This document summarizes research on optimized cooperative spectrum sensing in clustered cognitive radio networks. The key points are:
1) Secondary users are grouped into clusters and transmit a power function of their observations to a fusion center on orthogonal channels to detect the presence of primary users.
2) The goal is to maximize the probability of detection for a given false alarm probability by optimizing the number of clusters, power function exponent, and linear combining coefficients at the fusion center.
3) Analytical expressions for the probability of detection and false alarm are derived based on the conditional mean and variance of the combined signal at the fusion center under the two hypotheses.
Cooperative-hybrid detection of primary user emulators in cognitive radio net...IJECEIAES
Primary user emulator (PUE) attack occurs in Cognitive Radio Networks (CRNs) when a malicious secondary user (SU) poses as a primary user (PU) in order to deprive other legitimate SUs the right to free spectral access for opportunistic communication. In most cases, these legitimate SUs are unable to effectively detect PUEs because the quality of the signals received from a PUE may be severely attenuated by channel fading and/or shadowing. Consequently, in this paper, we have investigated the use of cooperative spectrum sensing (CSS) to improve PUE detection based on a hybrid localization scheme. We considered different pairs of secondary users (SUs) over different received signal strength (RSS) values to evaluate the energy efficiency, accuracy, and speed of the new cooperative scheme. Based on computer simulations, our findings suggest that a PUE can be effectively detected by a pair of SUs with a low Root Mean Square Error rate of 0.0047 even though these SUs may have close RSS values within the same cluster. Furthermore, our scheme performs better in terms of speed, accuracy and low energy consumption rates when compared with other PUE detection schemes. Thus, it is a viable proposition to better detect PUEs in CRNs.
Effective capacity in cognitive radio broadcast channelsMarwan Hammouda
Abstract—In this paper, we investigate effective capacity by
modeling a cognitive radio broadcast channel with one secondary transmitter (ST) and two secondary receivers (SRs) under quality-of-service constraints and interference power limitations.We initially describe three different ooperative channel sensing strategies with different ard-decision combining algorithms at the ST, namely OR, Majority, and AND rules. Since the channel sensing occurs with possible errors, we consider a combined
interference power constraint by which the transmission power of the secondary users (SUs) is bounded when the channel is sensed as both busy and idle. Furthermore, regarding the channel sensing decision and its correctness, there exist ...
A CRITICAL REVIEW OF THE ROUTING PROTOCOLS FOR COGNITIVE RADIO NETWORKS AND A...cscpconf
We present a critical review and analysis of different categories of routing protocols for cognitive radio networks. We first classify the available solutions to two broad categories: those
based on full spectrum knowledge (typically used to establish performance benchmarks) and those based on local spectrum knowledge (used for real-time implementation). The full spectrum knowledge based routing solutions are analyzed from a graph-theoretic point of view, and we review the layered graph, edge coloring and conflict graph models. We classify the various local spectrum knowledge based routing protocols into the following five categories: Minimum power, Minimum delay, Maximum throughput, Geographic and Class-based routing. A total of 25 routing protocols proposed for cognitive radio networks have been reviewed. We discuss the working principle and analyze the pros and cons of the routing protocols. Finally, we propose an idea of a load balancing-based local spectrum knowledge-based routing protocol for cognitive radio ad hoc networks.
Adaptive Resource Allocation in MIMO-OFDM Communication Systemijsrd.com
Multiple Input and Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) system have the potential to achieve very high capacity depending on the propagation environment. The objective of this paper is the adaptive resource allocation in MIMOOFDM system using the waterfilling algorithm. Water filling solution is implemented for allocating the power in order to increase the channel capacity. The total system capacity is maximised subject to the constraints on total power, signal to noise ratio, and proportional fairness. Channel is assumed as a flat fading channel and the comparison is made for different 2x2, 2x3, 3x2 and 4x4 MIMO-OFDM systems using waterfilling algorithm with allocated power. Also in order to prove that the MIMOOFDM with waterfilling algorithm provides the best performance a comparison with various SISO - OFDM is done.
Resource Allocation in MIMO – OFDM Communication System under Signal Strength...Kumar Goud
Abstract: - Multiple Inputs and Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) system have the potential to attain high capability on the propagation setting. The aim of this paper is that the adaptive resource allocation in MIMO-OFDM system uses the water filling formula. Water filling answer is enforced for allocating the ability so as to extend the data rate. The overall system capability is maximised subject to the constraints on total power, signal to noise quantitative relation, and proportionality. Channel is assumed as a flat attenuation channel and therefore the comparison is created for various 2×2, 2×3, 3×2 and 4×4 MIMO-OFDM systems and water filling formula with allotted power. Supported the capability contribution from the relaying terminal, a brand new parameter referred to as cooperation constant is introduced as an operate of the relaying sub channel. This parameter is employed to switch the target parameter of the subcarrier allocation procedure. Fairness-oriented [Fading Channel] and throughput-oriented [Near finish Channel] algorithms square measure elite from the literature to check the planned technique. Each algorithms square measure changed to use the mean of cooperation constant within the objective parameter of the subcarrier allocation procedure and shown to own a much better total turnout with none sacrifice.
Keywords - MIMO-OFDM; Water filling Algorithm; Subcarrier Resource Allocation
Cooperative-hybrid detection of primary user emulators in cognitive radio net...IJECEIAES
Primary user emulator (PUE) attack occurs in Cognitive Radio Networks (CRNs) when a malicious secondary user (SU) poses as a primary user (PU) in order to deprive other legitimate SUs the right to free spectral access for opportunistic communication. In most cases, these legitimate SUs are unable to effectively detect PUEs because the quality of the signals received from a PUE may be severely attenuated by channel fading and/or shadowing. Consequently, in this paper, we have investigated the use of cooperative spectrum sensing (CSS) to improve PUE detection based on a hybrid localization scheme. We considered different pairs of secondary users (SUs) over different received signal strength (RSS) values to evaluate the energy efficiency, accuracy, and speed of the new cooperative scheme. Based on computer simulations, our findings suggest that a PUE can be effectively detected by a pair of SUs with a low Root Mean Square Error rate of 0.0047 even though these SUs may have close RSS values within the same cluster. Furthermore, our scheme performs better in terms of speed, accuracy and low energy consumption rates when compared with other PUE detection schemes. Thus, it is a viable proposition to better detect PUEs in CRNs.
Effective capacity in cognitive radio broadcast channelsMarwan Hammouda
Abstract—In this paper, we investigate effective capacity by
modeling a cognitive radio broadcast channel with one secondary transmitter (ST) and two secondary receivers (SRs) under quality-of-service constraints and interference power limitations.We initially describe three different ooperative channel sensing strategies with different ard-decision combining algorithms at the ST, namely OR, Majority, and AND rules. Since the channel sensing occurs with possible errors, we consider a combined
interference power constraint by which the transmission power of the secondary users (SUs) is bounded when the channel is sensed as both busy and idle. Furthermore, regarding the channel sensing decision and its correctness, there exist ...
A CRITICAL REVIEW OF THE ROUTING PROTOCOLS FOR COGNITIVE RADIO NETWORKS AND A...cscpconf
We present a critical review and analysis of different categories of routing protocols for cognitive radio networks. We first classify the available solutions to two broad categories: those
based on full spectrum knowledge (typically used to establish performance benchmarks) and those based on local spectrum knowledge (used for real-time implementation). The full spectrum knowledge based routing solutions are analyzed from a graph-theoretic point of view, and we review the layered graph, edge coloring and conflict graph models. We classify the various local spectrum knowledge based routing protocols into the following five categories: Minimum power, Minimum delay, Maximum throughput, Geographic and Class-based routing. A total of 25 routing protocols proposed for cognitive radio networks have been reviewed. We discuss the working principle and analyze the pros and cons of the routing protocols. Finally, we propose an idea of a load balancing-based local spectrum knowledge-based routing protocol for cognitive radio ad hoc networks.
Adaptive Resource Allocation in MIMO-OFDM Communication Systemijsrd.com
Multiple Input and Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) system have the potential to achieve very high capacity depending on the propagation environment. The objective of this paper is the adaptive resource allocation in MIMOOFDM system using the waterfilling algorithm. Water filling solution is implemented for allocating the power in order to increase the channel capacity. The total system capacity is maximised subject to the constraints on total power, signal to noise ratio, and proportional fairness. Channel is assumed as a flat fading channel and the comparison is made for different 2x2, 2x3, 3x2 and 4x4 MIMO-OFDM systems using waterfilling algorithm with allocated power. Also in order to prove that the MIMOOFDM with waterfilling algorithm provides the best performance a comparison with various SISO - OFDM is done.
Resource Allocation in MIMO – OFDM Communication System under Signal Strength...Kumar Goud
Abstract: - Multiple Inputs and Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) system have the potential to attain high capability on the propagation setting. The aim of this paper is that the adaptive resource allocation in MIMO-OFDM system uses the water filling formula. Water filling answer is enforced for allocating the ability so as to extend the data rate. The overall system capability is maximised subject to the constraints on total power, signal to noise quantitative relation, and proportionality. Channel is assumed as a flat attenuation channel and therefore the comparison is created for various 2×2, 2×3, 3×2 and 4×4 MIMO-OFDM systems and water filling formula with allotted power. Supported the capability contribution from the relaying terminal, a brand new parameter referred to as cooperation constant is introduced as an operate of the relaying sub channel. This parameter is employed to switch the target parameter of the subcarrier allocation procedure. Fairness-oriented [Fading Channel] and throughput-oriented [Near finish Channel] algorithms square measure elite from the literature to check the planned technique. Each algorithms square measure changed to use the mean of cooperation constant within the objective parameter of the subcarrier allocation procedure and shown to own a much better total turnout with none sacrifice.
