We study the impact of a reconfigurable intelligent surface (RIS) in mitigating coverage gaps and enhancing transmission reliability in an industrial internet of things (IIoT) network deployed in a warehouse. First, we study a single blockage scenario and characterize the correlation between blocking events of the base station (BS)-user and the RIS-user links and study its impact on the probability of establishing a viable reflected link. Then, by considering multiple blockages, we derive the distribution of the signal to noise ratio (SNR) as a function of data size, blockage density, and the warehouse size. Finally, we compare the outage performance of this RIS-assisted system with that operated with network-controlled relays, and demonstrate that while the relays provide a higher reliability beyond a certain blockage threshold, increasing the number of RISs may help mitigate this effect. These insights offer valuable design guidelines for deploying RIS-aided IIoT networks in dense blockage environments.

Molecular communication (MC) is a promising communication paradigm that utilizes molecules as information carriers, mimicking natural biological processes. Out of various modulations to encode information onto signaling molecules, on-off keying (OOK) modulation has gained popularity due to its simplicity and efficiency. However, when the channel is unknown, for example, in cases where nodes are mobile, the OOK modulation-based M C systems suffer from a high bit error probability. In this paper, we investigate dynamic MC system with mobile transmit and receiver devices. We consider a variant of ratio-shift-keying (RSK) where the information is encoded in the ratio of the concentration of two different types of signaling molecules with the same propagation characteristics. We derive the optimal maximum likelihood (ML) decoder for OOK and RSK-based MC system. We also present a simpler representation of the optimal decoder under the Poisson assumption and show that the ML decoder for RSK modulation doesn't require channel information, in contrast with the ML decoder for OOK-based MC systems. We further investigate the bit error rate for the considered system. We show that RSK performs better than OOK in a dynamic MC system where the channel varies with time. This is because the ratio of the concentrations of the two types of information molecules is preserved at the receiver, offering improved robustness to variations in channel conditions. Therefore, RSK comes to the rescue in case of unknown or difficult to estimate channel environments. Via numerical investigations, we present various design insights, including optimal symbol design, and the gain of RSK over OOK as a function of node mobility.

This work analyzes the performance of a cache-enabled vehicular communication network with platooned vehicular users aided by base stations (BSs) for cellular connectivity. We consider a caching scheme that prioritizes searching for files within the same platoon to minimize latency and resorts to the BS connection if the file is unavailable in the platoon. The file access probability representing the probability of the typical vehicular user acquiring a file from another vehicle in the same platoon or from a BS is presented. We also study the design of optimal caching placement that maximizes the total file access probability subject to memory constraints. Further, design insights are provided with the help of derived expressions and numerical results. Results indicate that based on the system parameters and relative link quality of vehicular and cellular links, it may be optimal to cache more popular files or may not be optimal to cache any file at all.

Millimeter-waves’ propagation characteristics create opportunities for spatio-temporal spectrum sharing in a variety of contexts, including cognitive spectrum sharing (CSS). However, CSS with omnidirectional sensing is not efficient at mmWave frequencies due to their directional transmission, as this limits secondary networks’ ability to access the spectrum. This inspired us to create an analytical approach using stochastic geometry to examine the implications of directional sensing in millimeter-wave (mmWave) CSS. We explore a cognitive network where multiple secondary transmitter-receiver pairs coexist with multiple primary transmitter-receiver pairs. The positions of the secondary transmitters are modelled using a Poisson point process with corresponding secondary receivers located around them. A threshold on directional transmission is imposed on each secondary transmitter to limit its interference at the primary receiver. We derive the medium-access-probability of a secondary user along with the fraction of the secondary transmitters active at a time-instant. To understand cognition’s feasibility, we derive the primary and secondary links’ coverage probabilities. We provide various design insights. For example, we investigate the interference-threshold’s optimal value while ensuring both link’s coverage and its dependence on various parameters. We find that directionality improves both links’ performance. Further, allowing location-aware secondary-directionality can help achieve similar coverage for all secondary links.

