Two-person Cooperative Games

Ecological data are often lognormally distributed. Nutrient concentrations, population densities and biomasses, rates of production and other flows are always positive, and generally have standard deviations that increase as the mean increases. Lognormally distributed variables have these characteristics, whereas normally distributed variables can be negative and have a standard deviation that does not change as the mean changes. Lognormal errors arise when sources of variation accumulate multiplicatively, whereas normal errors arise when sources of variation are additive. Given a normally distributed random variable Y, one can calculate a lognormally distributed random variable Z = exp(Y) where exp stands for the exponential function (exp(x) = e x). The mean Z and the standard deviation s Z of the lognormal variable are related to the mean Y and standard deviation s Y of the normal variable by) 2 / exp() exp(2 Y s Y Z = [1] 5. 0 2 ] 1) [exp(− = Y Z s Z s [2] Equation 1 can be used to correct for transformation bias in logarithmic regression. Suppose that lognormally-distributed observations Z have been log transformed as Y = log(Z) to fit a regression model such as ε + =) , (ˆ b X f Y [3] where Y is the log-transformed response variable which is predicted to be Y ˆ computed from the function f, X is a matrix of predictors, b is a vector of parameters, and the errors ε are normally distributed with mean zero and standard deviation s ε. Predictions Z ˆ in the original units are calculated using equation 1 as ] 2) ˆ exp[(ˆ 2 ε s Y Z + = [4] Note that estimates the median prediction of Z, which will be smaller than the mean for a lognormally distributed variate. Thus it makes sense to adjust the median upward, as in equation 4.) ˆ exp(Y Equation 1 is also used in drawing random numbers from a lognormal distribution. Generators for normally-distributed random variables Y are common. Suppose we draw many values of Y with mean zero and standard deviation s Y. Then from equation 1, the mean of exp(Y) will not be 1 = e 0 ; instead the mean of exp(Y) will be. Generally, however, one would prefer to have the mean of a set of lognormally distributed random numbers be 1. This can be accomplished by shifting the random numbers to Y) 2 / exp(2 Y …

対数正規分布(Lognormal Distribution)のあてはめについて

Dynamic spectrum access in cognitive radio networks can greatly improve the spectrum utilization efficiency. Nevertheless, interference may be introduced to the Primary User (PU) when the Secondary Users (SUs) dynamically utilize the PU's licensed channels. If the SUs can be synchronous with the PU's time slots, the interference is mainly due to their imperfect spectrum sensing of the primary channel. However, if the SUs have no knowledge about the PU's exact communication mechanism, additional interference may occur. In this paper, we propose a dynamic spectrum access protocol for the SUs confronting with unknown primary behavior and study the interference caused by their dynamic access. Through analyzing the SUs' dynamic behavior in the primary channel which is modeled as an ON-OFF process, we prove that the SUs' communication behavior is a renewal process. Based on the Renewal Theory, we quantify the interference caused by the SUs and derive the corresponding close-form expressions. With the interference analysis, we study how to optimize the SUs' performance under the constraints of the PU's communication quality of service (QoS) and the secondary network's stability. Finally, simulation results are shown to verify the effectiveness of our analysis.

Renewal-Theoretical Dynamic Spectrum Access in Cognitive Radio Networks with Unknown Primary Behavior

Dynamic spectrum access in cognitive radio networks can greatly improve the spectrum utilization efficiency. Nevertheless, interference may be introduced to the Primary User (PU) when the Secondary Users (SUs) dynamically utilize the PU's licensed channels. If the SUs can be synchronous with the PU's time slots, the interference is mainly due to their imperfect spectrum sensing of the primary channel. However, if the SUs have no knowledge about the PU's exact communication mechanism, additional interference may occur. In this paper, we propose a dynamic spectrum access protocol for the SUs confronting with unknown primary behavior and study the interference caused by their dynamic access. Through analyzing the SUs' dynamic behavior in the primary channel which is modeled as an ON-OFF process, we prove that the SUs' communication behavior is a renewal process. Based on the Renewal Theory, we quantify the interference caused by the SUs and derive the corresponding closed-form expressions. With the interference analysis, we study how to optimize the SUs' performance under the constraints of the PU's communication quality of service (QoS) and the secondary network's stability. Finally, simulation results are shown to verify the effectiveness of our analysis.

Renewal-theoretical dynamic spectrum access in cognitive radio network with unknown primary behavior

In this work we seek to characterise the performance of spatial modulation (SM) and spatial multiplexing (SMX) with an experimental test bed. Two National Instruments (NI)-PXIe devices are used for the system testing, one for the transmitter and one for the receiver. The digital signal processing that formats the information data in preparation of transmission is described along with the digital signal processing that recovers the information data. In addition, the hardware limitations of the system are also analysed. The average bit error ratio (ABER) of the system is validated through both theoretical analysis and simulation results for SM and SMX under line of sight (LoS) channel conditions.

