to an alternative paradigm for tackling challenging distributed processing tasks using data-driven tools. A popular framework is distributed reinforcement learning, in which each agent is equipped with a local deep neural network (DNN) trained to autonomously adjust its decisions for decentralized resource allocation [13], [14]. However, such approaches typically treat nodes independently and remain agnostic to the underlying graph structures, thereby limiting their ability to generalize across unseen network topologies. An alternative direction is the learn-to-optimize paradigm [15], which casts tasks such as resource allocation as an optimization problem and trains DNN or unfolded optimizers to rapidly generate valid solutions. This paradigm has shown success in centralized resource allocation problems [16] as well as in decentralized consensus optimization [17]. In the context of decentralized processing of graph signals, graph neural networks (GNNs) have been demonstrated to provide graph-aware architectures that can be trained for distributed optimization, with architectures designed for power allocation in single-channel settings [18], over-the-air aggregation [19], link sparsification [20], and wireless federated learning enhancement [21]. These advances motivate the adaptation of GNN-based optimization methodologies to the challenging scenario of distributed resource allocation in multi-channel MANETs. In this work, we develop a GNN-based algorithm, termed MANET-GNN, for decentralized power allocation in multichannel MANETs. Our design (i) explicitly exploits the graph topology of the network to capture the structured interactions among nodes; (ii) scales efficiently with both the number of devices and the available frequency bands; (iii) generalizes across different network topologies and channel conditions, and
(iv) enables near-instantaneous inference, making it suitable for real-time deployment in dynamic MANET environments. Inspired by learned optimization techniques [22], our approach begins by formulating the multi-channel resource allocation problem as a constrained optimization task, aiming to maximize throughput between a given transmitter–receiver pair in the MANET. While this optimization problem is inherently non-convex and requires a centralized solver, we leverage it to guide the training of our dedicated MANET-GNN architecture that requires solely local channel state information (CSI), while being inherently amenable to distributed execution over varying graphs and channel conditions. Our unsupervised training procedure facilitates learning based on the optimization objective by incorporating a dedicated smooth-min approximation. We then conduct numerical evaluations, demonstrating that MANET-GNN consistently enables high-throughput multichannel communication across diverse MANET topologies, achieving performance that is competitive with fully centralized optimization while operating in a fully decentralized manner. The remainder of this paper is organized as follows: Section II introduces the system model and problem formulation; Section III presents the proposed decentralized learned optimization framework, which we evaluate in Section IV. Finally, Section V concludes the paper.
Fig. 1: Multi-channel MANET, B = 3, |V| = 5. TABLE I: Key variables and parameters Symbol (b) wi→j (t) (b) hi→j (t) (b) pi→j (t) (b) si (t) N (j)
Definition AWGN noise at link (i, j) on channel b Channel coefficient between nodes i and j on channel b Power allocated by node i to node j on channel b Transmitted signal from node i on channel b Set of neighboring nodes of node j
B. Power Allocation II. S YSTEM M ODEL We aim to determine the power allocation across B frequency (b) In this section, we formulate the system model for bands for all links in the MANET (i.e., {pi→j (t)} for all multi-channel MANETs. We commence with presenting the (i, j) ∈ E), such that the end-to-end communication rate between communication system in Subsection II-A, and formulate the the source and destination is maximized while satisfying per-node decentralized power allocation optimization problem in Subsecpower constraints. We next cast this task as an optimization settion II-B, which constitutes the starting point for MANET-GNN. ting, based on which we formulate our power allocation problem. A. Communication System Model We consider a block-fading multi-hop MANET with reciprocal links comprised of B channels (e.g., multiple physical channels, or multi-carrier signaling). We model the network topology as an undirected graph G = (V, E), where V represents the set of nodes and E represents the set of wireless links. In each block of index t, a link (i, j) ∈ E is represented using a B × 1 vector (1) (B) (b) [hi→j (t), . . . , hi→j (t)], with hi→j (t) ∈ C being the realization of the bth channel in the link. In each block t, one node uTx ∈ V acts as the source and another uRx ∈ V as the destination, while the remaining nodes serve as relays (see Fig. 1). Both the wireless channels and the network topology vary over time in a blockwise manner, capturing the dynamic nature of ad hoc networks. (b) Let yi→j (t) denote the received signal over link (i, j) ∈ E on channel b during block t. The received signal is given by (b)
(b)
(b)
(b)
(b)
yi→j (t) = hi→j (t) pi→j (t) si (t) + wi→j (t), (b)
(1)
1) Constrained Optimization: Since we operate on a signal block, we next omit the block index t for brevity, and stack the power allocation as the B × |V| × |V| tensor P , with [P ]b,i,j = (b) pi→j . For a given frequency band b and link (i → j) ∈ E, the achievable rate for the AWGN channel in (1) is given by: ! (b) 2 (b) 2 hi→j pi→j (b) Ri→j = log2 1 + . (2) σb2 Let Φb denote the set of all available paths between the source and destination on band b. A path ϕ ∈ Φb is defined as an ordered sequence of edges connecting the source to the destination in the graph G, where an edge (i → j) exists only (b) if hi→j > 0. The achievable rate of a path ϕ on band b is (b) (b) determined by its bottleneck link, i.e., Rϕ = min Ri→j . (i→j)∈ϕ
We impose two constraints on the transmit powers: •
Per-node power limit: the overall power allocated by PB P (b) 2 each node i ∈ V holds b=1 (j)∈N (i) pi→j ≤ 1.