Keywords - MIMO-OFDM; Water filling Algorithm; Subcarrier Resource Allocation
LARGE-SCALE MULTI-USER MIMO APPROACH FOR WIRELESS BACKHAUL BASED HETNETScsandit
In this paper, we consider the optimization of wireless capacity-limited backhaul links in future heterogeneous networks (HetNets). We assume that the HetNet is formed with one macro-cell base station (MBS), which is associated with multiple small-cell base stations (SBSs). It is also assumed both the MBS and the SBSs are equipped with massive arrays, while all mobiles users (macro-cell and small-cell users) have single antenna. For the backhaul links, we propose to use a capacity-aware beamforming scheme at the SBSs and MRC at the MBS. Using particle swarm optimization (PSO), each SBS seeks the optimal transmit weight vectors that maximize the backhaul uplink capacity and the access uplinks signal-to-interference plus noise ratio (SINR). The performance evaluation in terms of the symbol error rate (SER) and the ergodic system capacity shows that the proposed capacity-aware backhaul link scheme achieves similar or better performance than traditional wireless backhaul links and requires considerably less computational complexity.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Computational Engineering Research(IJCER) ijceronline
nternational Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
An approach to control inter cellular interference using load matrix in multi...eSAT Journals
Abstract
This paper deals with reduction of inter cellular interference in Multi-carrier communication systems. In the past, Load Matrix(LM) is proposed to allocate power to different users in a network based upon Signal to noise plus interference ratio (SNIR) so as to reduce inter cellular interference and is observed for single carrier systems. In Multi carrier systems the SNIR is affected distinctly in each carrier thus a single SNIR for power allocation is not optimal. In this paper, to obtain the optimization of power allocation in Multi-Carrier system, Load Matrix coding with bifurcated SNIR (LM-BFSNIR) is proposed. Using this approach it is observed that inter cellular interference is reduced better when compared to a single carrier system evaluated over a 3GPP-LTE standard.
Keywords−Power allocation, Inter cellular interference, Multi-Carrier mobile Communication system.
Implementation of Vacate on Demand Algorithm in Various Spectrum Sensing Netw...IJERA Editor
In present days the wireless communications are widely increases because of this reason spectrum utilization can be rapidly increased.For efficient usage of spectrum we can implement the Vacate on demand algorithm in different networks. CR users also need to sense the spectrum and vacate the channel upon the detection of the PU‟s presence to protectPUs from harmful interference. To achieve these fundamental CR functions, CR users usually coordinate with each other by using a common medium for control message exchange ensuring a priority of PUs over CR users. This paper presents the Vacate on Demand (VD) algorithm which enables dynamic spectrum access and ensures to vacate the assigned channel in case of PU activity and move the CR user to some other vacant channel to make spectrum available to PUs as well as to CR users. The basic idea is to use a ranking table of the available channels based on the PU activity detected on each channel. To improve the spectrum efficiency we can implement the Vacate on demand algorithm in MANET Network.
A SURVEY ON OPTIMIZATION BASED SPECTRUM SENSING TECHNIQUES TO REDUCE ISI AND ...IJNSA Journal
Cognitive radio is emerging technologies in OFDM based wireless systems which are very important for spectrum sensing. By using cognitive radio (CR) high data can be transferred with low bit error rate. The key idea of OFDM is to split the total transmission bandwidth into the subcarriers which further reduce the intersymbol interference (ISI) and peak to average power ratio(PAPR) in the signal. There are many optimization based spectrum sensing techniques are existing for efficient sensing purpose but each has its own advantages and disadvantages. This leads to start the comprehensive study for reducing PAPR and ISI(Intersymbol interference) in terms of FPGA based partial configuration. In the first part of review OFDM characteristics of the signal has compared with several optimizations based ISI reduction techniques. The second part is to compare the various spectrum sensing techniques in cognitive radio engine and its application in FPGA.
Pilot Decontamination over Time Frequency and Space Domains in Multi-Cell Ma...IJECEIAES
In this article, we show that Pilot contamination problem can be seen as a source separation problem using time, frequency, and space domains. Our method capitalizes on a nonunitary joint diagonalization of spatial quadratic time-frequency (STFD) signal representation to identify the desired and interfering users. We first compute the noise subspace from the STFD matrices selected appropriately. Secondly, we use the noise subspace obtained to estimate the Elevation (El) and the Azimuth (Az) angles for which the MUSIC cost function is maximized. Numerical simulations are provided to illustrate the effectiveness and the behavior of the proposed approach.
Mobile Primary User in Cognitive Radio State of the Arts and Recent Advancesjosephjonse
The processing of primary user mobility with static or mobile secondary user in the context of cognitive radio (CR) has recently been the subject of several studies and discussions all over the world. These studies are seeking to broaden the horizons of CR implementation beyond the formalism described in the diverse existing standards. The mobility of primary users is likely to reduce the overall performance of the Cognitive Radio Network (CRN) and affects the different phases of the cognitive cycle. Said mobility alters the network’s topology, the channel’s availability, and affects spectrum sensing. This makes any endeavor aiming to implement CR technology complicated. This paper is devoted to the analysis and discussion of the scientific literature that has addressed the issue of the primary user’s mobility.
Routing in Cognitive Radio Networks - A SurveyIJERA Editor
Cognitive Radio Networks (CRNs) have been emerged as a revolutionary solution to migrate the spectrum
scarcity problem in wireless networks. Due to increasing demand for additional spectrum resources, CRNs have
been receiving significant research to solve issues related with spectrum underutilization. This technology
brings efficient spectrum usage and effective interference avoidance, and also brings new challenges to routing
in multi-hop Cognitive Radio Networks. In CRN, unlicensed users or secondary users are able to use
underutilized licensed channels, but they have to leave the channel if any interference is caused to the primary or
licensed users. So CR technology allows sharing of licensed spectrum band in opportunistic and non-interfering
manner. Different routing protocols have been proposed recently based on different design goals under different
assumptions.
Classical Discrete-Time Fourier TransformBased Channel Estimation for MIMO-OF...IJCSEA Journal
In this document, we look at various time domain channel estimation methods with this constraint of null carriers at spectrumborders.We showin detail howto gauge the importance of the “border effect” depending on the number of null carriers, which may vary from one system to another. Thereby we assess the limit of the technique discussed when the number of null carriers is large. Finally the DFT with the truncated singular value decomposition (SVD) technique is proposed to completely eliminate the impact of the null subcarriers whatever their number. A technique for the determination of the truncation threshold for any MIMO-OFDM system is also proposed.
MPC-EAR : Maximal Power Conserved And Energy Aware Routing in Ad hoc Networksijsrd.com
Power preservation in wireless ad hoc networks is a decisive factor as energy resources are inadequate at the electronic devices in use. Power-aware routing strategies are fundamentally route selection strategies built on accessible ad hoc routing protocols. This paper proposed a new Maximal Power Conserved And Energy Aware Routing (MPC-EAR ) topology for mobile ad hoc networks that enhances the network life span. Simulation results prove that the projected protocol has a higher performance other minimal energy usage, energy level aware and energy conserving routing protocols such as MTPR, MMECR and CMMECR.
Ergodic capacity analysis for underlay cognitive radio systemijmnct
Cognitive radio technology has been proposed as a viable solution to the spectrum scarcity problem faced
by world today. The technology allows opportunistic spectrum access to the licensed frequency band by
unlicensed user without causing any harmful interference to the licensed primary user. In this paper,
ergodic channel capacity is investigated for underlay spectrum sharing system under maximum and
received power constraint at licensed primary receiver. The time varying discrete time fading channels are
assumed to undergo Rayleigh flat fading environment. Numerical simulations have been done to support
theoretical results
Comparative Study of Different Non-Cooperative Techniques in Cognitive RadioRSIS International
Wireless technology is expanding its domain and with it
is growing the need for more frequencies for communication.
Cognitive radio offers a solution to this problem by using the
concept of Dynamic spectrum access instead of fixed spectrum
allocation. Such radios are capable of sensing the RF spectrum
for identifying idle frequency bands. It then transmits
opportunistically so as to avoid interference with primary user
over same band. In cognitive radio, intelligent spectrum sensing
forms the major and most important part. Out of the various
sensing techniques, we will give an overview of some of the
prominent non-cooperative techniques. The paper deals with
comparative study of these methods.
Study and Analysis Capacity of MIMO Systems for AWGN Channel Model ScenariosIJERA Editor
Future wireless communication systems can utilize the spatial properties of the wireless channel to enhance the spectral efficiency and therefore increases its channel capacity. This can be designed by deploying multiple antennas at both the transmitter side and receiver side. The basic measure of performance is the capacity of a channel; the maximum rate of communication for which arbitrarily small error probability can be achieved. The AWGN (additive white Gaussian noise) channel introduces the notion of capacity through a heuristic argument. The AWGN channel is then used as a basic building block to check the capacity of wireless fading channels in contrast to the AWGN channel. There is no single definition of capacity for fading channels that is applicable in all situations. Several notions of capacity are developed, and together they form a systematic study of performance limits of fading channels. The various capacity measures allow us to observe clearly the various types of resources available in fading channels: degrees of freedom, power and diversity. The MIMO systems capacity can be enhanced linearly with large the number of antennas. This paper elaborates the study of MIMO system capacity using the AWGN Channel Model, Channel Capacity, Channel Fast Fading, Spatial Autocorrelation and Power delay profile for various channel environments.
