331 resultados para downlink LTE schedulers
Resumo:
El estándar LTE se ha posicionado como una de las claves para que los operadores de telecomunicación puedan abordar de manera eficiente en costes el crecimiento de la demanda de tráfico móvil que se prevé para los próximos años, al ser una tecnología más escalable en el núcleo de la red y más flexible en la interfaz radio que sus predecesoras. En este sentido, es necesario también que los reguladores garanticen un acceso al espectro radioeléctrico adecuado, equitativo y no discriminatorio, que permita un entorno estable para el despliegue de redes de comunicaciones móviles avanzadas. Además de la flexibilización del marco regulador del espectro radioeléctrico en Europa, que ha permitido el despliegue de nuevas tecnologías en las bandas de frecuencia históricas de GSM, se ha puesto a disposición espectro adicional para sistemas IMT en nuevas bandas de frecuencia, lo que ha planteando a su vez nuevos retos para la tecnología y la regulación. La fragmentación del espectro disponible para comunicaciones móviles ha impulsado el desarrollo de técnicas de agregación de portadoras en las nuevas versiones del estándar LTE, que permiten explotar mejor los recursos radio en su conjunto. No obstante, el espectro inferior a 1 GHz sigue siendo escaso, ya que el tráfico móvil aumenta y la banda de 900 MHz aún se utiliza para servicios GSM, lo que no ha conseguido sino agravar la disputa entre los servicios de radiodifusión terrestre y de comunicaciones móviles por la parte superior de la banda UHF. En concreto, la banda de 700 MHz se perfila como una de las próximas para aumentar el espectro disponible para los servicios en movilidad, si bien su liberación por parte de las actuales redes de Televisión Digital Terrestre presenta no pocas dificultades en los Estados miembros en los que ésta es la principal plataforma audiovisual de acceso gratuito, abriendo un debate sobre el modelo audiovisual a largo plazo en Europa. Por otro lado, las políticas públicas de promoción del acceso a la banda ancha rápida y ultrarrápida de la presente década han establecido objetivos ambiciosos para el año 2020, tanto en el ámbito europeo como en los diferentes Estados miembros. La universalización del acceso a redes de banda ancha de al menos 30 Mbps constituye uno de los principales retos. Las expectativas generadas por la tecnología LTE y la puesta a disposición de nuevas bandas de frecuencia hace posible que los servicios de acceso fijo inalámbrico adquieran especial relevancia ante los objetivos de política pública establecidos que, como ha sido reconocido en diversas ocasiones, no podrán lograrse sino con un compendio de diferente tecnologías. Para esta Tesis Doctoral se han desarrollado una serie modelos tecnoeconómicos con el objetivo de realizar un análisis prospectivo que evalúa tres casos de especial relevancia en el despliegue de redes LTE: en primer lugar, la valoración económica de la banda de 700 MHz; en segundo lugar, la evaluación de modelos de negocio y reducción de costes considerando tecnologías femtocelulares; y finalmente, la viabilidad de las redes LTE de acceso fijo inalámbrico para el cierre de la brecha digital en el acceso a la banda ancha de 30 Mbps. En relación con la aplicación del análisis tecnoeconómico para la valoración del espectro de 700 MHz, los resultados obtenidos ponen de manifiesto dos cuestiones fundamentales. En primer lugar, la necesidad de asignar a los operadores más espectro para satisfacer las previsiones de demanda de tráfico móvil a medio plazo. En segundo, existe una diferencia notable en los costes de despliegue de una red LTE cuando se dispone de espectro en frecuencias inferiores a 1 GHz y cuando no, pero esta diferencia de costes disminuye a medida que se añade nuevo espectro sub-1GHz. De esta manera, la atribución de la banda de 700 MHz a servicios de comunicaciones móviles supone una reducción relevante en los costes de despliegue si el operador no dispone de espectro en la banda de 800 MHz, pero no así si ya dispone de espectro en bandas bajas para el despliegue. En este sentido, puede concluirse que el precio que los operadores estarán dispuestos a pagar por el espectro de la banda de 700 MHz dependerá de si ya tienen disponible espectro en la banda de 800 MHz. Sin embargo, dado que la competencia por ese espectro será menor, los ingresos esperables en las licitaciones de esta nueva banda serán en general menores, a pesar de que para algunos operadores este espectro sería tan valioso como el de 800 MHz. En segundo lugar, en relación con el despliegue de femtoceldas pueden extraerse algunas conclusiones en términos de ahorro de costes de despliegue y también de cara a la viabilidad de los modelos de negocio que posibilitan. El ahorro que supone la introducción de femtoceldas en el despliegue de una red LTE frente al caso de un despliegue exclusivamente macrocelular se ha demostrado que es mayor cuanto