Vehicular platooning is a promising solution to increase road capacity and ensure a seamless traffic flow. Despite its relevance in the current vehicular networks, its rigorous system-level analysis has not been performed yet. In this work, we develop a comprehensive framework to model and analyze a vehicular communication network with platooned traffic. The network of roads is modeled as a Poisson line process (PLP) and vehicles are placed on each road according to an independent Matérn cluster process (MCP) to capture platooning. The resulting point process formed by the locations of the vehicles is a Cox process driven by a PLP, which we term as the PLP-MCP. We first characterize PLP-MCP and present some of its key properties. Assuming that the cellular BSs are distributed as an independent Poisson point process (PPP), we then derive the load distribution on the typical BS of the network which is an important ingredient in the analysis of many key performance metrics, such as coverage probability and the rate distribution over the network. We then provide several system-design insights, including the impact of platooning on coverage probability.

In this paper, we present a comprehensive analytical framework for the system level analysis of THz cellular networks, which incorporates all key features of THz propagation, including blocking, directionality and scattering. This framework is particularly novel from the perspective of including the effect of scattering that has been largely ignored in such analyses thus far. We model the locations of the THz base-stations (BSs) as a homogeneous Poisson point process (PPP) and users (UEs) as another independent point process (PP). Further, the blockages and scatterers are modeled using a Boolean process and an independent PPP, respectively. The framework also incorporates distinction of line-of-sight (LOS), non-line-of-sight (NLOS) links, a realistic bounded path-loss model with absorption losses, and antenna directivity. Using the proposed framework, we first characterize the interference caused by BSs and scatterers via its Laplace transform (LT). We then derive the SINR (signal to interference plus noise ratio) coverage probability. With the help of a dummy exponential random variable (RV), we also derive the exact mean SINR. Our analysis concretely demonstrates that the scatterers have a significant impact on the coverage probability. Further, our results show that the coverage probability does not always increase with the increasing density of THz BSs.

In post-selection hypothesis testing, a third outcome is added, corresponding to not selecting any of the hypotheses. In this paradigm, minimum error for various cases is characterized in literature conditioned on the fact that one of the selected outcomes occurs. However, not selecting any of the hypotheses decimates the quality of testing. There is no discussion on the quality of post-selection hypothesis testing. In this work, we characterize the quality of post-selection hypothesis testing by defining a new metric acceptance. We find out measurements which lead to optimal post-selection error. For these measurements, we have derived the expression for acceptance in post-selection symmetric and asymmetric hypothesis testing problems. We have also given closed-form expressions in some specific cases.

Molecular communication has emerged as a promising candidate to provide communication capability to nano-networks. In this paper, we model and analyze a molecular ad hoc network (MolAN) consisting of multiple molecular communication links in a 3D medium. The transmitter end of each link has individual data to communicate to the receiver. We first develop an analytical framework to model the MoIAN. In particular, we model the receivers as marked Poisson point process with transmit message as their marks. We then compute the mean signal strength, inter-symbol-interference and co-channel interference for degradable and non-degradable molecules. We derive the performance of the network in terms of the probability of successful bit detection. We also study the network throughput as a function of link active probability to show the existence of an optimal network density. Finally, we present some numerical results to derive interesting design insights.

Molecular communication (MC) can enable the transfer of information between nanomachines using molecules as the information carrier. In MC systems, multiple receiver nanomachines often co-exist in the same communication channel to serve common or different purposes. However, the analytical channel model for a system with multiple fully absorbing receivers (FARs), which is significantly different from the single FAR system due to the mutual influence of FARs, does not exist in the literature. The analytical channel model is essential in analyzing systems with multiple FARs, including MIMO, SIMO, and cognitive molecular communication systems. In this work, we derive an analytical expression for the hitting probability of a molecule emitted from a point source on each FAR in a diffusion-based MC system with$N$FARs. Using these expressions, we derive the channel model for a SIMO system with a single transmitter and multiple FARs arranged in a uniform circular array (UCA). We then analyze the communication performance of this SIMO system under different cooperative detection schemes and develop several interesting insights.