Joint Cooperative Spectrum Sensing and MAC Protocol Design for Multi-channel ...Polytechnique Montreal
In this paper, we propose a semi-distributed cooperative spectrum sen
sing (SDCSS) and channel access framework
for multi-channel cognitive radio networks (CRNs). In particular, we c
onsider a SDCSS scheme where secondary
users (SUs) perform sensing and exchange sensing outcomes with ea
ch other to locate spectrum holes. In addition,
we devise the
p
-persistent CSMA-based cognitive MAC protocol integrating the SDCSS to
enable efficient spectrum
sharing among SUs. We then perform throughput analysis and develop
an algorithm to determine the spectrum
sensing and access parameters to maximize the throughput for a given
allocation of channel sensing sets. Moreover,
we consider the spectrum sensing set optimization problem for SUs to maxim
ize the overall system throughput. We
present both exhaustive search and low-complexity greedy algorithms
to determine the sensing sets for SUs and
analyze their complexity. We also show how our design and analysis can be
extended to consider reporting errors.
Finally, extensive numerical results are presented to demonstrate the sig
nificant performance gain of our optimized
design framework with respect to non-optimized designs as well as the imp
acts of different protocol parameters on
the throughput performance.
LARGE-SCALE MULTI-USER MIMO APPROACH FOR WIRELESS BACKHAUL BASED HETNETScsandit
In this paper, we consider the optimization of wireless capacity-limited backhaul links in future heterogeneous networks (HetNets). We assume that the HetNet is formed with one macro-cell base station (MBS), which is associated with multiple small-cell base stations (SBSs). It is also assumed both the MBS and the SBSs are equipped with massive arrays, while all mobiles users (macro-cell and small-cell users) have single antenna. For the backhaul links, we propose to use a capacity-aware beamforming scheme at the SBSs and MRC at the MBS. Using particle swarm optimization (PSO), each SBS seeks the optimal transmit weight vectors that maximize the backhaul uplink capacity and the access uplinks signal-to-interference plus noise ratio (SINR). The performance evaluation in terms of the symbol error rate (SER) and the ergodic system capacity shows that the proposed capacity-aware backhaul link scheme achieves similar or better performance than traditional wireless backhaul links and requires considerably less computational complexity.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Computational Engineering Research(IJCER) ijceronline
nternational Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
An approach to control inter cellular interference using load matrix in multi...eSAT Journals
Abstract
This paper deals with reduction of inter cellular interference in Multi-carrier communication systems. In the past, Load Matrix(LM) is proposed to allocate power to different users in a network based upon Signal to noise plus interference ratio (SNIR) so as to reduce inter cellular interference and is observed for single carrier systems. In Multi carrier systems the SNIR is affected distinctly in each carrier thus a single SNIR for power allocation is not optimal. In this paper, to obtain the optimization of power allocation in Multi-Carrier system, Load Matrix coding with bifurcated SNIR (LM-BFSNIR) is proposed. Using this approach it is observed that inter cellular interference is reduced better when compared to a single carrier system evaluated over a 3GPP-LTE standard.
Keywords−Power allocation, Inter cellular interference, Multi-Carrier mobile Communication system.
Implementation of Vacate on Demand Algorithm in Various Spectrum Sensing Netw...IJERA Editor
In present days the wireless communications are widely increases because of this reason spectrum utilization can be rapidly increased.For efficient usage of spectrum we can implement the Vacate on demand algorithm in different networks. CR users also need to sense the spectrum and vacate the channel upon the detection of the PU‟s presence to protectPUs from harmful interference. To achieve these fundamental CR functions, CR users usually coordinate with each other by using a common medium for control message exchange ensuring a priority of PUs over CR users. This paper presents the Vacate on Demand (VD) algorithm which enables dynamic spectrum access and ensures to vacate the assigned channel in case of PU activity and move the CR user to some other vacant channel to make spectrum available to PUs as well as to CR users. The basic idea is to use a ranking table of the available channels based on the PU activity detected on each channel. To improve the spectrum efficiency we can implement the Vacate on demand algorithm in MANET Network.
A SURVEY ON OPTIMIZATION BASED SPECTRUM SENSING TECHNIQUES TO REDUCE ISI AND ...IJNSA Journal
Cognitive radio is emerging technologies in OFDM based wireless systems which are very important for spectrum sensing. By using cognitive radio (CR) high data can be transferred with low bit error rate. The key idea of OFDM is to split the total transmission bandwidth into the subcarriers which further reduce the intersymbol interference (ISI) and peak to average power ratio(PAPR) in the signal. There are many optimization based spectrum sensing techniques are existing for efficient sensing purpose but each has its own advantages and disadvantages. This leads to start the comprehensive study for reducing PAPR and ISI(Intersymbol interference) in terms of FPGA based partial configuration. In the first part of review OFDM characteristics of the signal has compared with several optimizations based ISI reduction techniques. The second part is to compare the various spectrum sensing techniques in cognitive radio engine and its application in FPGA.
Pilot Decontamination over Time Frequency and Space Domains in Multi-Cell Ma...IJECEIAES
In this article, we show that Pilot contamination problem can be seen as a source separation problem using time, frequency, and space domains. Our method capitalizes on a nonunitary joint diagonalization of spatial quadratic time-frequency (STFD) signal representation to identify the desired and interfering users. We first compute the noise subspace from the STFD matrices selected appropriately. Secondly, we use the noise subspace obtained to estimate the Elevation (El) and the Azimuth (Az) angles for which the MUSIC cost function is maximized. Numerical simulations are provided to illustrate the effectiveness and the behavior of the proposed approach.
Mobile Primary User in Cognitive Radio State of the Arts and Recent Advancesjosephjonse
The processing of primary user mobility with static or mobile secondary user in the context of cognitive radio (CR) has recently been the subject of several studies and discussions all over the world. These studies are seeking to broaden the horizons of CR implementation beyond the formalism described in the diverse existing standards. The mobility of primary users is likely to reduce the overall performance of the Cognitive Radio Network (CRN) and affects the different phases of the cognitive cycle. Said mobility alters the network’s topology, the channel’s availability, and affects spectrum sensing. This makes any endeavor aiming to implement CR technology complicated. This paper is devoted to the analysis and discussion of the scientific literature that has addressed the issue of the primary user’s mobility.
Routing in Cognitive Radio Networks - A SurveyIJERA Editor
Cognitive Radio Networks (CRNs) have been emerged as a revolutionary solution to migrate the spectrum
scarcity problem in wireless networks. Due to increasing demand for additional spectrum resources, CRNs have
been receiving significant research to solve issues related with spectrum underutilization. This technology
brings efficient spectrum usage and effective interference avoidance, and also brings new challenges to routing
in multi-hop Cognitive Radio Networks. In CRN, unlicensed users or secondary users are able to use
underutilized licensed channels, but they have to leave the channel if any interference is caused to the primary or
licensed users. So CR technology allows sharing of licensed spectrum band in opportunistic and non-interfering
manner. Different routing protocols have been proposed recently based on different design goals under different
assumptions.
Classical Discrete-Time Fourier TransformBased Channel Estimation for MIMO-OF...IJCSEA Journal
In this document, we look at various time domain channel estimation methods with this constraint of null carriers at spectrumborders.We showin detail howto gauge the importance of the “border effect” depending on the number of null carriers, which may vary from one system to another. Thereby we assess the limit of the technique discussed when the number of null carriers is large. Finally the DFT with the truncated singular value decomposition (SVD) technique is proposed to completely eliminate the impact of the null subcarriers whatever their number. A technique for the determination of the truncation threshold for any MIMO-OFDM system is also proposed.
MPC-EAR : Maximal Power Conserved And Energy Aware Routing in Ad hoc Networksijsrd.com
Power preservation in wireless ad hoc networks is a decisive factor as energy resources are inadequate at the electronic devices in use. Power-aware routing strategies are fundamentally route selection strategies built on accessible ad hoc routing protocols. This paper proposed a new Maximal Power Conserved And Energy Aware Routing (MPC-EAR ) topology for mobile ad hoc networks that enhances the network life span. Simulation results prove that the projected protocol has a higher performance other minimal energy usage, energy level aware and energy conserving routing protocols such as MTPR, MMECR and CMMECR.
Ergodic capacity analysis for underlay cognitive radio systemijmnct
Cognitive radio technology has been proposed as a viable solution to the spectrum scarcity problem faced
by world today. The technology allows opportunistic spectrum access to the licensed frequency band by
unlicensed user without causing any harmful interference to the licensed primary user. In this paper,
ergodic channel capacity is investigated for underlay spectrum sharing system under maximum and
received power constraint at licensed primary receiver. The time varying discrete time fading channels are
assumed to undergo Rayleigh flat fading environment. Numerical simulations have been done to support
theoretical results
Comparative Study of Different Non-Cooperative Techniques in Cognitive RadioRSIS International
Wireless technology is expanding its domain and with it
is growing the need for more frequencies for communication.
Cognitive radio offers a solution to this problem by using the
concept of Dynamic spectrum access instead of fixed spectrum
allocation. Such radios are capable of sensing the RF spectrum
for identifying idle frequency bands. It then transmits
opportunistically so as to avoid interference with primary user
over same band. In cognitive radio, intelligent spectrum sensing
forms the major and most important part. Out of the various
sensing techniques, we will give an overview of some of the
prominent non-cooperative techniques. The paper deals with
comparative study of these methods.
