Reliable detection of road users is critical to the safety of automated driving systems. While object detectors based on deep neural networks are widely used for this purpose, they remain susceptible to errors that could compromise safety. A promising strategy to mitigate these risks involves run-time perception monitoring mechanisms, commonly referred to in the literature as self-assessment or introspection. Current research in this area predominantly addresses anomaly detection, or monitoring camera-based 2D object detection, with insufficient focus on in-distribution errors and 3D object detection. Additionally, existing 2D studies often monitor activation patterns from the final layers of the network backbone, overlooking earlier activations that preserve higher spatial resolution. Yet, high-resolution early-layer activations can be valuable for detecting errors with sparse 3D point clouds. We also argue that not all objects in a scene should equally influence frame-level error detection, a factor often neglected in current methods. To address these gaps, we propose a novel self-assessment mechanism for 3D object detection that leverages activation patterns from multiple network layers. This mechanism employs spatial filtering to focus the model within an area of interest in the close vicinity of the ego vehicle. Additionally, it utilises an object filtering mechanism, which specifically targets the missed objects by excluding the points in those already detected. We evaluate our method using widely recognised object detectors and public datasets. Additionally, we demonstrate its robustness under domain shifts with real-world LiDAR data collected on motorways in diverse weather conditions. Results show the proposed mechanism provides 6% AUROC improvement over last-layer activation methods with spatial filtering on the NuScenes dataset. It also demonstrates a superior ability to transfer knowledge under domain shifts. Code is available at https://github.com/yatbazhakan/multi-layer-introspection .

Deep Reinforcement Learning (DRL) has demonstrated promising capability in solving complex control problems. However, DRL applications in safety-critical systems are hindered by the inherent lack of robust validation techniques to assure their performance in such applications. One of the key requirements of the verification process is the development of effective techniques to explain the system functionality, providing why the system produces specific results in given circumstances. Recently, interpretation methods based on the Counterfactual (CF) explanation approach have been proposed to address the problem of explanation in DRLs. This article proposes a novel CF explainer to interpret the decisions made by a black-box DRL. To evaluate the efficacy of the proposed explanation framework, we carried out several experiments in the domains of Automated Driving Systems (ADSs) and the Atari Pong game. Our analysis demonstrates that the proposed framework generates plausible and meaningful explanations for various decisions made by deep underlying DRLs. Additionally, we discuss the practical implications of our approach for various automotive stakeholders, illustrating its potential real-world impact. Source codes are available at https://github.com/Amir-Samadi/Counterfactual-Explanation .

Abstract In vehicular communications, channel estimation is a complex problem due to the joint time–frequency selectivity of wireless propagation channels. To this end, several signal processing techniques as well as approaches based on neural networks have been proposed to address this issue. Due to the highly dynamic and random nature of vehicular communication environments, precise characterization of temporal correlation across a received data sequence can enable more accurate channel estimation. This paper proposes a new pilot constellation scheme in combination with a small feed‐forward neural network to improve the accuracy of channel estimation in V2X systems while keeping low the implementation complexity. The performance is evaluated in typical vehicular channels using simulated BER curves, and it is found superior to traditional channel estimation methods and state‐of‐the‐art neural‐network‐based implementations such as feed‐forward and super‐resolution. It is illustrated that the improvement becomes pronounced for small subcarrier spacings (or low 5G numerologies); hence, this paper contributes to the development of more reliable mobile services across rapidly varying vehicular communication channels with rich multi‐path interference.

Accurate and reliable perception of the surrounding environment, e.g., detection and classification of nearby objects, is the primary and most important function of automated/autonomous vehicles. However, onboard perception systems face challenges in complex road segments due to various environmental effects, such as occlusions, or high sensor noise. A potential enhancement is to equip such environments with cost-effective infrastructures that perceive the environment and provide additional perception support to autonomous vehicles through vehicle-to-everything (V2X) communication technologies. This paper develops an experimental study of vehicle detection and tracking on a bird’s eye view (BEV) map using raw video collected from several low-cost roadside monocular cameras with overlapping views installed near a motorway junction to support the merging of autonomous vehicles. The paper explains how to produce vehicle tracks from the camera infrastructure and reports the real-world evaluation of the proposed solution on a physical test bed in the UK’s West Midland region.

In this paper we calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the k-th nearest node of the Cox point process driven by the Manhattan Poisson line process. The CDF is expressed as a sum over the integer partition function$p\!\left(k\right)$, which allows us to numerically evaluate the CDF in a simple manner. The distance distributions can be used to study the k-coverage of broadcast signals in intelligent transportation systems (ITS) transmitted from a \ac{RSU} that is located at an intersection. They can also be insightful for network dimensioning in urban vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the \ac{RSU} is located at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting. We corroborate the applicability of the distance distribution model using the map of an urban area.

