Category: 5G Technologies

Safe Model Predictive Control via Reliable Time-Series Forecasting

12/04/2023 / / 0 Comments

Motivation

The control of dynamical systems is the backbone of modern technologies, ranging from industrial processes to autonomous vehicles. In many of these scenarios, systems must be controlled while satisfying a set of safety and reliability constraints with respect to the unknown evolution of a target process. For example, as illustrated in Figure 1, autonomous vehicles or unmanned aerial vehicles (UAVs) must plan their trajectory while maintaining a safe distance from other vehicles or obstacles. To this end, predictions about the future evolution of the system must be used. In this context, a primary challenge is to ensure safety and reliability in the face of predictions that are often uncertain.

Figure 1: UAV tracking problem, an example of model predictive control in which the UAV must plan its path based on the unknown evolution of the object to be tracked.

Probabilistic Time Series-Conformal Risk Prediction

To support the deployment of reliable control mechanisms for dynamical system, in our work we have recently proposed probabilistic time series-conformal risk prediction (PTS-CRC). PTS-CRC is a novel post-hoc calibration procedure that operates on the predictions produced by any pre-designed probabilistic forecaster to yield reliable time series prediction sets. As illustrated in Figure 2, PTS-CRC generates predictive sets based on an ensemble of multiple prototype trajectories sampled from the probabilistic model, supporting the efficient representation of forking uncertainties. This contrasts with previous solutions that apply Conformal Prediction[1] to deterministic predictors (TS-CP)[2], which are bounded to produce compact prediction sets. Furthermore, sets produced by PTS-CRC can be calibrated to satisfy a wide array of reliability definitions, beyond the standard one of coverage.

Figure 2: Construction of a prototype-based set predictor based on 3 prototypical sequences.

PTS-CRC Based Model Predictive Control

Based on the reliability properties of PTS-CRC predictions, we devise a novel Model Predictive Control (MPC) framework that addresses open-loop and closed-loop control problems under general average constraints on the quality or safety of the control policy. The key idea is to derive the control by replacing constraints that depend on the unknown dynamics of the target process with those depending on the predictive sets output by PTS-CRC. The reliability requirements of PTS-CRC predictions translate into reliability requirements for the original control problem.

Experiments

We apply PTS-CRC-based MPC to wireless networking problems, specifically focusing on a scenario where a base station must modulate its future power allocation based on the unknown evolution of channel conditions. For instance, we address the challenge of controlling transmit power to maximize the communication rate at an unlicensed user while adhering to a safety requirement, expressed as the maximum interference experienced by a licensed user. By employing PTS-CRC, we can replace the unknown system evolution with efficient multimodal predictive sets that more effectively capture multimodal channel evolution compared to TS-CP (Figure 3). As exemplified in Figure 4, PTS-CRC-based power control leads to power allocations that achieve a higher communication rate compared to TS-CP.

Figure 3: Comparison between the prediction sets of TS-CP and PTS-CRC for the problem of channel gain evolution forecasting.

Figure 4: Comparison between the power control solution obtained using PTS-CRC and TS-CP based MPC.

References

[1] Vovk, Vladimir, Alexander Gammerman, and Glenn Shafer. “Algorithmic learning in a random world,” Vol. 29. New York: Springer, 2005.

[2] Stankeviciute, Kamile, Ahmed M Alaa, and Mihaela van der Schaar. “Conformal time-series forecasting.” Advances in neural information processing systems 34, 2021.

[3] Zecchin, Matteo, Sangwoo Park, and Osvaldo Simeone. “Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control.” arXiv preprint arXiv:2310.10299, 2023.

Safe and Data-Efficient Control and Monitoring of Wireless Networks using a Digital Twin

01/27/2023 / / 0 Comments

A digital twin (DT) consists of a high-fidelity virtual replica of a physical entity, the physical twin (PT), such that, in the words of DT pioneer Michael Grieves, “at its optimum, any information that could be obtained from inspecting a physical manufactured product can be obtained from its digital twin” [1]. Based on a fully automatized bi-directional flow of information [2], the DT uses the data collected from the physical world to maintain an up-to-date model of the PT, which in turn provides command and analysis functionalities to the PT (see Fig.1). With the ever-growing demand in communication resources, next-generation wireless networks will be required to adapt to a large number of scenarios, and DT platforms are increasingly seen as a promising data-driven solution to build intelligent wireless systems that can offer the necessary flexibility and responsiveness.