Study and Analysis Capacity of MIMO Systems for AWGN Channel Model ScenariosIJERA Editor
Future wireless communication systems can utilize the spatial properties of the wireless channel to enhance the spectral efficiency and therefore increases its channel capacity. This can be designed by deploying multiple antennas at both the transmitter side and receiver side. The basic measure of performance is the capacity of a channel; the maximum rate of communication for which arbitrarily small error probability can be achieved. The AWGN (additive white Gaussian noise) channel introduces the notion of capacity through a heuristic argument. The AWGN channel is then used as a basic building block to check the capacity of wireless fading channels in contrast to the AWGN channel. There is no single definition of capacity for fading channels that is applicable in all situations. Several notions of capacity are developed, and together they form a systematic study of performance limits of fading channels. The various capacity measures allow us to observe clearly the various types of resources available in fading channels: degrees of freedom, power and diversity. The MIMO systems capacity can be enhanced linearly with large the number of antennas. This paper elaborates the study of MIMO system capacity using the AWGN Channel Model, Channel Capacity, Channel Fast Fading, Spatial Autocorrelation and Power delay profile for various channel environments.
Joint Cooperative Spectrum Sensing and MAC Protocol Design for Multi-channel ...Polytechnique Montreal
In this paper, we propose a semi-distributed cooperative spectrum sen
sing (SDCSS) and channel access framework
for multi-channel cognitive radio networks (CRNs). In particular, we c
onsider a SDCSS scheme where secondary
users (SUs) perform sensing and exchange sensing outcomes with ea
ch other to locate spectrum holes. In addition,
we devise the
p
-persistent CSMA-based cognitive MAC protocol integrating the SDCSS to
enable efficient spectrum
sharing among SUs. We then perform throughput analysis and develop
an algorithm to determine the spectrum
sensing and access parameters to maximize the throughput for a given
allocation of channel sensing sets. Moreover,
we consider the spectrum sensing set optimization problem for SUs to maxim
ize the overall system throughput. We
present both exhaustive search and low-complexity greedy algorithms
to determine the sensing sets for SUs and
analyze their complexity. We also show how our design and analysis can be
extended to consider reporting errors.
Finally, extensive numerical results are presented to demonstrate the sig
nificant performance gain of our optimized
design framework with respect to non-optimized designs as well as the imp
acts of different protocol parameters on
the throughput performance.
A Review on Cooperative Communication Protocols in Wireless World ijwmn
Future generations of cellular communications requires higher data rates and a more reliable
transmission link with the growth of multimedia services, while keeping satisfactory quality of service, .
MIMO antenna systems have been considered as an efficient approach to address these demands by
offering significant multiplexing and diversity gains over single antenna systems without increasing
bandwidth and power. Although MIMO systems can unfold their huge benefit in cellular base stations,
but they may face limitations when it comes to their deployment in mobile handsets.
To overcome this drawback, relays (fixed or mobile terminals) can cooperate to improve the overall
system performance in cellular networks. Cooperative communications can efficiently combat the severity
of fading and shadowing through the assistance of relays. It has been found that using relays the capacity
and coverage of cellular networks can be extended without increasing mobile transmit power or
demanding extra bandwidth.
IMPROVING MANET ROUTING PROTOCOLS THROUGH THE USE OF GEOGRAPHICAL INFORMATIONijwmn
This paper provides a summary of our research study of the location-aided routing protocols for mobile
ad hoc networks (MANET). This study focuses on the issue of using geographical location information to
reduce the control traffic overhead associated with the route discovery process of the ad-hoc on demand
distance vector (AODV) routing protocol. AODV performs route discovery by flooding the whole
network with the route request packets. This results in unnecessarily large number of control packets
traveling through the network. In this paper, we introduced a new Geographical AODV (GeoAODV)
protocol that relies on location information to reduce the flooding area to a portion of the network that is
likely contains a path to destination. Furthermore, we also compared GeoAODV performance with that
of the Location Aided Routing (LAR) protocol and examined four mechanisms for reducing the size of the
flooding area: LAR zone, LAR distance, GeoAODV static, and GeoAODV rotate. We employed OPNET
Modeler version 16.0 software to implement these mechanisms and to compare their performance
through simulation. Collected results suggest that location-aided routing can significantly reduce the
control traffic overhead during the route discovery process. The comparison study revealed that the LAR
zone protocol consistently generates fewer control packets than other location-aided mechanisms.
However, LAR zone relies on the assumption that location information and traveling velocities of all the
nodes are readily available throughout the network, which in many network environments is unrealistic.
At the same time, the GeoAODV protocols make no such assumption and dynamically distribute location
information during route discovery. Furthermore, the collected results showed that the performance of
the GeoAODV rotate protocol was only slightly worse than that of LAR zone. We believe that even
though GeoAODV rotate does not reduce the control traffic overhead by as much as LAR zone, it can
become a preferred mechanism for route discovery in MANET.
BER Performance of Antenna Array-Based Receiver using Multi-user Detection in...ijwmn
Antenna promises to provide significant increases in system capacity and performance in
wireless systems. In this paper, a simplified, near-optimum array receiver is proposed,
which is based on the angular gain of the spatial filter. This detection is then analyzed by
calculating the exact error probability.The proposed model confirms the benefits of adaptive
antennas in reducing the overall interference level (intercell/intracell) and to find an
accurate approximation of the error probability. We extend the method that has been
proposed for propagation over Nakagami-m fading channels, the model shows good
agreements with simulation results.
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General analytical framework for cooperative sensing and access trade-off opt...Polytechnique Montreal
In this paper, we investigate the joint cooperative spectrum sensing and access design problem for multi-channel cognitive radio networks. A general heterogeneous setting is considered where the probabilities that different channels are available, SNRs of the signals received at secondary users (SUs) due to transmissions from primary users (PUs) for different users and channels can be different. We assume a cooperative sensing strategy with a general a-out-of-b aggregation rule and design a synchronized MAC protocol so that SUs can exploit available channels. We analyze the sensing performance and the throughput achieved by the joint sensing and access design. Based on this analysis, we develop algorithms to find optimal parameters for the sensing and access protocols and to determine channel assignment for SUs to maximize the system throughput. Finally, numerical results are presented to verify the effectiveness of our design and demonstrate the relative performance of our proposed algorithms and the optimal ones.
We consider a cognitive radio system with one secondary user (SU) accessing multiple channels via periodic sensing and spectrum handoff. We propose an optimal spectrum sensing and access mechanism such that the average energy cost of the SU, which includes the energy consumed by spectrum sensing, channel switching, and data transmission, is minimized, whereas multiple constraints on the reliability of sensing, the throughput, and the delay of the secondary transmission are satisfied. Optimality is achieved by jointly considering two fundamental tradeoffs involved in energy minimization, i.e., the sensing/transmission tradeoff and the wait/switch tradeoff. An efficient convex optimization procedure is developed to solve for the optimal values of the sensing slot duration and the channel switching probability. The advantages of the proposed spectrum sensing and access mechanism are shown through simulations.
Performance Analysis and Comparative Study of Cognitive Radio Spectrum Sensin...IOSR Journals
Abstract : In cognitive radio, spectrum sensing is an emergent technology to find available and unused spectrum for increasing spectrum utilization and to overcome spectrum scarcity problem without harmful interference to licensed users. Cooperative spectrum sensing is used to give reliable performance in terms of detection probability and false alarm probability as well as in order to reduce fading, noise and shadowing effects on cognitive radio users. In this paper according to detection performance and complexity various cooperative spectrum sensing schemes have been discussed. We have analyzed spectrum sensing with different fusion rules and their comparative behavior has also been studied. Furthermore, we introduced AND-OR fusion rules in 2-bit and 3-bit hard combination schemes. Keywords - Cognitive radio, cooperative spectrum sensing, energy detector, spectrum sensing, hard combination
Performance Analysis and Comparative Study of Cognitive Radio Spectrum Sensin...IOSR Journals
In cognitive radio, spectrum sensing is an emergent technology to find available and unused
spectrum for increasing spectrum utilization and to overcome spectrum scarcity problem without harmful
interference to licensed users. Cooperative spectrum sensing is used to give reliable performance in terms of
detection probability and false alarm probability as well as in order to reduce fading, noise and shadowing
effects on cognitive radio users. In this paper according to detection performance and complexity various
cooperative spectrum sensing schemes have been discussed. We have analyzed spectrum sensing with different fusion rules and their comparative behavior has also been studied. Furthermore, we introduced AND-OR fusion rules in 2-bit and 3-bit hard combination schemes
Shared Spectrum Throughput for Secondary UsersCSCJournals
The throughput performance of secondary users sharing radio spectrum with a licensed primary user is analyzed in this work. An asynchronous transmission, sensing and backoff protocol is proposed for the secondary user and modeled as a six state Markov process. The model parameters are derived as a function of the duty cycle and average duration that the channel is unoccupied by the primary user. The secondary user parameters include its continuous transmission duration or packet size and its backoff window size. The model results show that the probabilities of the secondary user being in the transmit state are relatively invariant to the duty cycle compared to the probability of being in the backoff state, particularly at low to moderate secondary packet sizes. The secondary user throughput is expressed as a function of the aforementioned parameters and shown to change significantly with duty cycle and secondary packet sizes. It is found that at very low duty cycles, the throughput variation is insensitive to backoff duration being random or fixed. The proposed transmission and sensing method is also shown to outperform a periodic sensing protocol. The regions of the parameter space wherein the backoff and retransmit probabilities of the secondary user are bounded by specified performance metrics are derived. The sensitivity of the throughput in the presence of a cooperative and non- cooperative secondary user is also investigated.