where si (t) is the unit amplitude signal transmitted by the (b) • Non-negativity: all settings hold pi→j ≥ 0. (b) ith node on channel b, while wi→j (t) ∼ CN (0, σb2 ) is additive white Gaussian noise (AWGN). For convenience, the key Accordingly, we formulate the task of power allocation variables used in the system model are summarized in Table I. for optimizing end-to-end communications in multi-channel
MANETs as the following optimization problem P ⋆ = argmax P ∈P
B X b=1
max
(b)
min Ri→j ,
ϕ∈Φb (i→j)∈ϕ
A. MANET-GNN (3)
where the feasible set of power allocations is defined as: n o P = P ∈ [0, 1]B×n×n : [P ]:,i,: 2 ≤ 1, ∀i ∈ V . (4) The formulation in (3) allows the usage of different paths in different channels (as the path with the highest rate ϕ ∈ Φb is selected in each channel b). 2) Problem Formulation: Our goal is to design a policy for setting the power allocations P based on the formulated optimization objective in (3). While the power allocation problem in (3) is formulated as a centralized optimization setting, i.e., a mapping (b) of the full MANET CSI {hi→j }(i,j)∈E,b∈{1,...B} into P ⋆ , we aim to design a method that meets the following requirements: R1 Decentralized operation, i.e., each node i sets its own (b) (b) {pi→j } based on its local CSI {ĥi→j }(j)∈N (i),b∈{1,...B} . R2 Limited latency optimization, where each node i is allowed to exchange at most L messages with its neighbors N (i). R3 The method should be applicable on different topologies. (b) R4 The local CSI {ĥi→j }(j)∈N (i),b∈{1,...B} , may be a noisy estimate of the actual CSI. To cope with R1-R4, we assume access to CSI from various MANETs during design, represented by the data set n o|D| (b) D = {hi→j,d }(i,j)∈Ed ,b∈{1,...B} , Gd = (Vd , Ed ) . (5)
1) Gated GNN: Our main building block is a learned message passing module, which updates each node’s local embedding based on a single round of information exchange with its neighbors. While generic message passing networks treat all neighbors equally, we utilize a gated GNN layer that accounts for per-link channel states, allowing the model to prioritize stronger or weaker links per channel adaptively. Features: The lth gated GNN layer (implementing the lth message exchange round), applied at the ith node, processes its (l) local node features, denoted xi , and outgoing edge features, (l) denoted {ei→j }j∈N (i) . It uses these features to generate (l) messages to all its neighbors, denoted {mi→j ∈ RB }j∈N (i) , and generate updated B × 1 node and edge features, respectively (l+1) (l+1) denoted xi and {ei→j }j∈N (i) . Architecture: The layer is comprised of: (l) (l) 1) An encoder with parameters θe that maps xi and (l) (l+1) {ei→j } into (i) updated edge features {ei→j } using layer normalization and an edge-gated fully-connected (FC) layer with a learnable sigmoid gate; and (ii) a set of (l) messages {mi→j }j∈N (i) using subsequent Feature-wise Linear Modulation (FiLM) [27]. (l) 2) An aggregator with parameters θa that combines the (l) received messages {mj→i }j∈N (i) and applies an FC layer (l+1) to obtain residual update of the node features into xi , (l)
(l)
The encoder θe and aggregator θa are shared by all nodes. 2) Overall Algorithm: The overall algorithm consists d=1 of stacking L − 1 gated GNN layers with dedicated input Note that (5) does not contain ’ground-truth’ allocations, and that pre-processing. The output of these layers is fed to a shared its CSIs come from different MANETs with different topologies. decoder that produces the final per-link per-band power (b) allocations {pi→j } using one last message exchange round. The full architecture is illustrated in Fig. 2. III. D ECENTRALIZED L EARNED O PTIMIZATION Input Processing: While the node and edge features generated In this section, we present our proposed decentralized learned by each layer are B × 1 vectors, the initial values have different optimization framework. To address the challenging requirements dimensions to embed the required information. Specifically, each (1) R1–R4, we propose to tune the power allocation policy by initial edge feature vector ei→j is obtained by stacking the real B leveraging the optimization formulation in (3) through learned and imaginary parts of the estimated link CSI, {ĥ(b) i→j }b=1 . The optimization tools. Our design builds upon the recent empirical input node-features are B + 3 × 1 vectors, whose first B entries success of GNNs in