menor es el ancho de banda disponible para la red macrocelular. En esta línea, para un operador convergente el despliegue de femtoceldas tiene sentido económico si el ancho de banda disponible es escaso (en torno a 2x10 MHz), que, en el caso de España, puede reflejar el caso de los operadores del segmento fijo que son nuevos entrantes en el móvil. Por otro lado, los modelos de acceso abierto son interesantes para operadores exclusivamente móviles, porque consiguen flexibilizar los costes sustituyendo estaciones base macrocelulares por el despliegue de femtoceldas, pero necesitan desplegarse en zonas con una densidad de población relativamente elevada para que éstas descarguen tráfico de varios usuarios de la red macrocelular simultáneamente. No obstante, las femtoceldas son beneficiosas en todo caso si es el usuario quien asume los costes de la femtocelda y el backhaul, lo que sólo parece probable si se integran en el modelo de negocio de comercialización de nuevos servicios. Por tanto, el despliegue de femtoceldas en buena parte de la casuística estudiada sólo tiene sentido si consiguen aumentar los ingresos por usuario comercializando servicios de valor añadido que necesiten calidad de servicio garantizada y exploten a la vez de esa forma su principal ventaja competitiva respecto a la tecnología WiFi. Finalmente, en relación con el papel de la tecnología LTE para la provisión de servicios de acceso fijo inalámbrico para la banda ancha de 30 Mbps, se ha desarrollado un modelo TD-LTE y mediante la metodología de análisis tecnoeconómico se ha realizado un estudio prospectivo para el caso de España. Los resultados obtenidos preciden una huella de cobertura de FTTH del 74% para 2020, y demuestran que una red TD-LTE en la banda de 3,5 GHz resulta viable para aumentar la cobertura de servicios de 30 Mbps en 14 puntos porcentuales. Junto con la consideración de la cobertura de otras redes, la cobertura de 30 Mbps de acuerdo a la viabilidad de los despliegues alcanzaría el 95% en España en el año 2020. Como resumen, los resultados obtenidos muestran en todos los casos la capacidad de la tecnología LTE para afrontar nuevos desafíos en relación con el aumento del tráfico móvil, especialmente crítico en las zonas más urbanas, y el cierre de la brecha digital en el acceso a la banda ancha rápida en las zonas más rurales. ABSTRACT The LTE standard has been pointed out as one of the keys for telecom operators to address the demand growth in mobile traffic foreseen for the next years in a cost-efficient way, since its core network is more scalable and its radio interface more flexible than those of its predecessor technologies. On the other hand, regulators need to guarantee an adequate, equitable and non-discriminatory access to radio spectrum, which enable a favorable environment for the deployment of advanced mobile communication networks. Despite the reform of the spectrum regulatory framework in Europe, which allowed for the deployment of new technologies in the historic GSM bands, additional spectrum has been allocated to IMT systems in new frequency bands, what in turn has set out new challenges for technology and regulation. The current fragmentation of available spectrum in very different frequency bands has boosted the development of carrier aggregation techniques in most recent releases of the LTE standard, which permit a better exploitation of radio resources as a whole. Nonetheless, spectrum below 1 GHz is still scarce for mobile networks, since mobile traffic increases at a more rapid pace than spectral efficiency and spectrum resources. The 900 MHz frequency band is still being used for GSM services, what has worsen the dispute between mobile communication services and terrestrial broadcasting services for the upper part of the UHF band. Concretely, the 700 MHz frequency band has been pointed out as one of the next bands to be allocated to mobile in order to increase available spectrum. However, its release by current Digital Terrestrial Television networks is challenging in Member States where it constitutes the main free access audiovisual platform, opening up a new debate around the audiovisual model in the long term in Europe. On the other hand, public policies of the present decade to promote fast and ultrafast broadband access has established very ambitious objectives for the year 2020, both at European and national levels. Universalization of 30 Mbps broadband access networks constitutes one of the main challenges. Expectations raised by LTE technology and the allocation of new frequency bands has lead fixed wireless access (FWA) services to acquire special relevance in light of public policy objectives, which will not be met but with a compendium of different technologies, as different involved stakeholders have acknowledged. This PhD Dissertation develops techno-economic models to carry out a prospective analysis for three cases of special relevance in LTE networks’ deployment: the spectrum pricing of the 700 MHz frequency band, an assessment of new business models and cost reduction considering femtocell technologies, and the feasibility of LTE fixed wireless access networks to close the 30 Mbps broadband access gap in rural areas. In the first place and regarding the application of techno-economic analysis for 700 MHz spectrum pricing, obtained results reveal two core issues. First of all, the need to allocate more spectrum for operators in order to fulfill mobile traffic demand in the mid-term. Secondly, there is a substantial difference in deployment costs for a LTE network when there is sub-1GHz spectrum available and when there is not, but this difference decreases as additional sub-1GHz spectrum is added. Thus, the allocation of 700 MHz band to mobile communication services would cause a relevant reduction in deployment costs if the operator does not count on spectrum in the 800 MHz, but not if it already has been assigned spectrum in low frequencies for the deployment. In this regard, the price operators will be willing to pay for 700 MHz spectrum will depend on them having already spectrum in the 800 MHz frequency band or not. However, since competition for the new spectrum will not be so strong, expected incomes from 700 MHz spectrum awards will be generally lower than those from the digital dividend, despite this spectrum being as valuable as 800 MHz spectrum for some operators. In the second place, regarding femtocell deployment, some conclusions can be drawn in terms of deployment cost savings and also with reference to the business model they enable. Savings provided by a joint macro-femto LTE network as compared to an exclusively macrocellular deployment increase as the available bandwidth for the macrocells decreases. Therefore, for a convergent operator the deployment of femtocells can only have economic sense if the available bandwidth is scarce (around 2x10 MHz), which might be the case of fix market operators which are new entrant in mobile market. Besides, open access models are interesting for exclusively mobile operators, since they make costs more flexible by substituting macrocell base stations by femtocells, but they need to be deployed relatively densely populated areas so that they can offload traffic from several macrocell users simultaneously. Nonetheless, femtocells are beneficial in all cases if the user assumes both femtocell and backhaul costs, which only seems probable if they are integrated in a business model commercializing new services. Therefore, in many of the cases analyzed femtocell deployment only makes sense if they increase revenues per user through new added value services which need from guaranteed quality of service, thus exploiting its main competitive advantage compared to WiFi. Finally, regarding the role of LTE technology in the provision of fixed wireless access services for 30 Mbps broadband, a TD-LTE model has been developed and a prospective study has been carried out through techno-economic methodology for the Spanish case. Obtained results foresee a FTTH coverage footprint of 74% households for 2020, and prove that a TD-LTE network in the 3.5 GHz band results feasible to increase 30 Mbps service coverage in additional 14 percentage points. To sum up, obtained results show LTE technology capability to address new challenges regarding both mobile traffic growth, particularly critical in urban zones, and the current digital divide in fast broadband access in most rural zones.
Resumo:
Abstract Mobile Edge Computing enables the deployment of services, applications, content storage and processing in close proximity to mobile end users. This highly distributed computing environment can be used to provide ultra-low latency, precise positional awareness and agile applications, which could significantly improve user experience. In order to achieve this, it is necessary to consider next-generation paradigms such as Information-Centric Networking and Cloud Computing, integrated with the upcoming 5th Generation networking access. A cohesive end-to-end architecture is proposed, fully exploiting Information-Centric Networking together with the Mobile Follow-Me Cloud approach, for enhancing the migration of content-caches located at the edge of cloudified mobile networks. The chosen content-relocation algorithm attains content-availability improvements of up to 500 when a mobile user performs a request and compared against other existing solutions. The performed evaluation considers a realistic core-network, with functional and non-functional measurements, including the deployment of the entire system, computation and allocation/migration of resources. The achieved results reveal that the proposed architecture is beneficial not only from the users’ perspective but also from the providers point-of-view, which may be able to optimize their resources and reach significant bandwidth savings.
