# Optimization Techniques in Resource allocation of Wireless Communication Systems

Scientific Study 2016 58 Pages

## Excerpt

## Contents

**CHAPTER 1 INTRODUCTION**

**1.1 INTRODUCTION TO RESOURCE ALLOCATION IN WIRELESS COMMUNICATION SYSTEMS**

**1.2 MOTIVATION FOR THE WORK**

**1.3 OBJECTIVES OF THE WORK**

**CHAPTER 2 LITERATURE REVIEW**

**2.1 DYNAMIC RESOURCE ALLOCATION TECHNIQUES**

**2.1.1 MARGIN ADAPTIVE TECHNIQUES**

**2.1.2 RATE ADAPTIVE TECHNIQUES**

**CHAPTER 3 RESOURCE ALLOCATION IN MULTIPLE INPUT MULTIPLE OUTPUT - ORTHOGONAL FREQUENCY DIVISION MULTIPLE ACCESS SYSTEM USING GENETIC ALGORITHM.**

**3.1 INTRODUCTION**

**3.2 SYSTEM MODEL**

**3.3 SUBCHANNEL EXCHANGE ALGORITHM**

**3.4 SUBCHANNEL ALLOCATION BASED ON GA**

**3.5 FAIRNESS**

**3.6 SIMULATION PARAMETERS**

**3.7 RESULTS AND DISCUSSION**

**CHAPTER 4 CONCLUSION AND FUTURE WORK**

**4.1 CONCLUSION**

**4.2 SCOPE FOR FUTURE ENHANCEMENTS **

**REFERENCES**

## CHAPTER 1 INTRODUCTION

### 1.1 INTRODUCTION TO RESOURCE ALLOCATION IN WIRELESS COMMUNICATION SYSTEMS

The future Wireless Communication Systems (WCS) are supposed to provide high data rate to support personal and multimedia communications irrespective of the users' mobility and location. These services include heterogeneous classes of traffics such as voice, file transfer, web browsing, wireless multimedia, teleconferencing, and interactive games. In recent years, data and multimedia services have become important in wireless communications. As a result, bandwidth requirement and number of users become delicate problems. To support high data rate requirement for future WCS, it is essential to efficiently allocate the limited resources. The major challenges are the dynamic nature of wireless channel, limited resources such as power,frequency spectrum, and diversified Quality of Service (QoS) requirements.

Orthogonal Frequency Division Multiplexing (OFDM) is a special case of multicarrier transmission that supports high data rate operation. OFDM is a modulation and multiplexing technique appropriate for current and future wireless networks. OFDM divides the available bandwidth into a number of parallel independent orthogonal subchannels and their bandwidth is much less than the coherence bandwidth of the channel. The wide band frequency selective fading channel is converted into several narrow band flat fading channels. OFDM is an excellent method to overcome multipath fading effects.

One of the goals of WCS is to enhance the capacity of the channel. Multiple Access Technique (MAT) permits several mobile users to share the given bandwidth in an effective way. Basically there are four multiple access techniques available namely, Time Division Multiple Access (TDMA), Frequency Division Multiple access (FDMA), Code Division Multiple Access (CDMA) and Space Division Multiple Access (SDMA). MAT is employed in terms of fixed time slots, fixed subchannels, and unique codes in TDMA, FDMA and CDMA respectively. SDMA makes use of the spatial separation of the users to optimize the bandwidth. MAT can be combined with OFDM in terms of frequency, time or code separation between the users. The difficult task is to assign the scarce radio resources like subchannels, time slots, bits and power to multiple users.

Orthogonal Frequency Division Multiple Access (OFDMA) is an extended version of OFDM with multiple access technique. It is the combination of OFDM and FDMA. OFDMA uses OFDM as the modulation technique and takes the benefits of multiuser diversity to get better spectral efficiency.OFDMA permits different users to transmit the data simultaneously over different subchannels.All the users may not get good quality channel at all the times. A channel viewed as deep faded by one user may look good for another user.