solving learned optimization tasks [13], are set to an initial power division, while the remaining 3 entries [23], exploiting their inherent ability to operate in a decentralized form a one-hot encoding of the role of node i (Tx, Rx, or relay). manner (R1) while naturally adapting to different network Output Processing: Every node performs L − 1 rounds of topologies (R3) [24]. Specifically, we introduce a dedicated decentralized message passing with its neighbors, thus updating GNN architecture, termed MANET-GNN, that is inspired by its local embedding. After these rounds, each node broadcasts message-passing networks [25] and explicitly constrains the its final embedding once to its direct neighbors. Then for each number of message exchanges to meet the latency requirement in (i → j), the node i applies a decoder, comprised of an FC layer R2 (see Subsection III-A). Furthermore, to enhance robustness with B outputs and softplus activation, whose parameters are under imperfect channel knowledge as noted in R4, we devise in denoted by θd , to the concatenation of the final edge embedding (L) (L) Subsection III-B an unsupervised training procedure that directly and the endpoint embeddings, i.e., to [e(L) ∥ xj ]. The i→j ∥ xi optimizes the power allocation objective as a discriminative resulting non-negative B × 1 vectors are normalized over all machine learning model [26] while accounting for the expected edges to produce the local power allocation [P ]:,i,: . noisiness of the local CSI. This design yields a principled framework that not only aligns with the optimization formulation B. Training Our training procedure of MANET-GNN tunes the weights but also satisfies the practical requirements of decentralized (l) (l) and real-time operation in multi-channel MANETs. θ = [θd , {θa , θe }L−1 l=1 ], based on the unlabeled data (5) and
Fig. 2: MANET-GNN architecture block diagram. the optimization objective in (3). To enable unsupervised learning using standard gradient-based training methods, we utilize a relaxation of the objective (3), and formulate an optimization-oriented loss measure, combined with a noisy-CSI-aware training scheme. Relaxed Objective: The objective in (3) includes a min operator over all links which limits accounting for the entire MANET in training. To mitigate this effect on gradient-based training, we utilize a surrogate rate objective, defined as (b)
R̃(P ; {hi→j }) =
B X
(b)
max smin(i→j)∈ϕ Ri→j ,
(6)
where smin is the smooth-min operator, defined as X sminτ {sk } = −τ log exp − sτk , τ > 0,
(7)
b=1
ϕ∈Φb
the loss terms using the true CSI), as a form of adversarial learned optimization [29]. The overall training procedure based on stochastic gradient descent is summarized as Algorithm 1. Algorithm 1: Training MANET-GNN Init : Initial parameters θ; # batches Q; noise σ; Learning rate η; hyperparameters δ, L, λ Input : Training set D 1 for epoch = 0, 1, . . . , epochmax − 1 do 2 Randomly divide D into Q batches {Dq }Q q=1 ; 3 for q = 1, . . . , Q do (b) 4 Apply GNN θ to {hi→j,d }d∈Dq + CN (0, σ 2 ); 5 Compute loss LDq via (10); 6 Update θ ← θ − η∇θ LDq (θ);
k
which converges to the true minimum as τ → 0+ . Loss: Our loss balances two aspects arising from viewing MANET-GNN as a learned optimization solver. The first term evaluates it based on the surrogate rate at its output, i.e., −1 Lrate D (θ) =
|D|
|D| X
(L−1)
R̃(Pd
(b)
(θ); {hi→j,d }),
(8)
d=1
(l)
where Pd (θ) is the power allocation obtained by applying the decoder θd to the output of the lth gated GNN layer in MANET-GNN applied to the dth sample. The second loss term treats MANET-GNN as a decentralized descent method optimizer, in which each message passing round should monotonically increase the resulting rate. This form of regularization is known to facilitate and stabilize learning of DNN-aided optimizers [28]. The resulting loss term is given by |D| L−2 X X −1 Lmono (θ) = ReLU δ− D |D|(L − 2) d=1 l=1 (l+1) (b) (l) (b) R̃(Pd (θ); {hi→j,d })− R̃(Pd (θ); {hi→j,d }) , (9) where δ is a hyperparameter that enforces a positive margin. Noisy-CSI-Aware Training: The formulation of the loss terms in (8)-(9) combined with the surrogate objective in (6) enables training MANET-GNN using standard gradient-based learning, with an overall loss of the form mono LD (θ) = Lrate (θ), D (θ) + λLD
(10)
where λ is a regularization coefficient. Following [16], we enhance robustness and the ability to cope with noisy CSI by providing the model noisy CSI during training (while computing