As depicted in Fig. 1, in a recent work to be presented at the IEEE International Conference on Communications, we consider a DT that autonomously learns a model of a wireless network, providing a safe sandbox environment for network optimization and analysis, while also enabling monitoring and prediction features. The main motivation for our work  stems from the realization that, in real-world scenarios, it is challenging to transfer sufficient data to and from the PT in a way that “any information that could be obtained from inspecting the PT can be obtained from its DT”. In light of this, we propose to leverage Bayesian methods to learn a DT model that is aware of “what it knows” as much as it is aware of “what it does not know”; taking into account the epistemic uncertainty arising from limited PT-to-DT communication [3].

 

Figure 1 – The digital twin (DT) platform for the control and analysis of the communication system studied in this work. The physical twin (PT) consists of a group of K devices receiving correlated data and communicating over a shared multi-packet reception (MPR) channel. The DT platform operates along the phases of model learning (step 1) and policy optimization (step 2) ; while also enabling functionalities such as prediction, counterfactual analysis and monitoring (step 3) .

 

The Physical Twin

We consider a PT system made of a group of devices, referred to as agents, that attempt to communicate with a single base station (BS) over a shared multi-packet reception (MPR) channel [4]. Each agent is equipped with a limited-capacity buffer, and packet generation is taken to be correlated in-time and among agents. At any given time slot, each agent can take an action to decide whether or not to transmit a packet from their buffer, which can be received at the BS depending on the MPR channel dynamics. Upon packet reception, the BS transmits acknowledgement signals to the corresponding agents before the next time slot.

Agents cannot communicate with each other and each agent can only sense its local state, which contains information about its packet generation, buffer occupancy and BS feedback at a given time. Given the collective states and actions of all agents, the PT system evolves to a new state according to a transition distribution that is unknown to the DT and describes the packet-generation, buffer and channel dynamics.

The Digital Twin

Model Learning

During model learning (step 1 in Fig. 1), the DT leverages sequences of states and actions collected from the PT to learn a parametric Bayesian model of the transition distribution. As opposed to frequentist learning, which only keeps the most probable model parameter, Bayesian learning keeps a (possibly infinite) ensemble of models, where the probability of each model is given by a posterior distribution. Given that all state variables are discrete, we represent the transition distribution using a categorical model and learn the corresponding posterior using the conjugate Dirichlet distribution [3]. In order to lower the spatial complexity of the model, we leverage prior information available at the DT about state transitions like data-generation clusters, known buffer dynamics, and symmetry of the MPR channel.

Policy Optimization: Safely Learn by Trial and Error

A medium access control (MAC) protocol at the PT can be established by providing each agent with a policy distribution that maps the sequence of locally observed states and actions into a new action. Using the learned model, we can safely asses new policies in virtual space by defining a reward function that yields positive values for desired behavior (e.g. successfully delivered packets) and negative penalties for undesired behavior (e.g. buffer overflow). Policy optimization (step 2 in Fig. 1) aims at providing an optimal policy to each agent that maximizes the expected sum of future rewards. This amounts to a Decentralized Markov Decision Process [5] problem that we tackle using the COunterfactual Multi-Agent (COMA) algorithm proposed in [6], in which we periodically sample a new transition distribution from the model posterior during training.

Monitoring: Let’s Agree to Disagree

After an initial model learning phase, the DT can provide monitoring features by checking whether newly received data fits previously observed transitions, or if it rather provides evidence of changed dynamics or anomalous behavior (step 3 in Fig. 1). To this end, we use a disagreement-based test metric that measures to which extent the Bayesian ensemble of models agree on the likelihood of the newly observed data. A large disagreement is taken as evidence of a large epistemic uncertainty compared to model-learning conditions, which in turn can indicate that the observation is anomalous.