The Poisson point process (PPP) is not always a realistic model for the locations of vehicles along a road, because it does not account for the safety distance a driver maintains from the vehicle ahead. In this article, we model the inter-vehicle distance equal to the sum of a constant hardcore distance and a random distance following the exponential distribution. Unfortunately, the probability generating functional of this point process is unknown. To approximate the Laplace transform of interference at the origin, we devise simple approximations for the variance and skewness of interference, and we select suitable probability functions to model the interference distribution. When the coefficient-of-variation and the skewness of interference distribution are high, the PPP (of equal intensity) approximation of the outage probability becomes loose in the upper tail. Relevant scenarios are associated with urban microcells and highway macrocells with a low density of vehicles. The predictions of PPP deteriorate with a multi-antenna maximum ratio combining receiver and temporal indicators related to the performance of retransmission schemes. Our approximations generate good predictions in all considered cases.

In this paper we analyze synthetic mobility traces generated for three-lane unidirectional motorway traffic to find that the locations of vehicles along a lane are better modeled by a hardcore point process instead of the widely-accepted Poisson point process (PPP). In order to capture the repulsion between successive vehicles while maintaining a level of analytical tractability, we make a simple extension to PPP: We model the inter-vehicle distance along a lane equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We calculate the J-function and the Ripley's K-function for this hardcore point process. We fit its parameters to the available traces, and we illustrate that the higher the average speed along a lane, the more prominent the hardcore component becomes. In addition, we consider a transmitter-receiver link on the same lane, and we generate simple formulae for the moments of interference under reduced Palm measure for that lane, and without conditioning for other lanes. We illustrate that under Rayleigh fading a shifted-gamma approximation for the distribution of interference per lane provides a very good fit to the simulated outage probability using the synthetic traces, while the fit using the PPP is poor.

The meta distribution of the signal-to-interference-ratio (SIR) is an important performance indicator for wireless networks because, for ergodic point processes, it describes the fraction of scheduled links that achieve certain reliability, conditionally on the point process. In this paper, we calculate the moments of the meta distribution in vehicular ad hoc networks (VANETs) along high-speed motorways. Due to the high speeds, the drivers maintain large safety distances, and the Poisson point process (PPP) becomes a poor deployment model. Because of that, we model the distribution of inter-vehicle distance equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We design a novel discretization model for the locations of vehicles which can be used to approximate well the meta distribution of the SIR due to the hardcore process. We validate the model against synthetic motorway traces. On the other hand, the PPP overestimates significantly the coefficient-of-variation of the meta distribution due to the hardcore process, and its predictions fail. In addition, we show that the calculation of the meta distribution becomes especially meaningful in the upper tail of the SIR distribution.

In this paper, we study the receiver performance with physical layer security in a Poisson field of interferers. We compare the performance in two deployment scenarios: 1) the receiver is located at the corner of a quadrant and 2) the receiver is located in the infinite plane. When the channel state information (CSI) of the eavesdropper is not available at the transmitter, we calculate the probability of secure connectivity using the Wyner coding scheme and show that hiding the receiver at the corner is beneficial at high rates of the transmitted code words and detrimental at low transmission rates. When the CSI is available, we show that the average secrecy capacity is higher when the receiver is located at the corner, even if the intensity of interferers in this case is four times higher than the intensity of interferers in the bulk. Therefore, boundaries can also be used as a secrecy enhancement technique for high-data-rate applications.

In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated overtime. All these features have an impact on the temporal properties of interference which is often neglected. In this paper, we show how to incorporate correlated user mobility into the interference and outage correlation models. We use the random waypoint mobility model over a bounded one-dimensional domain as an example model inducing correlation, and we calculate its displacement law at different locations. Based on that, we illustrate that the temporal correlations of interference and outage are location-dependent, being lower close to the center of the domain, where the level of mobility is higher than near the boundary. Close to the boundary, more time is also needed to see uncorrelated interference. Our findings suggest that an accurate description of the mobility pattern is important, because it leads to more accurate understanding/modeling of interference and receiver performance.

Interference statistics in vehicular networks have long been studied using the Poisson Point Process (PPP) for the locations of vehicles. In roads with a small number of lanes and restricted overtaking, this model becomes unrealistic because it assumes that the vehicles can come arbitrarily close to each other. In this paper, we model the headway distance (the distance between the head of a vehicle and the head of its follower) equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We study the mean, the variance, and the skewness of interference at the origin with this deployment model. Even though the pair correlation function becomes complicated, we devise a simple formulae to capture the impact of the hardcore distance on the variance of interference in comparison with a PPP model of equal intensity. In addition, we study the extreme scenario, where the interference originates from a lattice. We show how to relate the variance of interference due to a lattice to that of a PPP under Rayleigh fading.