Vehicular platooning is a promising way to facilitate efficient movement of vehicles with a shared route. Despite its relevance, the interplay of platooning and the communication performance in the resulting vehicular network (VN) is largely unexplored. Inspired by this, we develop a comprehensive approach to statistical modeling and system-level analysis of VNs with platooned traffic. Modeling the network of roads using the by-now well-accepted Poisson line process (PLP), we place vehicles on each road according to an independent Matérn cluster process (MCP) that jointly captures randomness in the locations of platoons on the roads and vehicles within each platoon. The resulting triply-stochastic point process is a PLP-driven-Cox process, which we term the PLP-MCP. We first present this new point process’s distribution and derive several fundamental properties essential for the resulting VN’s analysis. Assuming that the cellular base-stations (BSs) are distributed as a Poisson point process (PPP), we derive the distribution of the loads served by the typical BS and the BS associated with the typical user. In deriving the latter, we also present a new approach to deriving the length distribution of a tagged chord in a Poisson Voronoi tessellation. Using the derived results, we present the rate coverage of the typical user while considering partial loading of the BSs. We also provide a comparative analysis of VNs with and without platooning of traffic.

This work is focused on the system-level performance of a broadcast network. Since all transmitters in a broadcast network transmit identical signals, received signals from multiple transmitters can be combined to improve system performance. We develop a stochastic geometry-based analytical framework to derive the coverage of a typical receiver. We show that there may exist an optimal connectivity radius that maximizes the rate coverage. Our analysis includes the fact that users may have their individual content/advertisement preferences. We assume that there are multiple classes of users with each user class preferring a particular type of content/advertisements and the users will pay the network only when they can see content aligned with their interest. The operator may choose to transmit multiple contents simultaneously to cater to more users’ interests to increase its revenue. We present revenue models to study the impact of the number of contents on the operator revenue. We consider two scenarios for users’ distribution- one where users’ interest depends on their geographical location and the other where it doesn’t. With the help of numerical results and analysis, we show the impact of various parameters including content granularity, connectivity radius, and rate threshold and present important design insights.

In mmWave networks, a large or nearby object can obstruct multiple communication links, which results in spatial correlation in the blocking probability between a user and two or more base stations (BSs). This paper characterizes this blocking correlation and derives its impact on the signal-to-interference-plus-noise ratio (SINR) of a mmWave cellular network. We first present an exact analysis of a 1D network and highlight the impact of blocking correlation in the derived expressions. Gaining insights from the 1D analysis, we develop an analytical framework for a 2D network where we characterize the sum interference at the user by considering the correlation between the blocking of serving and interfering links. Using this, we derive the SINR coverage probability. Via simulations, we demonstrate that including blockage correlation in the analysis is required for accurate characterization of the system performance, in particular when the blocking objects tend to be large.

Wireless communications aided by reconfigurable intelligent surfaces (RISs) is a promising way to improve the coverage for cellular users. The controlled reflection of the signal from RISs is especially useful in mm-wave networks when the direct link between a cellular user and its serving base station (BS) is weak or unavailable due to blockages. But the joint blockage of the user-RIS and the user-BS links may significantly degrade the performance of RIS-aided transmissions. This paper aims to study the effect of joint blockages on downlink performance. When the RIS locations are coupled with BS locations, using tools from stochastic geometry, we obtain an optimal placement of RISs either to minimize the joint blockage probability of the user-RIS and the user-BS links or to maximize the downlink coverage probability. The results show that installing RISs on the street intersections improves the coverage probability. For users associated with BSs that are deployed sufficiently close to intersections, the intersection-mounted RISs offer a better coverage performance compared to BS-coupled RISs.

Molecular communication often involves coexisting links where certain links may have priority over others. In this work, we consider a system in three-dimensional (3-D) space with two coexisting communication links, each between a point transmitter and a spherical fully-absorbing receiver (FAR), where one link (termed primary) has priority over the second link (termed secondary). The system implements the underlay cognitive-communication strategy for the co-existence of both links, which use the same type of molecules for information transfer. The mutual influence of FARs existing in the same communication medium results in competition for capturing the information-carrying molecules. In this work, first, we derive an approximate hitting probability equation for a diffusion-limited molecular communication system with two spherical FARs of different sizes, considering the effect of molecular degradation. The derived equation is then used for the performance analysis of primary and secondary links in a cognitive molecular communication scenario. We show that the simple transmit control strategy at the secondary transmitter can improve the overall system’s performance. We study the influence of molecular degradation and decision threshold on the system performance. We also show that the parameters of the system need to be carefully set to improve the performance.