Bio-inspired route estimation in cognitive radio networks IJECEIAES
Cognitive radio is a technique that was originally created for the proper use of the radio electric spectrum due its underuse. A few methods were used to predict the network traffic to determine the occupancy of the spectrum and then use the ‘holes’ between the transmissions of primary users. The goal is to guarantee a complete transmission for the second user while not interrupting the trans-mission of primary users. This study seeks the multifractal generation of traffic for a specific radio electric spectrum as well as a bio-inspired route estimation for secondary users. It uses the MFHW algorithm to generate multifractal traces and two bio-inspired algo-rithms: Ant Colony Optimization and Max Feeding to calculate the secondary user’s path. Multifractal characteristics offer a predic-tion, which is 10% lower in comparison with the original traffic values and a complete transmission for secondary users. In fact, a hybrid strategy combining both bio-inspired algorithms promise a reduction in handoff. The purpose of this research consists on deriving future investigation in the generation of multifractal traffic and a mobility spectrum using bio-inspired algorithms.
The impact of M-ary rates on various quadrature amplitude modulation detectionIJECEIAES
The 5G system-based cognitive radio network is promised to meet the requirements of huge data applications with spectrum. However, the M-ary effect on the detection has not been thoroughly investigated. In this paper, an M-ary of quadrature amplitude modulation detection system is studied. Many rates are used in this study 4, 16, 64, and 256 constellation points. The detection system is applied to cooperative spectrum sensing to enhance the performance of detection for various rates of M-ary with low signal-to-noise ratio (SNR). Further, three kinds of signals based 5G system are sensed: filtered-orthogonal frequency division multiplexing (F-OFDM), filter bank multi-carrier (FBMC), and universal filtered multi-carrier (UFMC). The best detection performance is obtained when the M-ary=4 and number of SUs=50 user, whereas the worst detection performance is obtained when the M-ary=256 and number of SUs=10 user, as revealed in the simulation results. In addition, the detection performance for the F-OFDM signal is better than that of UFMC and FBMC signals for SNR <0 dB.
Beamforming with per antenna power constraint and transmit antenna selection ...sipij
In this paper, transmit beamforming and antenna selection techniques are presented for the Cooperative
Distributed Antenna System. Beamforming technique with minimum total weighted transmit power
satisfying threshold SINR and Per-Antenna Power constraints is formulated as a convex optimization
problem for the efficient performance of Distributed Antenna System (DAS). Antenna Selection technique is
implemented in this paper to select the optimum Remote Antenna Units from all the available ones. This
achieves the best compromise between capacity and system complexity. Dual polarized and Triple
Polarized systems are considered. Simulation results prove that by integrating Beamforming with DAS
enhances its performance. Also by using convex optimization in Antenna Selection enhances the
performance of multi polarized systems.
MULTI-STAGES CO-OPERATIVE/NONCOOPERATIVE SCHEMES OF SPECTRUM SENSING FOR COGN...ijwmn
Searching for spectrum holes in practical wireless channels where primary users experience multipath
fading and shadowing, with noise uncertainty, limits the detection performance significantly. Moreover, the
detection challenge will be tougher when different band types have to be sensed, with different signal and
spectral characteristics, and probably overlapping spectra. Besides, primary user waveforms can be known
(completely or partially) or unknown to allow or forbid cognitive radios to use specific kinds of detection
schemes! Hidden primary user’s problem, and doubly selective channel oblige the use of cooperative
sensing to exploit the spatial diversity in the observations of spatially located cognitive radio users.
Incorporated all the aforementioned practical challenges as a whole, this paper developed a new multistage detection scheme that intelligently decides the detection algorithm based on power, noise, bandwidth
and knowledge of the signal of interest. The proposed scheme switches between individual and cooperative
sensing and among featured based sensing techniques (cyclo-stationary detection and matched filter) and
sub-band energy detection according to the characteristics of signal and band of interest.Compared to the
existing schemes, performance evaluations show reliable results in terms of probabilities of detection and
mean sensing times under the aforementioned conditions.
MULTI-STAGES CO-OPERATIVE/NONCOOPERATIVE SCHEMES OF SPECTRUM SENSING FOR COGN...ijwmn
Searching for spectrum holes in practical wireless channels where primary users experience multipath
fading and shadowing, with noise uncertainty, limits the detection performance significantly. Moreover, the
detection challenge will be tougher when different band types have to be sensed, with different signal and
spectral characteristics, and probably overlapping spectra. Besides, primary user waveforms can be known
(completely or partially) or unknown to allow or forbid cognitive radios to use specific kinds of detection
schemes! Hidden primary user’s problem, and doubly selective channel oblige the use of cooperative
sensing to exploit the spatial diversity in the observations of spatially located cognitive radio users.
Incorporated all the aforementioned practical challenges as a whole, this paper developed a new multistage detection scheme that intelligently decides the detection algorithm based on power, noise, bandwidth
and knowledge of the signal of interest. The proposed scheme switches between individual and cooperative
sensing and among featured based sensing techniques (cyclo-stationary detection and matched filter) and
sub-band energy detection according to the characteristics of signal and band of interest.Compared to the
existing schemes, performance evaluations show reliable results in terms of probabilities of detection and
mean sensing times under the aforementioned conditions.
Spectrum sensing performance of cognitive radio under awgn and fading channel...eSAT Journals
Abstract Accurate sensing of the spectrum occupancy is essential for successful implementation of cognitive radio networks. However, due to higher levels of noise and multipath propagation effects of the channel, the sensing information of cognitive radio may not be accurate all the times. In this context, Receiver Operating Characteristics (ROC) of the system gives a measure of this information. It is a curve of probability of true detection with respect to probability of false detection. This paper presents the ROC of cognitive radio system for AWGN, Rayleigh and Rician channels. Keywords: Cognitive Radio, Spectrum Sensing, Primary User Detection, AWGN Channel, Rayleigh and Rician Channels
Medium Access Probability of Cognitive Radio Network Under ECC-33/Hata-Okumur...ijceronline
Cognitive radio detects the presence or absence of Primary User (PU) in its sensing region to provide the free radio spectrum to its Secondary user (SU). It is widely accepted a SU is only allowed to access a network of PU when no PU of that network is accessing the network at that moment. Sometimes SU misjudges the presence of PU inside the sensing region though the PU is in transmitting mode outside the sensing region which is termed as spatial false alarm. The incorporation of spatial false alarm makes the task more difficult. Previous literature performs this task using Lee’s path loss model .In our paper we have considered ECC-33/ Hata-Okumura Extended Model for two frequencies 1900MHz and 2100MHz as its frequency range is up to 3.5 GHz and compare the performance using different fading channels such as Rayleigh, Nakagami-m, Normal or Gaussian, Weibull, MRC Rayleigh and Selection Combining Rayleigh.
Similar to OPTIMIZED COOPERATIVE SPECTRUM-SENSING IN CLUSTERED COGNITIVE RADIO NETWORKS (20)
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OPTIMIZED COOPERATIVE SPECTRUM-SENSING IN CLUSTERED COGNITIVE RADIO NETWORKS
1. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
DOI : 10.5121/ijwmn.2013.5401 01
OPTIMIZED COOPERATIVE SPECTRUM-SENSING IN
CLUSTERED COGNITIVE RADIO NETWORKS
Birsen Sirkeci-Mergen and Wafa-Iqbal
Electrical Engineering, San Jose State University, San Jose, CA
birsen.sirkeci@sjsu.edu, wafa.iqbal1@gmail.com
ABSTRACT
In cognitive radio networks, the pertinent task of spectrum sensing at the Secondary Users (SUs)
can be achieved when the SUs cooperate in order to make a final decision about the presence of a
communicating Primary User (PU). In this paper, we study a two-hop relaying system in which
SUs are grouped into D clusters. The SUs transmit a simple power function (parameterized by p)
of their observationto a Fusion Centre (FC) using D orthogonal channels. The FC combines the
receptions from cooperating nodes linearly. The goal of this work is to maximize the probability
of detection over the parameters D (number of clusters), p (power function exponent), and
w(linear combining coefficients) for a given false alarm probability. Overall, this work quantifies
the advantages of optimal cooperation in primary detection in cognitive radio networks.
KEYWORDS
Wireless Networks, Relaying, Spectrum Sensing, Cognitive Radios, Cooperation, Fusion Centre.
1. INTRODUCTION
Wireless communication is progressing at an accelerated speed. Increasing variety of applications
and features of wireless devices is leading to demands for higher and higher data rates. However,
the bandwidth licensed to radio communication is limited. The infamous question is “How do we
get better data rates under limited bandwidth requirements to meet the demand?”.Efficient
spectrum utilization is the key to answer this question.
In 2002, Federal Communications Commission (FCC), the US government agency that regulates
the use of frequency bands of the electromagnetic spectrum, indicated that the licensed frequency
bands are unused 90% of the time[1]. In 2008, FCC ruled that unused portions of the RF
spectrum will be made available for public use under certain conditions. In the light of this rule,
spectrum efficiency can be improved if radio devices are equipped with technologies that take
advantage of the licensed spectrum when it is unused. An emerging advanced solution for
efficient spectrum utilization is the so-called cognitive radios.