The business potential of device-to-device (D2D) communication including public safety and vehicular communications will be realized only if direct communication between devices subscribed to different mobile operators (OPs) is supported. One possible way to implement inter-operator D2D communication may use the licensed spectrum of the OPs, i.e., OPs agree to share spectrum in a co-primary manner, and inter-operator D2D communication is allocated over spectral resources contributed from both parties. In this paper, we consider a spectrum sharing scenario, where a number of OPs construct a spectrum pool dedicated to support inter-operator D2D communication. OPs negotiate in the form of a non-cooperative game about how much spectrum each OP contributes to the spectrum pool. OPs submit proposals to each other in parallel until a consensus is reached. When every OP has a concave utility function on the box-constrained region, we identify the conditions guaranteeing the existence of a unique equilibrium point. We show that the iterative algorithm based on the OP's best response might not converge to the equilibrium point due to myopically overreacting to the response of the other OPs, while the Jacobi-play strategy update algorithm can converge with an appropriate selection of update parameter. Using the Jacobi-play update algorithm, we illustrate that asymmetric OPs contribute an unequal amount of resources to the spectrum pool; however, all participating OPs may experience significant performance gains compared with the scheme without spectrum sharing.

In order to harvest the business potential of deviceto-device (D2D) communication, direct communication between devices subscribed to different mobile operators should be supported. This would also support meeting requirements resulting from D2D relevant scenarios, like vehicle-to-vehicle communication. In this paper, we propose to allocate the multi-operator D2D communication over dedicated cellular spectral resources contributed from both operators. Ideally, the operators should negotiate about the amount of spectrum to contribute, without revealing proprietary information to each other and/or to other parties. One possible way to do that is to use the sequence of operators' best responses, i.e., the operators make offers about the amount of spectrum to contribute using a sequential updating procedure until reaching consensus. Besides spectrum allocation, we need a mode selection scheme for the multi-operator D2D users. We use a stochastic geometry framework to capture the impact of mode selection on the distribution of D2D users and assess the performance of the best response iteration algorithm. With the performance metrics considered in the paper, we show that the best response iteration has a unique Nash equilibrium that can be reached from any initial strategy. In general, asymmetric operators would contribute unequal amounts of spectrum for multi-operator D2D communication. Provided that the multi-operator D2D density is not negligible, we show that both operators may experience significant performance gains as compared to the scheme without spectrum sharing.

We consider two small cell operators deployed in the same geographical area, sharing spectrum resources from a common pool. A method is investigated to coordinate the utilization of the spectrum pool without monetary transactions and without revealing operator-specific information to other parties. For this, we construct a protocol based on asking and receiving spectrum usage favors by the operators, and keeping a book of the favors. A spectrum usage favor is exchanged between the operators if one is asking for a permission to use some of the resources from the pool on an exclusive basis, and the other is willing to accept that. As a result, the proposed method does not force an operator to take action. An operator with a high load may take spectrum usage favors from an operator that has few users to serve, and it is likely to return these favors in the future to show a cooperative spirit and maintain reciprocity. We formulate the interactions between the operators as a repeated game and determine rules to decide whether to ask or grant a favor at each stage game. We illustrate that under frequent network load variations, which are expected to be prominent in small cell deployments, both operators can attain higher user rates as compared to the case of no coordination of the resource utilization.

In environments with non-uniform user density and correlated slow fading, the Poisson Point Process (PPP) model fails to capture the distribution of aggregate interference. One way to overcome this issue is to divide the deployment area into multiple disjoint clusters and describe the interference from each cluster using a PPP with cluster-specific PPP intensity and pathloss model. Obviously, too few clusters do not describe the distribution of aggregate interference accurately, while on the other hand, too many clusters incur high computational and storage overheads. In this direction, we propose to divide the area according to a hierarchical clustering algorithm which uses the Akaike Information Criterion to balance between complexity and accuracy. The algorithm can be useful for database-assisted spectrum access. It allows a database to assess the interference between systems (overlapping in spectrum but not in space) in a low-complexity manner.