Past literature on the analysis of mmWave cellular network's performance in the presence of random blockages has assumed independent blocking of each link. In reality, a large blockage can block multiple links resulting in a correlation in blocking of these links. This paper focuses on deriving the impact of this correlation on the SINR performance of a mmWave cellular system. In particular, we consider the conditional probability of having line-of-sight (LoS) and non-LoS (NLoS) interferers conditioned on serving link being LOS or NLoS. We derive the distribution of the serving base-station (BS) distance from a typical user. We characterize the sum interference at the user by considering the correlation between blockage of serving and interfering links and derive the SINR coverage probability. Via numerical simulations, we show that including blockage correlation in the analysis is required in accurate characterization of the system performance, in particular when the blockages tend to be large.

Projection based algorithms are popular in the literature for online convex optimization with convex constraints and the projection step results in a bottleneck for the practical implementation of the algorithms. To avoid this bottleneck, we propose a projection-free scheme based on Frank-Wolfe: where instead of online gradient steps, we use steps that are collinear with the gradient but guaranteed to be feasible. We establish performance in terms of dynamic regret, which quantifies cost accumulation as compared with the optimal at each individual time slot. Specifically, for convex losses, we establish $\mathcal{O}\left( {{T^{1/2}}} \right)$ dynamic regret up to metrics of non-stationarity. We relax the algorithm’s required information to only noisy gradient estimates, i.e., partial feedback and derived the dynamic regret bounds. Experiments on matrix completion problem and background separation in video demonstrate favorable performance of the proposed scheme.

In this paper, we consider wireless sensor networks (WSNs) with sensor nodes exhibiting clustering in their deployment. We model the coverage region of such WSNs by Boolean Poisson cluster models (BPCM) where sensors nodes' location is according to a Poisson cluster process (PCP) and each sensor has an independent sensing range around it. We consider two variants of PCP, in particular Matérn and Thomas cluster process to form Boolean Matérn and Thomas cluster models. We first derive the capacity functional of these models. Using the derived expressions, we compute the sensing probability of an event and compare it with sensing probability of a WSN modeled by a Boolean Poisson model where sensors are deployed according to a Poisson point process. We also derive the power required for each cluster to collect data from all of its sensors for the three considered WSNs. We show that a BPCM WSN has less power requirement in comparison to the Boolean Poisson WSN, but it suffers from lower coverage, leading to a trade-off between per-cluster power requirement and the sensing performance. A cluster process with desired clustering may provide better coverage while maintaining low power requirements.

Ecosystem of a forest suffers from many adverse events such as wild-fire which can occur randomly anywhere in the forest and grows in size with time. This paper aims to analyze performance of a network of randomly deployed wireless sensors for the early detection of these time-critical and time-evolving events in a forest. We consider that the forest lies in a confined space (e.g. a circular region) and the wireless sensors, with fixed sensing range, are deployed within the boundary of forest itself. The sensing area of the network is modeled as a finite Boolean-Poisson model. In this model, the locations of sensors are modeled as a finite homogeneous Poisson Point Process (PPP) and the sensing area of each sensor is assumed to be a finite set. This paper aims to answer questions about the proximity of a typical sensor from a randomly occurred event and the total sensing area covered by sensors. We first derive the distribution of contact distance of a FHPPP and the expression of the capacity functional of a finite Boolean-Poisson model. Using these, we then derive the probability of sensing the event at time t, termed event-sensing probability.

Data transmission rate in molecular communication systems can be improved by using multiple transmitters and receivers. In molecular multiple-input multiple-output (MIMO) systems which use only single type of molecules, the performance at the destination is limited by inter-symbol interference (ISI), inter-link interference (ILI) and multi-user interference (MUI). This work proposes a new hybrid modulation for a system with multiple transmitters and receivers which uses different types of molecules to eliminate ILI. Further, to enhance the data rate of the proposed system under ISI and MUI, Mary CSK modulation scheme is used between each transmitter-receiver pair. In this paper, the random locations of transmitters present in the three dimensional (3-D) space are modeled as homogeneous Poisson point process (HPPP). Using stochastic geometry tools, analytical expression is derived for the probability of symbol error for the aforementioned scenario. Finally, the performance of the proposed system is compared using the different existing modulation schemes such as on-off keying (OOK), binary concentration shift keying (BCSK) and quadruple concentration shift keying (QCSK) to develop several important insights.