In Multiple Input Multiple Output (MIMO) system, multiple transmit and receive antennas are used to enhance the spectral efficiency and throughput of WCS. MIMO utilizes the benefits of spatial diversity by SDMA. MIMO-OFDM is the combination of OFDM, FDMA and SDMA. MIMO-OFDM is used by the IEEE 802.16e and IEEE 802.11n standards. OFDMA and MIMO can be combined to deliver the benefits of both the methods. High data rate needed for different applications is possible through OFDMA-MIMO.

In the case of the downlink scenario, the BS has to perform effective resource allocation to all the users with the limited bandwidth. In mobile communication, the mobile terminals (users) are estimating the accurate channel condition and feedback the information to the BS. This data is utilized by the transmitter for allocating the subchannels to the users based on the channel gains. After the allocation of the number of subchannels decided by the BS, the same thing is communicated to the receivers through a separate control channel. In a single cell environment, the users are at different locations from the centralized Base Station (BS). The users nearer to BS can have better signal level than the users far away from BS. Based on the Signal to Noise Ratio (SNR), the channel allocation is made and it results in unbalanced allocation to the users who are nearer to the cell boundary. As frequency spectrum and power resources are limited, resource allocation is an effective way to share the resources according to the requirement of each user.

The research broadly addresses problems of allocating the resources like subchannels and power to the users in multiuser wireless system for OFDM, OFDMA and MIMO-OFDMA with perfect Channel State Information (CSI) known at the transmitter using different optimization techniques.

### 1.2 MOTIVATION FOR THE WORK

High data rate wireless communication systems have to increase the overall capacity significantly to satisfy a large number of users. Proficient allocation of resources like bandwidth, bit and power to the users are essential due to the inadequate resources available at the BS. Also, the increased capacity must be fairly distributed to all the users to ensure the diverse QoS requirements. One of the main design goals of WCS is to support more number of users in a fair manner. This can be done by,

- Maximizing the system capacity considering transmit power as a constraint.

- Minimizing the transmit power considering the user’s data rate as the constraint.

- Fair allocation of resources

The research concentrates on maximizing the system capacity in a fair manner. The capacity maximization and fairness are achieved by optimizing the objectives with the use of optimization techniques like Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and their hybrid combination namely PSO-GA and GA-PSO. The scarce resources like bandwidth, power, subchannel and bit allocations can be proficiently made to enhance the throughput and to achieve the maximum capacity. There should be a tradeoff between the system capacity and fairness. Optimization techniques are used for resource allocation and are focused towards maximization of the sum capacity or to minimize the overall transmit power of a multiuser OFDM system.

### 1.3 OBJECTIVES OF THE WORK

Resource allocation plays a vital role in WCS. OFDM supports high data rate applications suitable for Wi-Fi and Wimax standards. The BS has to efficiently allocate the scarce resources to all the users in downlink transmission. The goal of the research is to develop an efficient downlink resource allocation algorithm which provides improved capacity at low computational complexity. It also aims to provide fairness to the users. Fairness is used to ensure that all the users or applications are receiving the fair share of the resources. Fairness in simple terms is to provide all the users with same data rate. All the users are equally sharing the limited resources. However, fairness results in poor utilization of available resources, unable to satisfy the needs of different users that are of diverse nature. There must be a compromise between capacity and fairness. Proportional rate constraints enforce the users with proportional fairness. The idea is to develop an efficient optimization algorithm for allocating the limited resources to improve the capacity in multiuser environment based on OFDM and MIMO.

## CHAPTER 2 LITERATURE REVIEW

This section discusses the related works carried out in the downlink resource allocation. Basically there are two categories of RA techniques namely, static and dynamic allocation methods. FDMA and TDMA are static allocation based methods. Dynamic Resource Allocation (DRA) is classified into Margin ADaptive (MAD) and Rate ADaptive (RAD). RAD is divided into fixed rate and variable rate allocation. The role and usage of various optimization techniques, scheduling, cross layer operation involved in the resource allocation process and the importance of maintaining the fairness among the users is also discussed.