Results

We evaluate the proposed DT platform on a simulated scenario consisting of 4 devices distributed across 2 data-generation clusters. The MPR channel allows for the successful delivery of one or two simultaneous packets; while more than two simultaneous transmissions cause the loss of all packets. Each device is equipped with a buffer with single-packet capacity.

During policy optimization, we reward successfully delivered packets, while we penalize buffer overflows, caused by generating a new packet on an already full buffer. We analyze the performance of the policy trained inside the Bayesian model across different sizes of model-learning datasets, and compare it to a policy trained inside the corresponding maximum a posteriori (MAP) frequentist model, and to an oracle-aided policy that is trained using the ground-truth transition distribution.

 

 

Figure 2 – Throughput and buffer overflow probability as a function of the size of the dataset available in the model learning phase for the proposed Bayesian model-based approach (orange), as well as the oracle-aided model-free (blue) and frequentist model-based (green) benchmarks.

From Fig. 2, we observe that, in regimes with high data availability during the model learning phase, both Bayesian and frequentist model-based methods yield policies with similar performance to the oracle-aided benchmark. In the low-data regime, however, Bayesian learning achieves superior performance compared to its frequentist counterpart.

To asses the performance of anomaly detection, we assume that an anomalous event occurs where a device is disconnected, resulting in an anomalous packet-generation distribution in the corresponding cluster. We compare the performance of the disagreement metric using the Bayesian model to a log-likelihood criterion using the frequentist MAP model for model-learning datasets comprising 20 and 50 transitions and report the results in the receiver operating curves (ROC) in Fig. 3.

Figure 3 – Receiver operating curves (ROC) of the Bayesian (orange) and frequentist (green) anomaly detection tests for model-learning dataset sizes comprising 20 (solid lines) and 50 (dashed lines) transitions.

Bayesian anomaly detection is observed to uniformly outperform its frequentist counterpart, achieving a higher area under the ROC in Fig. 3.

 

For a more formal presentation of our proposed Bayesian framework for wireless networks DTs and more details on the experimental procedure, please refer to our paper at this link and to the extended version at this link.

References

[1] M. Grieves and J. Vickers, “Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems,” in Transdisciplinary perspectives on complex systems. Springer, 2017, pp. 85–113.

[2] W. Kritzinger, M. Karner, G. Traar, J. Henjes, and W. Sihn, “Digital twin in manufacturing: A categorical literature review and classification,” IFAC-PapersOnLine, vol. 51, no. 11, pp. 1016–1022, 2018.

[3] O. Simeone, Machine Learning for Engineers. Cambridge University Press, 2022.

[4] L. Tong, Q. Zhao, and G. Mergen, “Multipacket reception in random access wireless networks: From signal processing to optimal medium access control,” IEEE Communications Magazine, vol. 39, no. 11, pp. 108–112, 2001.

[5] F. A. Oliehoek and C. Amato, A concise introduction to decentralized POMDPs. Springer, 2016.

[6] J. Foerster, G. Farquhar, T. Afouras, N. Nardelli, and S. Whiteson, “Counterfactual multi-agent policy gradients,” in Proceedings of the AAAI conference on artificial intelligence, vol. 32, no. 1, 2018.

“Hyper-Learning” How to Transfer from Uplink to Downlink for Massive MIMO

07/15/2021 / / 0 Comments

Problem

Most cellular deployments rely on frequency division duplex (FDD) due to its lower latency and greater coverage potential. In FDD, uplink and downlink channels use different carrier frequencies. Therefore, as illustrated in Fig. 1, with FDD, downlink channel state information (CSI) cannot be directly obtained from uplink pilots due to a lack of full reciprocity between uplink and downlink channels.

Fig.1 FDD massive MIMO system over multipath channels with partial reciprocity

The conventional solution to this problem is to leverage downlink training and feedback from the devices. This, however, generally causes a prohibitively large downlink and uplink overhead in massive multiple-input multiple-output (MIMO) systems owing to the need to transmit a pilot sequences of length proportional to the number of antennas.