We show that two point processes Φeqand Φeq2, which were claimed by Yin and Haas to be equivalent in terms of their signal-to-interference-plus-noise ratio (SINR), are, in fact, not SINR equivalent. We discuss the importance of this distinction and explain how the correction impacts the results derived in the original paper.

Competing cellular operators aggressively share infrastructure in many major US markets. If operators also share spectrum licenses, intra- cellular interference will become correlated with inter-cellular interference. We propose a mathematical framework to model a two-operator millimeter-wave (mmWave) cellular network with co- located base-stations (BSs). We then characterize the SINR distribution for an arbitrary network to understand the impact of varying the spatial correlation between the operators' networks. An interesting observation is that sharing spectrum and infrastructure yields a higher rate coverage probability for higher rate thresholds, but has a lower coverage for lower thresholds. This suggests that networks catering for low-rate, limited-QoS devices, are at a disadvantage when spectrum and infrastructure are shared.

Blocking objects (blockages) between a transmitter and receiver cause wireless communication links to transition from line-of-sight (LOS) to non-LOS propagation, which can greatly reduce the received power, particularly at the higher frequencies such as millimeter wave. We consider a cellular network in which a mobile user attempts to connect to two or more base stations (BSs) simultaneously, to increase the probability of at least one LOS link, which is a form of macrodiversity. We develop a framework for determining the LOS probability as a function of the number of BSs, when taking into account the correlation between blockages: for example, a single blockage close to the device-including the user's own body-could block multiple BSs. We consider the impact of the size of blocking objects on the system's n th order LOS probability and show that macrodiversity gains are higher when the blocking objects are small. We also show that the BS density must scale as the square of the blockage density to maintain a given level of LOS probability.

We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional sub-6-GHz cellular systems are: 1) vulnerability to blocking and 2) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: 1) mmWave systems are significantly more noise-limited than at sub-6 GHz for most parameter configurations; 2) initial access is much more difficult in mmWave; 3) self-backhauling is more viable than in sub-6-GHz systems, which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and 4) in sharp contrast to sub-6-GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

Sharing the spectrum among multiple operators seems promising in millimeter wave (mmWave) systems. One explanation is the highly directional transmission in mmWave, which reduces the interference caused by one network on the other networks sharing the same resources. In this paper, we model a mmWave cellular system where an operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to another operator. This secondary network has a restriction on the maximum interference it can cause to the original network. Using stochastic geometry, we derive expressions for the coverage and rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. Results show that the restricted secondary operator can achieve good coverage with a small impact on the original operator. Our results also illustrate that the spectrum sharing gains increase with narrow beams and when the network densifies.

In conventional applications of time division duplex (TDD) in cellular systems, the time resource split between uplink (UL) and downlink (DL) is fixed across all base stations (BSs) in the network. This leads to under utilization of BS resources when there is a mismatch between the expected and experienced UL/DL traffic in a given cell. A dynamic split that varies in each cell is desirable, but is challenging due to the high interference experienced by UL receivers in one cell from DL transmissions in adjacent cells. This paper analyzes the performance of UL users in dynamic TDD enabled next generation cellular networks using a stochastic geometry framework. The analysis highlights the trade-off between spectral efficiency and resource utilization for dynamic TDD. With appropriate interference mitigation, dynamic TDD offers a significant gain in data rates as compared to static TDD, which is higher when the BSs are lightly loaded and/or the fraction of UL users is low.