7
(l)
(l)
return θ = [θd , {θe , θa }L−1 l=1 ]
C. Discussion The proposed MANET-GNN framework provides a principled mechanism for meeting the requirements R1-R4. First, its decentralized message-passing design inherently ensures that each node sets its local power allocations based solely on its local CSI, thus satisfying R1. The explicit limitation on the number of messagepassing rounds guarantees bounded latency and communication overhead, directly addressing R2. The use of GNNs further enables generalization across unseen network topologies (R3) while the noisy CSI-aware training in Algorithm 1 equips the model with robustness to estimated CSI errors (R4). Several follow-up directions naturally arise from this work. One can potentially expand the optimization task beyond power allocation to also include channel assignment among users, thereby adapting the design to distributed OFDMA systems. Another interesting aspect concerns the optimization objective in (3), which assumes the common setting where different messages are encoded across different channels. Extending the framework to scenarios where relays can re-encode or combine messages across channels would require reformulating the objective and adapting the architecture accordingly, which we leave for future research. IV. E XPERIMENTAL S TUDY A. Experimental Setup We evaluate MANET-GNN in MANETs with |V| = 10 nodes, with B = 6 channels per-link representing orthogonal frequency division multiplexing (OFDM) signaling with B subbands1 . 1 The source code used in our empirical study, along with the hyperparameters is available at https://github.com/AlterTomer/Decentralized-MANET
B. Results Full CSI: Fig. 3a reports the average achievable rate as a function of the signal-to-noise ratio (SNR) under full CSI availability. The proposed MANET-GNN consistently outperforms B3 in the low- and medium-SNR regimes, and achieves comparable performance in the high-SNR regime. It achieves approximately 85% of the rate achieved by the centralized solver B2, while requiring only a fixed number L of local message-passing rounds and no global CSI. The naive equal-split baseline B4 yields the lowest rates across all regimes, highlighting the necessity of topology and channel-aware coordination. Noisy CSI: We next evaluate the ability of MANET-GNN to cope with noisy CSI estimates R4. To that aim, we utilize its noisy CSI-aware training, in which the forward pass uses noisy (a) Rayleigh fading, full CSI. CSI, obtained via linear minimum mean-squared error channel estimation using 4 pilots for each subband, while the loss is calculated with the corresponding true CSI. The resulting rate versus SNR is reported in Fig. 3b. There, we observe that our MANET-GNN decentralized optimizer handles well estimated CSI as it achieves ∼ 80 − 85% of the achievable rate compared to the centralized optimizer and ∼ 35 − 40% improvement from the best single channel search, when operating with noisy CSI. In Fig. 3b the algorithms are provided with noisy CSI, which MANET-GNN learns to cope with well in its training procedure in Algorithm 1. To show that its noisy CSI-aware training does not notably degrade its performance when the trained MANET-GNN is provided with accurate CSI, we report in Table II the mean rates achieved when MANET-GNN is tested with true full CSI while trained with either noisy (estimated) CSI or with full (true) CSI. We note in Table II that our (b) Rayleigh fading, noisy CSI. noisy CSI-aware training, which was shown in Fig. 3b to Fig. 3: Mean rate versus SNR for considered algorithms. notably enhance decentralized optimization when provided with estimated CSI, hardly degrades performance when provided The topologies are randomized as Erdos–Renyi graphs with with true CSI, as the estimation-aware model achieves ∼ 98% edge probability 0.5, leading to relatively dense graphs. The of the achievable rate of a model trained using true CSI only. multi-subband links were generated using the Rayleigh fading Scalability: We conclude by assessing the ability of MANETmodel. The training set (5) contains 4,000 randomly generated GNN to hold R3, i.e., that it can be applied on different topologies. topologies with randomized transmitter/receiver placements. As the results reported so far utilized multiple different topologies We compare the following algorithms: but with