Exponential growth of capacity demand is making energy efficient cellular network densification an important issue. As a network is dimensioned based on the busy hour capacity demand, a large portion of network capacity remains idle for a big part of the day. Unfortunately, the power consumption of a base station does not scale down proportionally when load decreases. In this paper, a heterogeneous network (HetNet) consisting of macro and micro base station (BS) is considered. In order to save energy, we vary the density of micro BS based on the offered load and divide the load between the two layers in an energy efficient manner. With this scheme, 30% energy saving is achievable. In our analysis, we incorporate the efficiency characteristics of a realistic power amplifier (PA) and energy-delay trade-off. The analysis suggests that efficient power amplifiers and small additional flow transfer delay not only reduce the overall energy consumption but also impact the densification and load sharing in the cellular network. The results of this paper indicate that for energy efficient operation, the configuration of HetNet needs to be dynamic to cope with the temporal variation of capacity demands as well as the load needs to be shared between different layers properly.

In this paper, we study the energy-delay trade-off in the downlink of a proportional-fair cellular system with inter-cell interference and fading, while incorporating the efficiency characteristics of realistic amplifiers(PA). We study the potential for energy saving by lowering the transmission power level at different user locations in a cell at the cost of additional flow level delay. We identify the transmission power levels at different locations so that the energy consumption at the base station is minimized and the flow level delay is controlled. We formulate the energy minimization problem in a game theoretic framework and prove the convergence of the best response iteration algorithm. The energy saving potential is found to depend on the network load and the efficiency characteristics of the PAs. There is a significant potential for energy saving when the network operates under low to medium loads and efficient PAs are utilized. For example, with envelope tracking PA, around 90% of energy can be saved by introducing small additional flow level delay when the network load is less than 75%. Motivated by the fact that the network load keeps varying throughout the day, we take a daily traffic model and demonstrate the potential for energy saving by this scheme.

The authors consider a short-range cognitive network with secondary users (SUs) generating voice calls. The SUs measure the TV spectrum and classify the measured bands as either idle or occupied. When most of the measured bands are detected to be occupied, there might not be enough capacity to serve all the SUs' calls. In this study the authors identify the minimum required number of measured bands such that the probability to serve all the secondary calls is controlled. The detection performance requirements imposed by the primary systems are also satisfied. The authors formulate this problem as an optimisation problem with optimisation parameters the number of users measuring each band and the measurement time. For a small number of SUs the authors identify the minimum required number of measured bands by using exhaustive search. For a large number of users the authors propose to solve the optimisation problem by means of a greedy algorithm. The algorithm is verified against the exhaustive search results and it is found to perform remarkably well. Therefore it is suitable for practical secondary systems searching for sharing opportunities over the TV spectrum.

The main requirement for secondary operation over the TV white spaces is interference control. In this paper, we propose an interference control scheme that allows multiple secondary systems to maintain their aggregate interference at the TV receivers under specific protection limits. The main characteristic of the proposed scheme is the small signaling overhead required for the cooperation between the secondary systems. The secondary systems need only to communicate their locations to a central network controller. The controller can then allocate the transmission power levels to the different systems such that the TV receivers are sufficiently protected. At the same time, the sum of the transmission power levels allocated to the secondary systems is maximized.

In this paper, we establish a channel ranking strategy for wireless sensor networks (WSN) in the presence of WLAN interference. The packet delivery ratio (PDR) of a sensor link is the performance metric used for channel ranking. The PDR is defined as a function of the signal-to-interference-and-noise-ratio (SINR) at the sensor and the time domain transmission characteristics of the interferer that is, the activity factor and the traffic pattern. The PDR is estimated at the sensor by using spectrum measurements. When the channel bandwidth of the interferer is large and the measurement time is also limited, the traffic pattern cannot be satisfactorily predicted for each measured channel. Because of that it is proposed to utilize Poisson and periodic traffic patterns to obtain bounds on the performance of channel ranking. Given the channel measurement time upper and lower bounds on the ranking error probability are calculated by using Poisson and periodic traffic patterns respectively. Even though the traffic pattern of WLAN interference is usually modeled with phase-type (PH) distributions, the periodic and the Poisson traffic patterns allow us to bypass the traffic pattern estimation process and relatively rank the channels based on their SINR and activity factor estimates.

The estimation of the total interference generated from a secondary system is essential for protecting the primary receivers. However, interference level estimation from a large number of secondary transmitters is a challenging problem. In this paper, we estimate the aggregate interference as an integration over the power spatial density in the secondary system's deployment area. We modify such integration-based model to contain the correlation in shadow fading. We apply the model on a cellular system downlink and study how well the proposed analytical model describes the interference level in correlated and non-correlated slow fading environment. The analysis indicates that for cell size less than five km the integration based model describes interference relatively well. For larger cell sizes, the interference is dominated by a few strong sources and has to be computed by summing over the power of all individual transmitters. It is also illustrated that the full correlated and independent slow fading provide two extremes of the amount of generated interference. The complex estimation of the impact of the fading cross correlation can be avoided by using those two extreme models as bounds to the interference level.