Resumo:
In this paper, the implementation aspects and constraints of the simplest network coding (NC) schemes for a two-way relay channel (TWRC) composed of a user equipment (mobile terminal), an LTE relay station (RS) and an LTE base station (eNB) are considered in order to assess the usefulness of the NC in more realistic scenarios. The information exchange rate gain (IERG), the energy reduction gain (ERG) and the resource utilization gain (RUG) of the NC schemes with and without subcarrier division duplexing (SDD) are obtained by computer simulations. The usefulness of the NC schemes are evaluated for varying traffic load levels, the geographical distances between the nodes, the RS transmit powers, and the maximum numbers of retransmissions. Simulation results show that the NC schemes with and without SDD, have the throughput gains 0.5% and 25%, the ERGs 7 - 12% and 16 - 25%, and the RUGs 0.5 - 3.2%, respectively. It is found that the NC can provide performance gains also for the users at the cell edge. Furthermore, the ERGs of the NC increase with the transmit power of the relay while the ERGs of the NC remain the same even when the maximum number of retransmissions is reduced.
Resumo:
This research is focused on the optimisation of resource utilisation in wireless mobile networks with the consideration of the users’ experienced quality of video streaming services. The study specifically considers the new generation of mobile communication networks, i.e. 4G-LTE, as the main research context. The background study provides an overview of the main properties of the relevant technologies investigated. These include video streaming protocols and networks, video service quality assessment methods, the infrastructure and related functionalities of LTE, and resource allocation algorithms in mobile communication systems. A mathematical model based on an objective and no-reference quality assessment metric for video streaming, namely Pause Intensity, is developed in this work for the evaluation of the continuity of streaming services. The analytical model is verified by extensive simulation and subjective testing on the joint impairment effects of the pause duration and pause frequency. Various types of the video contents and different levels of the impairments have been used in the process of validation tests. It has been shown that Pause Intensity is closely correlated with the subjective quality measurement in terms of the Mean Opinion Score and this correlation property is content independent. Based on the Pause Intensity metric, an optimised resource allocation approach is proposed for the given user requirements, communication system specifications and network performances. This approach concerns both system efficiency and fairness when establishing appropriate resource allocation algorithms, together with the consideration of the correlation between the required and allocated data rates per user. Pause Intensity plays a key role here, representing the required level of Quality of Experience (QoE) to ensure the best balance between system efficiency and fairness. The 3GPP Long Term Evolution (LTE) system is used as the main application environment where the proposed research framework is examined and the results are compared with existing scheduling methods on the achievable fairness, efficiency and correlation. Adaptive video streaming technologies are also investigated and combined with our initiatives on determining the distribution of QoE performance across the network. The resulting scheduling process is controlled through the prioritization of users by considering their perceived quality for the services received. Meanwhile, a trade-off between fairness and efficiency is maintained through an online adjustment of the scheduler’s parameters. Furthermore, Pause Intensity is applied to act as a regulator to realise the rate adaptation function during the end user’s playback of the adaptive streaming service. The adaptive rates under various channel conditions and the shape of the QoE distribution amongst the users for different scheduling policies have been demonstrated in the context of LTE. Finally, the work for interworking between mobile communication system at the macro-cell level and the different deployments of WiFi technologies throughout the macro-cell is presented. A QoEdriven approach is proposed to analyse the offloading mechanism of the user’s data (e.g. video traffic) while the new rate distribution algorithm reshapes the network capacity across the macrocell. The scheduling policy derived is used to regulate the performance of the resource allocation across the fair-efficient spectrum. The associated offloading mechanism can properly control the number of the users within the coverages of the macro-cell base station and each of the WiFi access points involved. The performance of the non-seamless and user-controlled mobile traffic offloading (through the mobile WiFi devices) has been evaluated and compared with that of the standard operator-controlled WiFi hotspots.
Resumo:
In this paper a new approach to the resource allocation and scheduling mechanism that reflects the effect of user's Quality of Experience is presented. The proposed scheduling algorithm is examined in the context of 3GPP Long Term Evolution (LTE) system. Pause Intensity (PI) as an objective and no-reference quality assessment metric is employed to represent user's satisfaction in the scheduler of eNodeB. PI is in fact a measurement of discontinuity in the service. The performance of the scheduling method proposed is compared with two extreme cases: maxCI and Round Robin scheduling schemes which correspond to the efficiency and fairness oriented mechanisms, respectively. Our work reveals that the proposed method is able to perform between fairness and efficiency requirements, in favor of higher satisfaction for the users to the desired level. © VDE VERLAG GMBH.