the same number of nodes, here we show that MANETGNN can be trained and tested on topologies that do not differ B1 MANET-GNN with L = 4 message exchange rounds. solely in their connectivity, but also in their sizes. B2 Centralized optimizer which tackles (3) using a To that aim, we train two MANET-GNN models with centralized gradient-based solver (AdamW [30]) with identical architecture and hyperparameters, both with B=6: one global CSI that jointly updates all power variables. on MANETs with |V|=8 nodes and one on |V|=10. We then B3 Best single channel, that assigns all power to a single band evaluate both models on the same test set composed of random b ∈ {1, . . . , B}, selecting the one that optimizes the rate. MANETs of size |V| = 10. We compute the mean end-to-end B4 Equal-split, where each node splits its power equally over rate using the power allocations predicted by (i) MANET-GNN all existing outgoing links and all B bands. trained on |V|=10 (“10→10”); and (ii) MANET-GNN trained We note that B2 is a fully centralized method, while B4 is on |V|=8 (“8→10”). As shown in Fig. 4, the 8→10 curve a decentralized local method that involves no collaboration or SNR (dB) -10 -5 0 5 10 message exchanges. In principle, B3 can be computed in a decentralized manner using the Bellman-Ford algorithm [31]. However, True CSI 0.0200 0.0580 0.162 0.385 0.742 this requires a number of B × 1 messages (the transmission Estimated CSI 0.0196 0.05684 0.158 0.377 0.727 occurs on all available bands) per node that grows asymptotically at least as O(|V|) (as opposed to exactly L messages of size B TABLE II: MANET-GNN rate when tested with true CSI and per node as in MANET-GNN), and thus we evaluate it centrally. trained with true and estimated CSI.
Fig. 4: Scalability results: MANET-GNN trained on |V| ∈ {8, 10} and tested on |V| = 10. closely tracks the 10→10 curve across the entire SNR range, indicating strong size-generalization. Any gap that appears is modest, consistent with the increased interference coupling on larger graphs. Overall, these results validate that a MANET-GNN trained on smaller topologies can be deployed on larger ones without retraining as long as the feature dimension is unchanged. V. C ONCLUSIONS In this work, we proposed MANET-GNN, a decentralized GNN architecture for power allocation in multi-channel MANETs. By formulating the task as a constrained optimization problem and embedding message-passing operations into the GNN design, our approach enables low-latency distributed operation under noisy CSI while scaling across network sizes and topologies. Numerical evaluations demonstrate that MANET-GNN achieves near-centralized performance, outperforming conventional decentralized baselines. R EFERENCES [1] B. Tavli and W. Heinzelman, Mobile Ad hoc networks. Springer, 2006. [2] D. Kafetzis, S. Vassilaras, G. Vardoulias, and I. Koutsopoulos, “Softwaredefined networking meets software-defined radio in mobile ad hoc networks: state of the art and future directions,” vol. 10, pp. 9989–10 014, 2022. [3] T. Xie, H. Zhao, J. Xiong, and N. I. Sarkar, “A multi-channel MAC protocol with retrodirective array antennas in flying ad hoc networks,” IEEE Trans. Veh. Technol., vol. 70, no. 2, pp. 1606–1617, 2021. [4] M. A. Karabulut, A. S. Shah, and H. Ilhan, “A novel MIMO-OFDM based MAC protocol for VANETs,” IEEE Trans. Intell. Transp. Syst., vol. 23, no. 11, pp. 20 255–20 267, 2022. [5] J. Chen, J. Wang, J. Wang, and L. Bai, “Joint fairness and efficiency optimization for CSMA/CA-based multi-user MIMO UAV ad hoc networks,” vol. 18, no. 7, pp. 1311–1323, 2024. [6] D. Kanellopoulos and V. K. Sharma, “Survey on power-aware optimization solutions for MANETs,” Electronics, vol. 9, no. 7, p. 1129, 2020. [7] S. Singh and C. S. Raghavendra, “PAMAS—power aware multi-access protocol with signalling for ad hoc networks,” Comput. Commun. Rev., vol. 28, no. 3, pp. 5–26, 1998. [8] W. Ye, J. Heidemann, and D. Estrin, “An energy-efficient MAC protocol for wireless sensor networks,” in IEEE INFOCOM, vol. 3, 2002, pp. 1567–1576. [9] D. Kim, J. Garcia-Luna-Aceves, K. Obraczka, J.-C. Cano, and P. Manzoni, “Power-aware routing based on the energy drain rate for mobile ad hoc networks,” in IEEE ICCCN, 2002, pp. 565–569. [10] B. Karp and H.-T. Kung, “GPSR: Greedy perimeter stateless routing for wireless networks,” in ACM MobiCom, 2000, pp. 243–254.
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