We consider a short range cognitive network searching for spectrum holes from very wide bandwidth. In practice, one cognitive user can sense only a small portion of spectrum. Unfortunately, in fading environment a reliable detection scheme requires measurements collected by multiple users. Because of that, it is unreasonable to expect a small-sized network to sense the complete candidate bandwidth. In this paper we propose an algorithm for optimal sensing of multiple spectrum bands by multiple cognitive users. The user allocation is optimized so that the expected opportunistic throughput is maximized and the total power spent for spectrum measurements is controlled. As a constraint we use the detection performance requirements imposed by the primary systems. For a small number of spectrum bands the optimal solution can be found by exhaustive search. For a large number of spectrum bands we view the spectrum sensing as a multiple choice knapsack problem. By using algorithms for this class of problems we propose two heuristics that are suitable for optimizing spectrum sensing in multiband cognitive networks. These algorithms provide quick, near optimal solutions and are therefore suitable for practical spectrum sensing systems.

In this paper we investigate the detection of OFDM primary signals using autocorrelation. The conventional model for signal detection in cognitive radio assumes that the primary signal is either absent or present with a fixed level. We show that the conventional model is the source of significant discrepancy between the analytical prediction of the detection algorithm and the simulations. We propose to design the autocorrelation-based detector using the uniform approximation for the distribution of the primary signal power. The uniform approximation allows to derive the optimal decision threshold by using the Lagrangian optimization. Finally, we are able to design the autocorrelation-based detector such that the spectrum reuse is enhanced and the analytical prediction of the detection algorithm achieves a better match with the simulation results.

The autocorrelation-based detection of OFDM signals with cyclic prefix is an appealing method for cognitive radio because it has low complexity and it allows to separate between different OFDM-based legacy systems. Unfortunately, it is also sensitive to noise estimation errors provided that a single estimate of the autocorrelation function is calculated. In this paper we design an autocorrelation-based detector for OFDM signals with cyclic prefix that is also robust in the low SNR under noise uncertainty. The proposed decision statistic allows us to calculate the error probabilities in a closed-form.

The primary signal detection is an essential operation for the secondary spectrum usage. In this paper we extend the covariance based detection for multiple-antenna receiver. The proposed method uses the noise power estimation and does not suffer from the noise level uncertainty. We analyze the detection algorithm and compute the distribution of the decision variable not only for the pure noise case but also for the jointly presence of primary signal and noise. By deriving the distribution of the primary signal in noise we are able to use the detection probability as the detector design constraint. Our analysis takes advantage of the high amount of samples available at the detector. The proposed method sets the foundation for the analysis of any detector that involves cross correlation, summing and squaring operations of samples.

Most algorithms for secondary spectrum usage are solely based on signal detection. The frequencies where the primary signal is detected with level comparable to the noise are considered occupied. As a result vast areas in the proximity of primary cells become illegal for spectrum reuse. In this paper we propose an algorithm that enhances spatial spectrum reuse by allowing secondary users to communicate in the presence of primary signal. We study how much the spectrum utilization is increased by using the proposed algorithm. The algorithm has multiple decision stages and it is based both on signal detection and generated interference estimation. It allows to minimize the decision errors and control the generated interference to primary user receivers. The algorithm is modeled by using Bayesian hypothesis testing approach. The required prior probabilities are related to the geographical interpretation of the studied system. The constructed model allows to find the optimal decision levels through the Lagrangian optimization. The algorithm performance is evaluated as a function of the number of measured power samples. Comparison to a simple detection based scheme indicates recognizable improvement especially for a low number of samples.

In this paper we analyze the performance of the distributed power detection algorithm operating in a shadowing environment and with communication constraints. A well performing detection algorithm is critical for detecting a primary user's signal for dynamic spectrum allocation purposes. Dynamic spectrum allocation allows a secondary user to use a spectrum chunk provided that the primary user is not disturbed. In a shadowing environment one secondary user could not guarantee a reliable detection of primary user's signal with acceptable false detection probability. The detection performance can be greatly enhanced by combining measurements from secondary users at a fusion centre. Such combining requires communication bandwidth. We provide equations and numerically compute the bounds for two extremes of communication requirements. In the first scheme the secondary users send a full loglikelihood ratio, which in principle would require infinite amount of communication capacity. In the second scheme the secondary users send to the fusion centre only one bit, describing the hard decision made based on the loglikelihood ratio. These two cases provide performance bounds for possible practical implementations.