Resumo:
Owing to the limited cell size of eNodeB (eNB), the relay node has emerged as an attractive solution for the long-term evolution (LTE) system. The nonlinear limit of the alternative method to multipleinput and multiple-output (MIMO) based on frequency division multiplexing (FDM) for orthogonal FDM (OFDM) is analysed over varying transmission spans. In this reported work, it is shown that the degradation pattern over the linear, intermixing and nonlinear propagation regions is consistent for the 2 and the 2.6 GHz bands. The proposed bands experienced a linear increase in the error vector magnitude (EVM) for both the linear and the nonlinear regions proportional to the increasing transmission spans. In addition, an optical launch power between -2 and 2 dBm achieved a significantly lower EVM than the LTE limit of 8% for the 10-60 km spans. © The Institution of Engineering and Technology 2014.
Resumo:
Mobile WiFi devices are becoming increasingly popular in non-seamless and user-controlled mobile traffic offloading alongside the standard WiFi hotspots. Unlike the operator-controlled hotspots, a mobile WiFi device relies on the capacity of the macro-cell for the data rate allocated to it. This type of devices can help offloading data traffic from the macro-cell base station and serve the end users within a closer range, but will change the pattern of resource distributions operated by the base station. We propose a resource allocation scheme that aims to optimize user quality of experience (QoE) when accessing video services in the environment where traffic offloading is taking place through interworking between a mobile communication system and low range wireless LANs. In this scheme, a rate redistribution algorithm is derived to perform scheduling which is controlled by a no-reference quality assessment metric in order to achieve the desired trade-offs between efficiency and fairness. We show the performance of this algorithm in terms of the distribution of the allocated data rates throughout the macro-cell investigated and the service coverage offered by the WiFi access point.
Resumo:
Mobile communication and networking infrastructures play an important role in the development of smart cities, to support real-time information exchange and management required in modern urbanization. Mobile WiFi devices that help offloading data traffic from the macro-cell base station and serve the end users within a closer range can significantly improve the connectivity of wireless communications between essential components including infrastructural and human devices in a city. However, this offloading function through interworking between LTE and WiFi systems will change the pattern of resource distributions operated by the base station. In this paper, a resource allocation scheme is proposed to ensure stable service coverage and end-user quality of experience (QoE) when offloading takes place in a macro-cell environment. In this scheme, a rate redistribution algorithm is derived to form a parametric scheduler to meet the required levels of efficiency and fairness, guided by a no-reference quality assessment metric. We show that the performance of resource allocation can be regulated by this scheduler without affecting the service coverage offered by the WLAN access point. The performances of different interworking scenarios and macro-cell scheduling policies are also compared.
Resumo:
Today, smart-phones have revolutionized wireless communication industry towards an era of mobile data. To cater for the ever increasing data traffic demand, it is of utmost importance to have more spectrum resources whereby sharing under-utilized spectrum bands is an effective solution. In particular, the 4G broadband Long Term Evolution (LTE) technology and its foreseen 5G successor will benefit immensely if their operation can be extended to the under-utilized unlicensed spectrum. In this thesis, first we analyze WiFi 802.11n and LTE coexistence performance in the unlicensed spectrum considering multi-layer cell layouts through system level simulations. We consider a time division duplexing (TDD)-LTE system with an FTP traffic model for performance evaluation. Simulation results show that WiFi performance is more vulnerable to LTE interference, while LTE performance is degraded only slightly. Based on the initial findings, we propose a Q-Learning based dynamic duty cycle selection technique for configuring LTE transmission gaps, so that a satisfactory throughput is maintained both for LTE and WiFi systems. Simulation results show that the proposed approach can enhance the overall capacity performance by 19% and WiFi capacity performance by 77%, hence enabling effective coexistence of LTE and WiFi systems in the unlicensed band.