State-of-the-art recent proposals to address the inefficiencies of this conventional solutions adopt machine learning (ML) tools. The use of ML is justified by the technical challenges arising from the lack of efficient optimal model-based methods.

In our recent work to be presented at SPAWC 2021, we contribute to this line of work by introducing a new ML-based solution that improves over the state of the art by leveraging partial channel reciprocity and the tool of hypernetworks.

Our approach

 

Fig. 2 The proposed HyperRNN architecture for end-to-end channel estimation based on temporal correlations and partial reciprocity

In this work, we propose a novel end-to-end architecture — HyperRNN — illustrated in Fig. 2. The main innovation of the approach is that simultaneously transmitted pilot symbols in the uplink, across multiple time slots, are leveraged to automatically extract long-term reciprocal channel features (see Fig. 1) via a hypernetwork that determines the weight of the downlink CSI estimation or beamforming network. Importantly, the long-term features implicitly underlie the discriminative mapping implemented by the hypernetwork between uplink pilots and downlink CSI estimation network, rather than estimated explicitly. The second main innovation is to incorporate recurrent neural networks (RNNs), in lieu of (feedforward) deep neural networks (DNNs) for both uplink and downlink processing in order to leverage the temporal correlation of the fading amplitudes.

Results

We compare the the normalized mean square error (NMSE) performance of our proposed HyperRNN and an earlier work based on end-to-end training procedure, downlink-based DNN (DL-DNN), which encompasses downlink pilot training, distributed quantization for the uplink and downlink channel estimation. Simulations are performed over the spatial channel model (SCM) standardized in 3GPP Release 16. Fig. 3 demonstrates the NMSE of the proposed HyperRNN and of the benchmark DL-DNN for channel estimation as a function of the number of paths. Larger performance gains can be achieved when the channel has a lower number of paths. In fact, in this regime, the invariant of the long-term features of the channel defines a low-rank structure of the channel that can be leveraged by the hypernetwork.

Fig. 3 NMSE of the HyperRNN and DL-DNN over frequency-flat fading channels having different number of paths for an FDD system

Full paper can be found here.

Privacy in Wireless Federated Learning is Free

11/04/2020 / / 0 Comments

–when the SNR is small enough

Problem Description 

Federated Learning (FL) refers to distributed protocols that avoid direct raw data exchange among the participating devices while training for a common learning task. This way, FL can potentially reduce the information on the local data sets that is leaked via communications. Nevertheless, the model updates shared by the devices may still reveal information about local data. For example, a malicious server could potentially infer the presence of an individual data sample from a learnt model by membership inference attack or model inversion attack. 

Differential privacy (DP) quantifies information leaked about individual data points by measuring the sensitivity of the disclosed statistics to changes in the input data set at a single data point. DP can be guaranteed by introducing a level of uncertainty into the released model that is sufficient to mask the contribution of any individual data point. The most typical approach is to add random perturbations, e.g., Gaussian. This suggests that,  when FL is implemented in wireless systems, the channel noise can directly act as a privacy-inducing mechanism. 

Suggested Solution 

In recent work, we have designed differentially private wireless distributed gradient descent via the direct, uncoded, transmission of gradients from devices to edge server. The channel noise is utilized as a privacy preserving mechanism and dynamic power control is separately optimized for orthogonal multiple access  (OMA) and non-orthogonal multiple access  (NOMA) protocols with the goal of minimizing the learning optimality gap under privacy and power constraints across a given number of communication blocks.  Our recent work to appear in IEEE Journal on Selected Areas in Communications tackles this problem. One of our main results shows that, as long as the privacy constraint level, measured via DP, is below a threshold that decreases with the signal-to-noise ratio (SNR), uncoded transmission achieves privacy “for free”, i.e., without affecting the learning performance. As our analysis demonstrates, channel noise added in the first iterations tends to impact convergence less significantly than the noise added in later iterations, whereas the privacy level depends on a weighted sum of the inverse noise power across the iteration. These properties, captured by compact analytical expressions derived in this paper, are leveraged for adaptive power allocation, yielding significant performance gains over standard static power allocation. 