Sharing the spectrum among multiple operators seems promising in millimeter wave (mmWave) systems. One explanation is the highly directional transmission in mmWave, which reduces the interference caused by one network on the other networks sharing the same resources. In this paper, we model a mmWave cellular system, where an operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to another operator. This secondary network has a restriction on the maximum interference it can cause to the original network. Using stochastic geometry, we derive expressions for the coverage and the rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. To explain economic tradeoffs, we consider a revenue-pricing model for both operators in the presence of a central licensing authority. Our results show that the original operator and central network authority can benefit from secondary licensing when the maximum interference threshold is properly adjusted. This means that the original operator and central licensing authority have an incentive to permit a secondary network to restrictively share the spectrum. Our results also illustrate that the spectrum sharing gains increase with narrow beams and when the network densifies.

The highly directional and adaptive antennas used in mmWave communication open up the possibility of uncoordinated sharing of spectrum licenses between commercial cellular operators. There are several advantages to sharing including a reduction in license costs and an increase in spectrum utilization. In this paper, we establish the theoretical feasibility of spectrum license sharing among mmWave cellular operators. We consider a heterogeneous multi-operator system containing multiple independent cellular networks, each owned by an operator. We then compute the signal-to-interference-and-noise ratio and rate distribution for downlink mobile users of each network. Using the analysis, we compare the systems with fully shared licenses and exclusive licenses for different access rules and explore the trade-offs between system performance and spectrum cost. We show that sharing spectrum licenses increases the per-user rate when antennas have narrow beams and is also favored when there is a low density of users. We also consider a multi-operator system where BSs of all the networks are co-located to show that the simultaneous sharing of spectrum and infrastructure is also feasible. We show that all networks can share licenses with less bandwidth and still achieve the same per-user median rate as if they each had an exclusive license to spectrum with more bandwidth.

Wireless network sensors today are deployed geographically in a random manner and are subjected to disturbances caused by natural forces, thereby necessitating real time and accurate estimation of the sensors' locations. In this paper, we consider wireless sensor self-localization problem where sensors are deployed according to a Poisson point process. We model such sensor networks under realistic assumptions about the wireless channel and measurement updates. We propose a novel distributed and sequential algorithm based on inter-node exchange of information for estimating sensor locations and analyze their performance through numerical simulations.

In this paper, we study the coverage probability of a K-tier multiple-input multiple-output heterogeneous cellular network (MIMO HetNet) assuming (i) zero-forcing precoding at all the base stations (BSs), (ii) Rayleigh fading, (iii) independent Poisson Point Process (PPP) model for the locations of BSs of each tier, and (iv) general cell selection rule that maximizes average received signal-to-interference-plus-noise ratio (SINR) at the users. Our analysis highlights key differences between MIMO HetNets and the more familiar single antenna HetNets in terms of cell selection. While it is challenging to derive exact cell selection rule to maximize average downlink SINR in MIMO HetNets, we show that adding an appropriately chosen per-tier selection bias yields a close approximation. The bias value for each tier is given in closed form. One interpretation of this result is that MIMO HetNets may balance load more naturally across different tiers in certain special cases compared to single antenna HetNets where an artificial selection bias is often needed for load balancing.

We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with K classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing signal-to-interference-plus-noise-ratio (SINR) at the receiver, we show that adding an appropriately chosen tier-dependent cell selection bias in the received power yields a close approximation. Assuming arbitrary selection bias for each tier, simple expressions for downlink coverage and rate are derived. For coverage maximization, the required selection bias for each tier is given in closed form. Due to this connection with biasing, multi-antenna HetNets may balance load more naturally across tiers in certain regimes compared to single-antenna HetNets, where a large cell selection bias is often needed to offload traffic to small cells.

Energy detection (ED) is a popular spectrum sensing technique in cognitive radio to detect the primary user. But the detection performance of ED deteriorates in the presence of noise uncertainty and exhibits associated SNR wall phenomenon. In this paper, the generalized energy detector (GED) is investigated, where the squaring operation of amplitude of received samples in conventional energy detector (CED) is replaced by an arbitrary positive operation p. Our aim is to study the effect of noise uncertainty on the detection performance of GED. We consider different distributions of noise uncertainty. Initially, uniform distribution of noise uncertainty is considered and an expression of the SNR wall for the same is derived. It is shown that the SNR wall for uniformly distributed noise uncertainty is independent of p. The study of the detection performance of GED is further extended for log-normally distributed noise uncertainty, where the SNR wall is calculated numerically.