IEEE Middle East Conference on Antennas and Propagation (MECAP 2010), 2010
In this paper we will be discussing the development of the Explicit Propagator integral equation,... more In this paper we will be discussing the development of the Explicit Propagator integral equation, its associated tensor Green function, and the numerical method used to evaluate the propagated fields. Because it is an exact solution, the propagator carries the complete wave nature of the field. A Green function propagator incorporated in the integral equation allows unlimited time and spatial
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2015
In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectru... more In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectrum holes not used by the primary users (PUs) and cease their transmissions whenever primary users reuse their spectrum bands. To study the mean time an SU spends in the system we propose a discrete-time multi-server access model. Since periodic sensing is commonly used to protect the PU, discrete-time models are more convenient to analyze the performance of the SU system. Additionally, a multi-server access model is assumed in order to give the SU the capability to access a channel that is not occupied by a PU or any other SUs. We derive the probability generating function of the number of connections in the system. Then we derive a formula for the mean response time of an SU. In the numerical results we show the relationship between the mean response time and the SU traffic intensity. In addition we show the effect of changing the number of channels in the system and the PU traffic intensity on the mean response time of an SU.
In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectru... more In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectrum holes not used by the primary users (PUs) and cease their transmissions whenever primary users reuse their spectrum bands. To study the mean time an SU spends in the system we propose a discrete-time multi-server access model. Since periodic sensing is commonly used to protect the PU, discrete-time models are more convenient to analyze the performance of the SU system. Additionally, a multi-server access model is assumed in order to give the SU the capability to access a channel that is not occupied by a PU or any other SUs. We derive the probability generating function of the number of connections in the system. Then we derive a formula for the mean response time of an SU. In the numerical results we show the relationship between the mean response time and the SU traffic intensity. In addition we show the effect of changing the number of channels in the system and the PU traffic intensity on the mean response time of an SU. Finally, simulation results validate the proposed theoretical model and reveal that the numerical results fit the simulated results well.
This paper is intended to give a complete formula for the free-space time-domain dyadic Green's f... more This paper is intended to give a complete formula for the free-space time-domain dyadic Green's function (TDDGF) for Maxwell's equations. The vector potential approach is used in solving Maxwell's equations in TD resulting in a new form for the source region term. This new form is different from that resulting from the state-space approach recently applied in literature. The source region term in the recently reported TD-DGF seems to be inconsistent with the well-known frequency domain results. This paper is intended to give a formula that is completely consistent with the frequency domain results. Also, it gives an interpretation of the seemingly inconsistency of the reported TD-DGF. A main advantage of the introduced form over the recently reported form is that it is applicable for different coordinate systems representing the source current. The paper also shows that the second derivative term in the recently reported field propagator formula is completely unnecessary. This leads to a great simplification in calculations as shown in the paper.
In this paper we will be discussing the development of the Explicit Propagator integral equation,... more In this paper we will be discussing the development of the Explicit Propagator integral equation, its associated tensor Green function, and the numerical method used to evaluate the propagated fields. Because it is an exact solution, the propagator carries the complete wave nature of the field. A Green function propagator incorporated in the integral equation allows unlimited time and spatial step sizes, thereby avoiding a common limitation of numerical solution methods that originate from differential equation expressions. A numerical method based on our recently derived integral equation and Green function provides accurate multiscale calculations while retaining the stability inherent in explicit methods. Numerical evaluation produces a field that is less susceptible to numerical dispersion than a purely numerical method and possesses the ability to seamlessly propagate between numerical spaces.
IEEE Middle East Conference on Antennas and Propagation (MECAP 2010), 2010
In this paper we will be discussing the development of the Explicit Propagator integral equation,... more In this paper we will be discussing the development of the Explicit Propagator integral equation, its associated tensor Green function, and the numerical method used to evaluate the propagated fields. Because it is an exact solution, the propagator carries the complete wave nature of the field. A Green function propagator incorporated in the integral equation allows unlimited time and spatial
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2015
In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectru... more In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectrum holes not used by the primary users (PUs) and cease their transmissions whenever primary users reuse their spectrum bands. To study the mean time an SU spends in the system we propose a discrete-time multi-server access model. Since periodic sensing is commonly used to protect the PU, discrete-time models are more convenient to analyze the performance of the SU system. Additionally, a multi-server access model is assumed in order to give the SU the capability to access a channel that is not occupied by a PU or any other SUs. We derive the probability generating function of the number of connections in the system. Then we derive a formula for the mean response time of an SU. In the numerical results we show the relationship between the mean response time and the SU traffic intensity. In addition we show the effect of changing the number of channels in the system and the PU traffic intensity on the mean response time of an SU.
In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectru... more In opportunistic spectrum access communication systems, secondary users (SUs) exploit the spectrum holes not used by the primary users (PUs) and cease their transmissions whenever primary users reuse their spectrum bands. To study the mean time an SU spends in the system we propose a discrete-time multi-server access model. Since periodic sensing is commonly used to protect the PU, discrete-time models are more convenient to analyze the performance of the SU system. Additionally, a multi-server access model is assumed in order to give the SU the capability to access a channel that is not occupied by a PU or any other SUs. We derive the probability generating function of the number of connections in the system. Then we derive a formula for the mean response time of an SU. In the numerical results we show the relationship between the mean response time and the SU traffic intensity. In addition we show the effect of changing the number of channels in the system and the PU traffic intensity on the mean response time of an SU. Finally, simulation results validate the proposed theoretical model and reveal that the numerical results fit the simulated results well.
This paper is intended to give a complete formula for the free-space time-domain dyadic Green's f... more This paper is intended to give a complete formula for the free-space time-domain dyadic Green's function (TDDGF) for Maxwell's equations. The vector potential approach is used in solving Maxwell's equations in TD resulting in a new form for the source region term. This new form is different from that resulting from the state-space approach recently applied in literature. The source region term in the recently reported TD-DGF seems to be inconsistent with the well-known frequency domain results. This paper is intended to give a formula that is completely consistent with the frequency domain results. Also, it gives an interpretation of the seemingly inconsistency of the reported TD-DGF. A main advantage of the introduced form over the recently reported form is that it is applicable for different coordinate systems representing the source current. The paper also shows that the second derivative term in the recently reported field propagator formula is completely unnecessary. This leads to a great simplification in calculations as shown in the paper.
In this paper we will be discussing the development of the Explicit Propagator integral equation,... more In this paper we will be discussing the development of the Explicit Propagator integral equation, its associated tensor Green function, and the numerical method used to evaluate the propagated fields. Because it is an exact solution, the propagator carries the complete wave nature of the field. A Green function propagator incorporated in the integral equation allows unlimited time and spatial step sizes, thereby avoiding a common limitation of numerical solution methods that originate from differential equation expressions. A numerical method based on our recently derived integral equation and Green function provides accurate multiscale calculations while retaining the stability inherent in explicit methods. Numerical evaluation produces a field that is less susceptible to numerical dispersion than a purely numerical method and possesses the ability to seamlessly propagate between numerical spaces.
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