Resumo:
Distributed Computing frameworks belong to a class of programming models that allow developers to
launch workloads on large clusters of machines. Due to the dramatic increase in the volume of
data gathered by ubiquitous computing devices, data analytic workloads have become a common
case among distributed computing applications, making Data Science an entire field of
Computer Science. We argue that Data Scientist's concern lays in three main components: a dataset,
a sequence of operations they wish to apply on this dataset, and some constraint they may have
related to their work (performances, QoS, budget, etc). However, it is actually extremely
difficult, without domain expertise, to perform data science. One need to select the right amount
and type of resources, pick up a framework, and configure it. Also, users are often running their
application in shared environments, ruled by schedulers expecting them to specify precisely their resource
needs. Inherent to the distributed and concurrent nature of the cited frameworks, monitoring and
profiling are hard, high dimensional problems that block users from making the right
configuration choices and determining the right amount of resources they need. Paradoxically, the
system is gathering a large amount of monitoring data at runtime, which remains unused.
In the ideal abstraction we envision for data scientists, the system is adaptive, able to exploit
monitoring data to learn about workloads, and process user requests into a tailored execution
context. In this work, we study different techniques that have been used to make steps toward
such system awareness, and explore a new way to do so by implementing machine learning
techniques to recommend a specific subset of system configurations for Apache Spark applications.
Furthermore, we present an in depth study of Apache Spark executors configuration, which highlight
the complexity in choosing the best one for a given workload.
Resumo:
This work introduces joint power amplifier (PA) and I/Q modulator modelling and compensation for LongTerm Evolution (LTE) transmitters using artificial neural networks (ANNs). The proposed solution util-izes a powerful nonlinear autoregressive with exogenous inputs (NARX) ANN architecture, which yieldsnoticeable results for high peak to average power ratio (PAPR) LTE signals. Given the ANNs learning capa-bilities, this one-step solution, which includes the mitigation of both PA nonlinearity and I/Q modulatorimpairments, is both accurate and adaptable
Resumo:
We study a multiuser multicarrier downlink communication system in which the base station (BS) employs a large number of antennas. By assuming frequency-division duplex operation, we provide a beam domain channel model as the number of BS antennas grows asymptotically large. With this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate before developing necessary conditions to asymptotically maximize the upper bound, with only statistical channel state information at the BS. Inspired by these conditions, we propose a beam division multiple access (BDMA) transmission scheme, where the BS communicates with users via different beams. For BDMA transmission, we design user scheduling to select users within non-overlapping beams, work out an optimal pilot design under a minimum mean square error criterion, and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. The proposed BDMA scheme reduces significantly the pilot overhead, as well as, the processing complexity at transceivers. Simulations demonstrate the high spectral efficiency of BDMA transmission and the advantages in the bit error rate performance of the proposed pilot sequences.
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We investigate the achievable sum rate and energy efficiency of zero-forcing precoded downlink massive multiple-input multiple-output systems in Ricean fading channels. A simple and accurate approximation of the average sum rate is presented, which is valid for a system with arbitrary rank channel means. Based on this expression, the optimal power allocation strategy maximizing the average sum rate is derived. Moreover, considering a general power consumption model, the energy efficiency of the system with rank-1 channel means is characterized. Specifically, the impact of key system parameters, such as the number of users N, the number of BS antennas M, Ricean factor K and the signal-to-noise ratio (SNR) ρ are studied, and closed-form expressions for the optimal ρ and M maximizing the energy efficiency are derived. Our findings show that the optimal power allocation scheme follows the water filling principle, and it can substantially enhance the average sum rate in the presence of strong line-of-sight effect in the low SNR regime. In addition, we demonstrate that the Ricean factor K has significant impact on the optimal values of M, N and ρ.
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We investigate the achievable ergodic sum-rate of multi-user multiple-input multiple-output systems in Ricean fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by utilizing the Mullen's inequality, which is then used to analyze the effect of channel mean information on the achievable sum-rate. With these results, a novel statistical-eigenmode space-division multipleaccess downlink transmission scheme is proposed. For this scheme, we derive an exact closed-form expression for the achievable ergodic sum-rate. Our results show that the achievable ergodic sum-rate converges to a saturation value in the high signal-to-noise ratio (SNR) region and reaches to a lower limit value in the lower Ricean K-factor range. In addition, we present tractable upper and lower bounds, which are shown to be tight for any SNR and Ricean K-factor value. Finally, the theoretical analysis is validated via numerical simulations.