Practical Implementation of Spatial Modulation

In this paper, we present interference models for cognitive radio (CR) networks employing various interference management mechanisms including power control, contention control or hybrid power/contention control schemes. For the first case, a power control scheme is proposed to govern the transmission power of a CR node. For the second one, a contention control scheme at the media access control (MAC) layer, based on carrier sense multiple access with collision avoidance (CSMA/CA), is proposed to coordinate the operation of CR nodes with transmission requests. The probability density functions (PDFs) of the interference received at a primary receiver from a CR network are first derived numerically for these two cases. For the hybrid case, where power and contention controls are jointly adopted by a CR node to govern its transmission, the interference is analyzed and compared with that of the first two schemes by simulations. Then, the interference PDFs under the first two control schemes are fitted by log-normal PDFs to reduce computation complexity. Moreover, the effect of a hidden primary receiver on the interference experienced at the receiver is investigated. It is demonstrated that both power and contention controls are effective approaches to alleviate the interference caused by CR networks. Some in-depth analysis of the impact of key parameters on the interference of CR networks is given as well.

Aggregate Interference Modeling in Cognitive Radio Networks with Power and Contention Control

http://home.eps.hw.ac.uk/~cw46/2013_Wang_PHYCOM151_13_09_308.pdf

Interference mitigation for cognitive radio MIMO systems based on practical precoding

In this paper, we present an interference model for cognitive radio (CR) networks employing power control or contention control scheme The probability density functions (PDFs) of the interference received at a primary receiver from a CR network are derived for two cases For the first case, a power control scheme is proposed to govern the transmission power of a CR node For the second one, a cognitive media access control (MAC) employs carrier sense multiple access with collision avoidance (CSMA/CA) based contention control to coordinate the operation of CR nodes with transmission requests These two control schemes are compared in terms of their resulting interference distributions It is demonstrated that both power and contention controls are effective approaches to alleviate the interference caused by CR networks Some in-depth analysis for the impact of key parameters on the interference of CR networks is given via numerical studies as well

/pdf/interference-modeling-for-cognitive-radio-networks-with-4mun42nqvr.pdf

Interference Modeling for Cognitive Radio Networks with Power or Contention Control

In this paper, we propose two subspace-projection-based precoding schemes, namely, full-projection (FP)- and partial-projection (PP)-based precoding, for a cognitive radio multiple-input multiple-output (CR-MIMO) network to mitigate its interference to a primary time-division-duplexing (TDD) system. The proposed precoding schemes are capable of estimating interference channels between CR and primary networks, and incorporating the interference from the primary to the CR system into CR precoding via a novel sensing approach. Then, the CR performance and resulting interference of the proposed precoding schemes are analyzed and evaluated. By fully projecting the CR transmission onto a null space of the interference channels, the FP-based precoding scheme can effectively avoid interfering the primary system with boosted CR throughput. While, the PP-based scheme is able to further improve the CR throughput by partially projecting its transmission onto the null space.

Interference Mitigation for Cognitive Radio MIMO Systems Based on Practical Precoding

adio spectrum is a scarce and precious natural resource that is signifi-cantly underutilized with current fixed spectrum-licensing policies [1].Thishasinspiredthedevelopmentofhierarchicalspectrum-sharingsys-tems, where secondary systems are allowed to access the underutilizedspectrumofincumbentswithoutcausingharmfulinterferencetolegacy/primarysystems.Inthisarticle,weareinterestedinanimportantparadigmofsecondarysystems known as cognitive radio (CR) networks [2], [3], where the secondaryterminals are envisioned to be capable of sensing and reasoning about theoper-atingradio environments andtherebyautonomously adjusting theirtransceiverparameterstoexploittheunderutilizedradioresourcesinadynamicfashion.Because of its spectrum-sharing nature, a CR network inevitably operates ininterference-intensiveenvironments.Effectiveinterferencemanagementisthere-fore essential to the coexistence of primary and CR networks. Interference man-agement mechanisms can be embedded into a CR network in various aspects ofsystem design from network planning, radio resource management, mediumaccess control (MAC) to physical-layer signal processing. Our interest in thisstudy lies on the physical-layer signal-processing schemes, commonly known asinterferencecancelation (IC)techniques.Intheliterature,onlyafewarticles[4]–[7]havestudiedICtechniquesinthecontextofCRnetworks.In[4],anopportun-istic IC scheme was proposed for CR receivers to adaptively cancel the primarysignals when they are decodable. In [5]–[7], active spectrum shaping, transmitbeamforming,andtransmitprecodingtechniqueswereinvestigatedforCRtrans-mitters, respectively. Apart from the aforementioned articles, there exist manyother IC techniques [8] that have been proposed and successfully applied to anumberofwirelesssystemstomitigatevarioustypesofinterference. The widelyused IC techniques include the filter-based approach (e.g., Wiener filter), trans-form-domainapproach(e.g.,wavelet,chirplet),cyclostationarity-basedapproach,higher order statistics-based approach, joint detection/multiuser detection(MUD),andspatialprocessing(e.g.,beamforming).ThesuccessoftheseICtech-niquesinspiresustostudytheirapplicationstoCRnetworks.

/pdf/interference-cancelation-and-management-techniques-4veye8wtwz.pdf

Zengmao Chen

Papers

Aggregate Interference Modeling in Cognitive Radio Networks with Power and Contention Control

Interference mitigation for cognitive radio MIMO systems based on practical precoding

Interference Modeling for Cognitive Radio Networks with Power or Contention Control

Interference Mitigation for Cognitive Radio MIMO Systems Based on Practical Precoding

Interference Cancelation and Management Techniques