Some Results 

The performance is first evaluated by using randomly generated synthetic dataset. In the considered range of DP level,  as illustrated in the figure below, NOMA with either adaptive or static power allocation (PA) achieves better performance than OMA. Furthermore, the proposed adaptive PA obtains a significant performance gain over static PA under stringent DP constraints, while the performance advantage of adaptive PA decreases as the DP constraint is relaxed. The figure also shows the threshold values of DP level beyond which the privacy “for free”.  

The performance is also evaluated by MNIST data set as summarized in the last figure. With conventional static PA, the increasing communication budget is seen to largely degrade performance. This is because more communication blocks may cause an increase in privacy loss. In contrast, adaptive PA is able to properly allocate power across the communication blocks thereby achieves a lower training loss.

Information-Centric Grant-Free Access for IoT Fog Networks: Edge vs Cloud Detection and Learning

06/13/2020 / / 0 Comments

Problem

With the advent of 5G, cellular systems are expected to play an increasing role in enabling Internet of Things (IoT). This is partly due to the introduction of NarrowBand IoT (NB-IoT), a cellular-based radio technology allowing low-cost and long-battery life connections, in addition to other IoT protocols that operate in the unlicensed band such as LoRa. However, these protocols allow for a successful transmission only when a radio resource is used by a single IoT device. Therefore, generally, the amount of resources needed scales with the number of active devices. This poses a serious challenge in enabling massive connectivity in future cellular systems. In our recent IEEE Transactions on Wireless Communications paper, we tackle this issue.

Figure 1: A Fog-Radio architecture where processing information from IoT devices, denoted by the theta symbol,  can take place either at the Cloud or the Edge Node.

Suggested Solution

In our new paper, we propose an information-centric radio access technique where IoT devices making (roughly) the same observation of a given monitored quantity, e.g., temperature, transmit using the same radio resource, i.e., in a non-orthogonal fashion. Thus, the number of radio resources needed scales with the number of possible relevant values observed, e.g., high or low temperature and not with the number of devices.

Cellular networks are evolving toward Fog-Radio architectures, as shown in Figure 1. In these systems, instead of the entire processing happening at the edge node, radio access related functionalities can be distributed between the cloud and the edge. We propose that detection in the IoT system under study be implemented at either cloud or edge depending on backhaul conditions and on the statistics of the observations.

Some Results

One of the important findings of this work is that cloud detection is able to leverage inter-cell interference in order to improve detection performance, as shown in the figure below. This is mainly due to the fact that devices transmitting the same values in different cells are non-orthogonally superposed and thus, the cloud can detect these values with higher confidence.

More details and results can be found in the complete version of the paper here.

Combining Cloud and Edge Processing for Optimal Wireless Content Delivery

03/19/2019 / / 0 Comments

Problem

Content delivery is one of the most important use cases for mobile broadband services in 5G networks. As seen in Fig. 1, in 5G systems, content can be potentially stored at distributed units, or edge nodes (ENs), and hence closer to the user, with the aim of minimizing delivery latency and network congestion. Furthermore, a cloud processor, also known as central unit, has typically access to the content library and connects to the ENs via finite capacity fronthaul links. The central unit is not only necessary to enable content delivery when the overall edge cache capacity is insufficient, but it can also foster cooperative transmission from the ENs to the users by sharing common information to the ENs. However, any transmission from cloud unit to the ENs comes at a latency cost due to the use of fronthaul links. How should edge and fronthaul resources be optimally combined to minimize delivery latency?

In a recent work just published on IEEE Transaction on Information Theory, we provided a conclusive answer to this question by taking an information-theoretic viewpoint, and making the following simplifying assumptions:

1) only uncoded edge caching is allowed;
2) the cloud can only send fractions of contents via the fronthaul links;
3) the ENs are constrained to use standard linear precoding on the wireless channel;
4) The signal to noise ratio is sufficiently large.