A cognitive radio (CR) is a transceiver technology in which frequency spectrum is continuously
sensed for unoccupied spaces. In a CR system, the primary user (PU) is the one who has licensed
privilege to transmit in a particular frequency band and other users known as secondary users
(SU) are the unlicensed users who desire to share the spectrum. The available unused frequency
bands are called ‘spectrum holes’. SUs sense the spectrum for spectrum holes continuously. A CR
is capable of not only sensing the spectrum, but also, monitoring, detecting and adapting its
communication channel access. For example, a CRcan intelligently adjust its transmission
parameters according to the availability in the frequency bands[2],[3]. CRtechnology has gained a
2. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
2
lot of attention in the last decade. Currently, communication standards are adaptingthis
technology [4].
Cooperative spectrum sensing is a scheme in which SUs cooperate with each other in a
distributed or centralized manner, in order to make the decision about spectrum availability. This
could be done via a Fusion Centre (FC). The SUs sense the channel for the presence of PUs and
relay a function of their observations to the FC for a collective decision. The choice of this
relaying is critical in order to optimize the overall performance at the FC.In the next subsection,
we summarize the recent relevant work on cooperative spectrum sensing.
1.1. Cooperative Spectrum Sensing
In cooperative spectrum sensing, the SUs collaborate with each other in sensing the spectrum [5].
If optimized, cooperation reduces the power requirements at the SUsand improves the sensing
performance even if it may introduce overhead for certain cases. In the case when SUs cooperate
through a FC, every SU transmits its received signal to the FC that makes a decision about the
presence of a PU based on the collective information from all the SUs.This is also called relay-
assisted cooperative spectrum sensing [6].
The transmissions of the SUs to the fusion center could be on orthogonal channels [6], [7]. In this
case, each SUforwards a function of their observation to the fusion center through and
individualorthogonal channel similar to the well-known time-division multiple-access (TDMA),
or frequency-division multiple-access (FDMA). On the other hand, transmissions of the SUs to
the fusion center could be non-orthogonal, that is cooperating SUs transmit a function of their
observation byusing the same channel. In the non-orthogonal channel model, it is assumed that
SUs are synchronized so that the received signal in the fusion center is the coherent sumof
transmitted signals by SUs[8], [9]. For orthogonal channels, the fusion center canuse various
combining techniques of the received vector to obtain the final decision. It is shown in [10][11]
that the probability of error for coherent orthogonal channel system will not improve with the
increasing number of SUs. On the otherside, the performance of the non-orthogonal channel
systemimproves with the increasing number of SUs due to the array gain [9], [10].
It iswell-known that in order to have an energy-efficient and reliable spectrum sensing, it is
important for SUs to cooperate with each other when sensing for the PUs. However, one has to
carefully weigh the trade-offs between the achievable Cooperative Gain and the incurred
Cooperative Overhead[12]. In the case of orthogonal access between SUs and a FC, each radio is
dedicated anorthogonal channel, and the requirement for bandwidth scales by the number of SUs.
Then, the receptions from SUs at the FC are combined. In general, the linear combining
techniquesare attractive, because, they are simple compared to non-linear techniques, and when
the weighting coefficients are optimized, the improvement in the probability of detection at the
fusion center is significant. Onthe other hand, in the case when non-orthogonal access is utilized
from SUs to the FC, bandwidth requirements are negligible. Furthermore, the additive noise in the
non-orthogonal channelis negligible, especially for large networks, compared to orthogonal
channels since it is independent of the number of SUs. The gains due to optimized weighting
coefficients in orthogonal channels and the independence of noises from the number of SUs in
non-orthogonal channels posea trade-off. In order to optimizethis trade-off, one scheme proposed
in [13]by the first author: group-orthogonal multiple access channel (MAC) approach for
spectrum sensing. In group- orthogonal MAC, SUs utilize the available orthogonal channels in
clusters, and each SU transmit to the FC the energy of its reception from the PUs. In [13], authors
exploit the benefits of both orthogonal and non-orthogonal transmissions byfinding the optimal
3. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
3
number of users that should be in an orthogonal group and the optimal linear weighting
coefficients at the FC.
In this paper, we study optimal relaying function at SUs under different channel access schemes
from the SUs to the FC. The considered cases are orthogonal, non-orthogonal and group-
orthogonal multiple-access channels (MACs). In the group-orthogonal case, SUs are clustered
into D groups that transmit on D orthogonal channels. In fact, orthogonal MAC and non-
orthogonal MAC are special cases of group-orthogonal MAC when D=number of SUs, and D=1,
respectively. The expressionsfor the probability of detection as a function of probability of false
alarm under different group sizes and mappings arederived and analysed. This paper optimizes
the performance over a set of relay functions and channel access schemes. This will help the SUs
to make intelligent decisions when selectinghow and what to send to FC,for given a probability of
false alarm in detecting the spectrum availability.
The rest of the paper is organized as follows. In Section 2, we give the problem formulation. In
Section 3, we derive theoptimal number of groups and weighting coefficientunder certain
assumptions. Simulationresults are given in Section 4. Finally, Section 5 concludesthe paper.
2. SYSTEM MODEL
We consider a cognitive radio network that is composed of aPU, multiple SUs and a FC-which
could also be one of the SUs (see Fig. 1). Although the spectrum band under consideration is
licensed to the PUs, they may or may not be transmitting during the considered time-slot. Hence,
SUs need to decide whether thePUis idle (null hypothesis) or it is using the channel (alternative
hypothesis) in order to utilize the band efficiently. In the considered set-up, the decisions are
made cooperatively- that is each user makes decisions based on receptions from multiple SUs
which also serve as relays. When acting as relays, each SU makes an observation, and transmits a
signal based on solely its observation to the FC. We assume the FC combines the received signals
linearly and makes final decision about the existence of the primary based on the combined
signal. Linear combining at the FC is an attractive method primarily due to its simplicity. The two
hypotheses: H0 (no primary user exists) andH1 (at least one primary user exist) form a binary
hypothesis test given as below:
( ) ( )
( ) ( ) ( )
0
1
: 1,.... , 1,....
: 1,.... , 1,....
i i
i i i
H x k v k i M k N
H x k h s k v k i M k N
= = =
= + = =
wherexi(k) is the observed signal by the ith secondary user over N timeslots, s(k) is the
transmitted signal by the PU in the kth timeslot and vi(k)is the additive noise at the ith user in the
kth timeslot. The noisevi(k) is assumed be white Gaussian noise with zero mean and variance
2
and also vi(k)sare assumed to be independent and identically distributed (i.i.d.) over time index
k and user index i. The channel gains from the PU to the SUsare assumed to stay constant over the
observation interval (slow fading scenario).
In the network, each SU observes the channel for N timeslots and then forwards a power
function of the observed signal to the FC: ui = f(xi) = i |xi| p
where i = Pi / 2
{| | }iE x is the scaling
factor so that average transmission power is boundedbythe power constraint Pi. A common relay
operation is to send the energy of the observedsignal [13], which is equivalent to the case when p
4. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
4
is chosen to be 2, and i =1 in our scenario. Our goal is to optimize over the power function
exponent p so that the performance is improved.
Figure 1. Group-orthogonal MAC with M = 3D secondary users and D clusters
In the network, SUsare grouped into Dclusters (see Fig. 1). Each cluster is dedicated to on an
orthogonal channel, and users in the same cluster transmit on the same orthogonal channel. We
call this set-up group-orthogonal MAC (Multiple Access Channel). The clusters are assumed to be
pre-determined. For example, one could form clusters based on geographical proximity or signal
quality. However, the question of how the clusters are formed is out of scope of this paper. Let Sj
denote a set of users in the jth group where j=1…D. For simplicity in the analysis, we also
assume that clusters have equal number of nodes. Then, the combined signal in the jth orthogonal
channel can be written as:
j 1, ....
j
j m m j
m S
y g u n D
∈
= + =∑
where gm is the channel gain from SU to the FC and n j is the noise added at each channel and is
assumed to be i.i.d. white Gaussian noise with zero mean and variance σ2
. When information
5. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
5
from each group reaches the FC, it is linearly combined after being weighted. The weighting
vector is defined as w = [w1, w2, …, wD].
After combining, the signal observed at the FC is denoted by:
1 1 1j
D D D
c j j j m m j j
j j m S j
y w y w g u n w
= = ∈ =
= = +
∑ ∑ ∑ ∑
At the FC, the global test statistic ycis compared with γc to make a decision about PUs, that is
1
0
if y , decide that H has occurred,
if y , decide that H has occurred.
c c
c c
≥
<
3. OPTIMIZED COOPERATIVE SPECTRUM-SENSING
In this section, first we describe the performance metrics that are used, and then we describe the
optimization problem. Solution for the optimization problem is also provided.
3.1. Performance Metrics
We use the two important metrics: probability of detection Pd = P(H1| H1) and probability of false
alarm Pf = P(H1| H0). Our goal is to maximize the probability of detection, Pd, for a given
probability of false alarm,Pf. The optimization is over the set of parameter: as the number of
orthogonal channels D, therelaying function i |xi|p
, and weighting coefficients wjs.
In the following, we will use central limit theory [14] to derive analytical expressions for Pdand
Pf. We can argue that for large N (the observation time interval), xi can be assumed to be
asymptotically normally distributed as well as yjs and yc. For a normally distributed random
variableyc, the probability of detection and false alarm can be expressed as follows for a given
detection threshold γcat the FC:
1
1 1 1
1
[ | ] [ | ]
c c
d c c
c
E y H
P P H H P y H Q
Var y H
− = = ≥ =
(1)
0
1 0 0
0
[ | ] [ | ]
c c
f c c
c
E y H
P P H H P y H Q
Var y H
− = = ≥ =
(2)
2
/2
whe ( ) 1/ 2 denotes the Q-functire on.u
x
Q x e du
∞
−
= ∫
In order to find detection and false alarm probabilities based on the above mentioned formulas it
is required to find the conditional mean and variances under both hypotheses for a given
parameter set. Note that the Pd is actually a function of not only Pf,but also a function network
parameterssuch as the number of cluster (D), the relay function exponent (p), the FC combining
coefficients (w), channel coefficients between primary and cognitive radios (his), the channel
coefficients between the cognitive radios and the FC (gis), transmission power of the radios (Pis),
and the noise powers 2
and δ2
. Our goal is to maximize the probability of detection over the
6. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
6
parameters: (i) the number of clusters (D); (ii)the relaying function exponent (p); and (iii)
weighting coefficients at the FC, w, when the rest of the parameters are given.This implies that
the channel state information (CSI) is known for both links between PUs and SUs, and SUs and
the FC. Note that the channel fading coefficients his and gis are assumed to be slowly varying;
hence the CSI assumption is sensible. The following lemma provides an explicit analytical
expression for Pd as a function of Pf.
Lemma 1: For given probability of false alarm Pf, number of clusters D, relaying function
exponent p, and weighting coefficients w, if the channel gains |hi|2
s are all equal (|hi|2 =
α, i),
then the probability of detection Pd is given as follows for large N:
( )1
0 1 0
1
( , , )
c c f c
d
c
E y H E y H Q P Var y H
P D p Q
Var y H
− − + =
w (3)
where
0 1
2
0
2
1
[ | ] [ | ]
Var[ | ]
Var[ | ]
H H
c p D c p D
H H
c p D
H H
c p D
E y H A , E y H B ,
y H C ,
y H D ,
= =
=
=
g w g w
w G w + w w
w G w + w w
and
1 1
2 2
=[ ,..., ], G diag( ,..., ).
D D
D i i i i D i i i i
i S i S i S i S
g P g P g P g P
∈ ∈ ∈ ∈
=∑ ∑ ∑ ∑g
The coefficients Ap, Bp, Cp, and Dp depend on the relay function exponent p and are given as
follows:
1 2
1 2
2
1 1
1/2
, 2 , , ,
20 0
2 2
1 2 1 1 1
2 2 2
2 1
2
2
1
2
2 1 1 1 2 1 1 1
2 2 2 2
/
/
/p
N N
p p k p k p k p k
k k k k
p
p p N p
A
N N
p
B
p
p p p N p
C
− −
= = <
+ + − +
= Γ Γ + Γ
+
Γ = Φ Φ + Φ Φ + Γ
+ + + − +
= Γ − Γ Γ + Γ
∑ ∑ ∑
1 2
1 2
1 1
2 2 2
2 , , 2 , , ,
0 0
2
, 1 1 2
denotes the gamma funct
2 1 1 1 2 1 2 1
2 2 2 2
1 ( )
where , , , ( )
2 2 2
ion,
/
N N
p p k p k p k p k p k
k k k k k
p k
p p p p
D
p s k
F x
− −
= = <
+ + + +
= Γ Φ − Γ Φ Γ Φ + Γ Φ Φ
− −
Φ = Γ
∑ ∑ ∑ ∑
1 1 denotes the confand tluenF
hyper-geometric function[15].
Proof: Using Eqn. (2), for any givenPf, threshold γccan be written as:
( )1
0 0c c f cE y H Q P Var y H −
= + (4)
7. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
7
By substituting Eqn. (4) in Eqn. (1), we obtain Eqn. (3). The derivations for E[yc|H0], E[yc|H1],
Var[yc|H0], and Var[yc|H1] are given in the Appendix 3.1. ♦
It is important to note that Lemma 1 provides a formulation in which the dependences on the
optimization parameters (D, p, w) are partially decoupled. The variables w, gD and GD depend on
the cluster size D, the constants A p, B p, C p, and Dp depend on the relay function exponent p, and
the weighting coefficient w shows up explicitly in the expression. This will help solve the
optimization problem.
3.2. Optimized Cooperative Transmission and Reception
We formulate the optimization problem as follows. Given the channel gains (|hi|2
s, and gis), the
transmission powers of the SUs (Pis), and the noise powers 2
and δ2 ,
the goal is to maximize the
Pd for a given limit on false alarm probabilityPf:
, ,
max ( , , )d
D p
P D p
w
w
We make the following assumptions in order to solve this problem.
1. Uniform channel gains: |hi|2
= α, and gi= >0.
2. Uniform transmission powers: Pi = Pfor all i.
3. The orthogonal groups have equal number of SUs (assuming M/D is an integer).
4. The weighting coefficients,wis,are nonnegative.
Under these assumptions the following theorem provides the optimal D,and wfor a given p value.
Theorem 1:In the group-orthogonalMAC system, for a given relay power function with exponent
p, if channelgains are equal (|hi|2
= α,gi=), then the optimalweighting coefficients that
maximizes Pd(Eqn. (3)) are uniform for a given D, that is
wi = 1/D, i = 1 . . .D.
And the optimalD for given w and p is given as
2 2
2 2
(A )
( )
(A )
(
1
p p p
p p
p p p
p
f
f
B C PM
Q
D C
B C PM M
Q
D
P
P
D M P
− +
−
− +
−
>
≅ <
2 2 2 2
2 2 2
)
( )( )
(A )
otherwise
p
p p p
p p
M
C
Q f D C P C PM
B
P
−
−
−
−
where M
X denotes the divisor of M that is closed to X.
Proof:See Appendix 3.2. ♦
8. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
8
The theorem states optimal linear combining coefficients at the FC should be uniform for D
orthogonal channels and should sum to 1. This is very intuitive due to the assumptions on the
equal channel gains and noise powers, and also identical relay functions at the relays. On the
other hand, optimal Dhas three different regions: (i) when the false alarm probability is high
(Pf>PL), the optimal Dis equal to 1 which implies that non-orthogonal transmission is optimal; (ii)
when the false alarm probability is low (Pf<PH), the optimal Dis equal to M which implies that
each SU should transmit on an orthogonal channel and no clustering of SUs; and (iii) when the
false alarm probability is between PL and PH, optimal scheme is group-orthogonal transmission.
Note that for some special scenarios, the third region may merge with one of the other regions,
that is the rounding operation M
in the above equation may lead to D=1 or D=M.
Optimization over the relaying function exponent p can be done by replacing the optimal values
for D and w obtained in Theorem 1 in Eqn. 3, and by using an optimization toolbox for nonlinear
integer programming.
4. SIMULATIONS
In this section, we provide probability of detection versus probability of false alarmcurves for
different values of p and D. For all the simulations, the number of users M=4, observation time
N=1, the channel gains |hi|2
= α =100, gi= β= 1, relay transmission powers P =1, and noise
powers σ2
= 1, and δ2
= 5. Below,Pd denotes the probability of detection and Pf denotes the
probability of false alarm. We assume the primary signal |s(k)|2
= 1/N, for all k, for simplicity.
In Fig.2, we display the Pd as a function of Pf when the relay function has exponent p=1 and
p=3. The curves for various channel access scenarios between relays and FCare shown:
orthogonal access (D=M =4), non-orthogonal access (D=1), and group-orthogonal access (D=2).
It is observed that for lower probability of false alarms, orthogonal MACgives the best probability
of detection, and for higher probability of false alarms, non-orthogonal MACgives the best
probability of detection. Using Theorem 1, we can obtain the boundaries of these two different
regions:Pf >0.2797 and Pf <0.2180 for p=1 and Pf >0.1180 and Pf <00885 for p=3, which are
consistent with the simulations.In Fig. 3, we display the zoomed curves corresponding to the
region 0.2180<Pf <0.2797for p=1. According to Theorem 3, in this region optimal D could be 1,
2, and 4 which is what we observe in Fig. 3. Overall, the relay function with exponent p=3
outperforms the relay function with p=1. Furthermore, we observe that therange of Pf where
group-orthogonal MAC is optimal is getting smaller with the increase in p.
9. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
9
Figure 2 Probability of detection (Pd) vs. Probability of false alarm (Pf) with p =1 and p=3
Figure 3Pdvs.Pf for different ranges of Pf : (0.21<Pf <0.29)
Next, we analyse different relay functions for a given channel access scheme in detail. In Fig. 4
and Fig.5, we plot the Pd vs.Pf curves for the non-orthogonal MAC (D=1), and orthogonal
MAC(D=M=4), respectively.It can be concluded that for a given D, there does not exist a single
relay function that performs optimally for all Pf values. In the limit where relay function
10. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
10
exponent p is large, the curves reduces to Pd = Pf line for any Dvalue. Similar behaviour is
observed for other D value.
Figure 4Pd vs. Pf for non-orthogonal channel (D = 1)
Figure 5Pd vs. Pf for orthogonal channel (D = M)
In Table 1, we display the optimal relay function exponent and optimal cluster size D for various
Pf values. It is important to note that optimal Dis always equal to 1, which implies that when
optimal relay function (or equivalently p) is selected for a given false alarm probability, then the
11. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
11
non-orthogonal scheme becomes optimal globally. In addition, as Pfincreases, the optimal relay
function exponent p decreases.