Some Results

Our work derives a caching and delivery policy that is able to offer a near optimal trade-off between fronthaul latency overhead and downlink transmission latency from the ENs to the users. Two key scenarios are identified that depend on key system parameters such as fronthaul capacity, edge cache capacity, and number of per-edge node antennas:

1) When the overall cache capacity of the ENs is smaller than a given threshold, as illustrated in Fig. 2, it is necessary to use both fronthaul and edge caching resources in order to minimize latency. Importantly, even when the edge resource alone would be sufficient to deliver all requested contents, the policy, it is generally required to make use of fronthaul resources in order to foster EN  cooperative transmission. In fact, when the fronthaul capacity is sufficiently large, the latency cost caused by a fronthaul delay does not offset the cooperative transmission gains in the downlink;

2) Otherwise, when edge cache capacity is above the given threshold, as seen in Fig. 2, only edge caching should be used. Under this condition, the gains due to enhanced EN cooperation do not overcome the latency associated with fronthaul transmission. Interestingly, the threshold on the edge cache capacity increases as the number of ENs’ antennas increases, since edge processing becomes more effective when more antennas are deployed.

The full paper can be found at ieeexplore (open access: arxiv)

How can heterogeneous 5G services coexist on a shared Fog-Radio architecture?

02/18/2019 / / 0 Comments

Problem

Figure 1: A Fog-Radio Architecture with coexisting 5G services (URLLC and eMBB)

In 5G, Ultra-Reliable Low-Latency Communications (URLLC) – catering to use cases such as vehicular-to-cellular communications and Industry 4.0 — and enhanced Mobile Broadband (eMBB) – with its support of applications such as virtual reality – will share the same radio interface and network architecture. The 5G network architecture will be fog-like (see Fig. 1), enabling a flexible split of network functionalities between cloud and edge nodes. The cloud generally enables centralised processing, but at the cost of an increased latency for fronthaul transfer, while the edge can provide low-latency feedback but subject to the constraints of local processing.

This raises the following questions:

  • How should radio resources be shared between the two services?
  • How should the URLLC and eMBB network slices be configured?

A Novel Solution

In a recent work just published on IEEE Access , we proposed a novel solution illustrated in Fig. 1, whereby

  • Baseband processing is carried out at the edge for the URLLC slice, hence ensuring low  latency, and centrally at the Base Band Unit (BBU) as in a C-RAN for the eMBB slice, with the aim of increasing spectral efficiency;
  • eMBB and URLLC services can share the same radio resources in a non-orthogonal fashion – an approach we define as Heterogeneous Non-Orthogonal Multiple Access.

Towards the goal of managing the interference between URLLC and eMBB packets arising from H-NOMA, we consider a number of practical approaches in order of complexity. For the uplink, we have:

  • Treating URLLC interference as noise: each edge node forwards both eMBB and URLLC signal to the BBU, where the eMBB signal is decoded while treating URLLC signal as noise;
  • Puncturing: each edge node discards the received eMBB signal whenever a URLLC user is transmitting;
  • Successive Interference Cancellation (SIC): each edge node decodes and cancels the URLLC signal before transmitting only the eMBB signal to the cloud.

And for the downlink we consider:

  • Superposition coding: each edge node transmits a superposition of both eMBB and URLLC signal to corresponding users;
  • Puncturing: each edge node discards the eMBB signal whenever a URLLC signal is generated at the edge node.

It is noted that there is no counterpart of successive interference cancellation for the downlink.

Some Results

Figure 2

To give a taste of the results in the paper, we now provide an example. In Fig. 2, we plot the eMBB average per-cell sum-rates (black curves) and URLLC per-cell outage capacity (red curves) for the uplink as function of the URLLC activation probability. The latter is a measure of the URLLC traffic load. In general, the results demonstrate the potential advantages of H-NOMA for both services, especially when the URLLC traffic load is sufficiently large and successive interference cancellation is enabled at the edge nodes.

Link to our paper: https://ieeexplore.ieee.org/stamp/stamp.jsparnumber=8612914

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