Table 1 Optimal D and p
Range of Pf Optimal p Optimal D
0<Pf < 0.001 >11 1
0.001<Pf < 0.003 11 1
0.004<Pf < 0.009 10 1
0.010<Pf < 0.026 9 1
0.027<Pf < 0.059 8 1
0.060<Pf < 0.126 7 1
0.127<Pf < 0.250 6 1
0.251<Pf < 0.487 5 1
0.488<Pf < 0.897 4 1
0.898<Pf < 0.998 3 1
0.999<Pf <1.000 2 1
Pf =1 1 1
Overall, the optimal relay function for any of the channel access schemes is always the power
function with high exponents for lower probability of false alarms.However, if the system is
robust enough to handle higher probability of false alarms, small power exponents such as p =1,2
or 3is the optimal choice of for the relay functions.It can also be concluded that globally non-
orthogonal scheme is optimal under the given assumptions.
5. CONCLUSIONS
In this paper, we studied a cognitive radio network in which SUs cooperate in order to make a
decision about the primary existence. The proposed scheme is distributed in the sense that the
cooperating SUs transmit a power function (parameterized with exponent p) of their local
observation, hence does not require any overhead due to cooperation. The SUs transmit to aFC
(which could also be one of the SUs) over D orthogonal channels, and FCcombines these
receptions linearly using weighting coefficients w. We provided analytical solutions and
simulations for maximizing the probability of detection at the fusion centre for a given false alarm
probability over the parameters D, p, and w. It is interesting that non-orthogonal channel access
becomes optimal globally when the best relaying function is utilized even though the orthogonal
or group-orthogonal access schemes require more bandwidth. This behaviour is not observed in
cooperation strategies whererelays simply send their energy to the fusion centre [13]. In
summary, this work shows the importance of optimization in cooperative cognitive radio
networks in order to extract the gains of cooperation for spectrum sensing with negligible
overhead.
6. APPENDICES
6.1. Proof of Lemma 1
Derivation of 0cE y H : For the first hypothesis 0H we derive the expected value as:
( )
1
0
1 1
00 0
(k )( )
N N
pp
i i
k k
N
p
i
k
E v kH vE x E k
− −
= =
−
=
=
=
∑ ∑ ∑
12. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
12
We know that ( )iv k is a zero-mean Gaussian ( )2
0, i and for such a random variable the
expected value of the absolute function is given by [16]:
2
1 1
.2 .
2
p
p p p
E
+ = Γ
X
Hence,
( )
2
1 1
2
00
1
2
12
2
2
p
p
pN
p
k
N
p
i
k
E v k
p
N p
=
− −
=
+
Γ + = Γ =
∑ ∑ (5)
Derivation of Normalization factor for Hypothesis 0H : All the above derived expressions are
yet not normalized there we need to find expressions for the normalization factors for every
hypothesis. The normalization factor hypothesis 0H can be derived as follows:
2 21 1
0
0 0
(k) E (k)
N N
p p
i i
k k
E x H v
− −
= =
=
∑ ∑
It can be easily derived that the expected value of square of sums is given by:
1 2
1 2
21 1
2
0 0
=
N N p pp p
k k k k
k k k k
E E E E
− −
= = <
+
∑ ∑ ∑X X X X
(6)
Since v i(k) is independent and identically distributed for each k, substituting the values of the
expectations in the above equation gives:
( )21
2 2 2
0
0
12 1 1
(k) 2 2
2 2
N
p p p p p
i
k
N NN p p
E x H
−
=
−+ +
= Γ + Γ
∑
(7)
Since cy is a linear combination of ix after being scaled by channel gain and weighting factor,
so the expected value of cy can be written as:
( )
2
0
2 2 2
1
2
2
12 1 1
2 2
2 2
p
p
H
c
p p p p
N p
E y H
N NN p p
+
Γ
=
−+ +
Γ + Γ
g w
(8)
Derivation of 1cE y H : For the second Hypothesis, 1H we derive the expected value as
( ) ( )
1
1
00
1
(k)
N
p
i i
p
k
N
i
k
E h s k vE H kx
−−
= =
=
+
∑ ∑
We see that x i(k) is a non-zero mean Gaussian random variable N(his(k), σ2
i) and for a Gaussian
random variable with mean µx and variance σ2
x
2 2
1 1
1
.2 .
1 12
. , ,
2 2 2
p
p
x
p x
x
p
p
E F
+
Γ − − =
X
where1 1F is the confluent hyper geometric function.Hence,
13. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
13
( ) ( )
1
0
N
p
i i
k
E h s k v k
−
=
+ ∑ =
( )
2 22
1
1 1 2
0
1
.2 .
.1 12
, ,
2 2 2
p
p
N
i
k
p
h s kp
F
−
=
+
Γ − −
∑
Using the assumptions we have made about the channel gain ih , we can simplify the expression as
following:
( ) ( )
21
2
1 1 2
1
0 0
1 1 1 ( )
2 , ,
2 2 2 2
N
p
p N
i
k k
i
p
E h s k v k
p p s k
F
−
= =
−
+ − −
= Γ
+
∑ ∑
Derivation of Normalization factor for Hypothesis 1H : Using(6), the normalization factor
hypothesis 1H can be derived as follows:
2
2 2
21
1 1 1 2
0
2 1
2
2 1 ( )2
(k) , ,
2 2 2
p
p
N
p
i
k k
p
p s k
E x H F
−
=
+
Γ − − = +
∑ ∑
1 2
2
1 22
1 1 1 12 2
( ) ( )1 1 1 1
2 , , , ,
2 2 2 2 2 2 2
p
p
k k
s k s kp p p
F F
<
− −+ − −
Γ
∑ (9)
Therefore, we can write the 1cE y H as:
1 2
1 1 2
0
1
1
1 1 , 1 ,2 1 2
2 0 1 2
1 1 ( )
, ,
2 2 2
2 1
1 2 1 ( ) 22
, ,
1 2 2 2
2
N
Hk
c
N
p k p k
k k k
p s k
F
E y H
p
p s k
F
p
−
=
−
= <
− −
=
+
Γ − − + Φ Φ + Γ
∑
∑ ∑
g w (10)
where
2
, 1 1 2
1 1 ( )
, , ,
2 2 2 2
p k
p s k
F
− − −
Φ =
. (11)
Derivation of 0cVar y H : For the first Hypothesis, 0H we derive the variance value as
( ) ( ) ( )( )
21 1
2
0
0
0 0
1
(k)
NN N
p pp
i i ii
k k
p
k
Var x H E v k E vV kar v k
− −−
= = =
= −
=∑ ∑ ∑
2
2 2
2 1 1 1
2 2
2 2
p
p p pN p p
N
+ +
= Γ − Γ
(12)
Using this expression and power normalization factor(7), we can find the 0cVar y H as:
14. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
14
( )
2
2 2
2
0
2 2 2
2 1 1 1
2 2
2 2
12 1 1
2 2
2 2
p
p p p
H H
c
p p p p
N p p
N
Var y H
N NN p p
+ + Γ − Γ
= + ∂ −+ + Γ + Γ
w Gw w w
(13)
Derivation of 1cVar y H : For the second Hypothesis, 1H we derive the variance value as
( ) ( ) ( ) ( )( )
21 1
2
1
0 0
(k)
N N
p pp
i i i i i
k k
Var x H E h s k v k E h s k v k
− −
= =
= + − +
∑ ∑
2
1
2 2
1 1 1 12 2
0
1 2 1 1 ( ) 1 1 1 ( )
2 , , 2 , ,
2 2 2 2 2 2 2
pN
p p p
k
p s k p p s k
F p F
−
=
+ − + − = Γ − − Γ −
∑
(14)
Using the power normalization factor in Eqns.(9), (14), and (11), we obtain
1 2
1 2
1 1
2 2 2
2 , ,
0 0 2
1
2 2
2 , , ,
1 2 1 1 1
2
2 2
1 2 1 1 1
2
2 2
N N
p p
p k p k
k k H H
c
p p
p k p k p k
k k k
p p
Var y H
p p
− −
= =
<
+ + Γ Φ − Γ Φ
= + ∂ + + Γ Φ + Γ Φ Φ
∑ ∑
∑ ∑
w Gw w w
(15)
6.2. Proof of Theorem 1
Under the given assumptions Pd simplifies as
2
1 2 2
1 1
2
2 2
1
( ) ( )
D D
p p i f p i
i i
d
D
p i
i
PM PM
A B w Q P C w
D D
P Q
PM
D w
D
−
= =
=
− + +
=
+
∑ ∑
∑
This formulation of Pd shows that Pd is a function of Σwi and Σwi
2
. However, note that Pd is
independent of Σwi. This can be shown easily by replacing γw instead w. Then, Pd becomes
independent of γ, hence we can claim that optimal w is such that Σwi =1.Furthermore, using the
above equation, we can see that the Pd is maximized when is Σwi
2
minimized assuming Σwi =1.
This is achieved when w = (1/D)[1 … 1].
Assuming w= (1/D)[1 … 1], we can take the derivative of Pd wrt.D and find the optimal D when
D є {1,2, … ,M}. Note that Dis an integer, and one has to pay attention to the boundary of the set
{1,2, … ,M} while finding the D that maximized Pd. This operation will give us the optimal
solution since D should be an integer.
15. International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013
15
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