### 2.1 DYNAMIC RESOURCE ALLOCATION TECHNIQUES

Resource allocation based on margin adaptive tends to minimize the overall transmit power consumption satisfying the recommended data rate for users and rate adaptive techniques aims to maximize the sum rate capacity subject to power constraint.

#### 2.1.1 MARGIN ADAPTIVE TECHNIQUES

Lawrey (1999) discussed about adaptive modulation to improve the spectral efficiency in multi user OFDM. The users are allocated with channels based on SNR values. The effect of frequency selective fading reduced by involving adaptive frequency hopping which in turn improves received power.

Wong et al (1999) discussed the margin adaptive RA problem with channel gain information. In the proposed approach, adaptive modulation is used along with subchannel allocation to reduce the overall required transmit power. An iterative adaptive subchannel allocation algorithm, followed by bit and power allocation algorithm is used to minimize the sum power consumption.

Kim et al (2001) suggested suboptimal method to perform subchannel and bit allocation. Nonlinear optimization problem is converted to a linear optimization problem to reduce the computational complexity. The obtained results are found to be closer to the optimal solution.

Kivanc et al (2003) proposed an optimal subchannel and power allocation method having low complexity to solve the MAD problem. It involves two steps of operation to determine the number of subchannels allocated to each user based on channel gain and to find the best subchannel to the users.

Ernest et al (2007) discussed and analyzed the performance of two different methods of OFDM namely MIMO-MC-CDMA and MIMO-OFDMA with and without fairness in a single cell multiuser environment with CSIT. An optimal power allocation and user selection algorithm is considered for both the cases. The performance of the OFDMA system is found to be better than MC-CDMA due to multiuser diversity and is appropriate for delay-sensitive applications.

Bae& Cho et al (2007) discussed about resource assignment for multihop OFDMA systems with perfect CSI. An efficient heuristic algorithm is proposed for subchannel allocation. Due to the exclusion of iterative computations, the computational complexity is reduced and fairness among users is maintained.

Reddy &Gajender (2007a) suggested the use of simple Genetic Algorithm for subchannel allocation to minimize the overall transmit power with the assumed CSI. The subchannels are assigned based on the requirements of the users. GA provides faster convergence and several subchannels are allocated to users without affecting the performance of the system.

Subchannel and power allocation based on Genetic Algorithm with the constraints on power and BER, to minimize the total transmit power in multiuser OFDM system is considered by Reddy et al (2007b). Subchannels are allocated to the user based on channel gains and power allocation by water filling method. Though the algorithm is found to be computationally complex, the obtained solutions are close to optimal values.

Tang & Zhang (2007) discussed the cross layer model for ARA over amplify-and-forward and decode-and-forward relay networks for multimedia communications to satisfy QoS requirement of users. The performance of the system is improved with amplify-and-forward and decode-and-forward relay network when compared with relay-less networks.

Falahati&Ardestani (2008) proposed a low complexity method for adaptive resource allocation in OFDM with fairness considering the proportional constraints by adopting two methods. The method is Initial Resource Allocation where equal power allocation is considered and the second one is Iterative Fairness Retrieve procedure to decrease the maximum proportionality deviation.

Tang & Zhang (2008) recommended the use of physical and MAC layer based DRA with diverse QoS requirements to improve the throughput in mobile wireless networks. The transmit power is significantly reduced by combining the power and time-slots for real time users. Admission control algorithms are also developed to improve the capacity. The suggested method is found to be better than the traditional power allocation algorithms.

Ahmed &Majunder (2008) proposed the use of GA and PSO separately for dynamic subchannel and bit allocations to reduce the transmit power in multiuser OFDM system. Every user is allocated a minimum of one subchannel even at the bad channel conditions. The performance of PSO in terms of convergence and computational time is found to be superior to that of GA.

Liu et al (2009) recommended GA to allocate resources adaptively in multiuser OFDM. The effective optimal power allocation algorithm is based on GA with proportional constraints to ensure that all the users are allocated with necessary data rate.

Premalatha&Natarajan (2009) suggested three different hybrid approaches based on PSO and GA for global maximization to overcome the premature convergence of the particles that are unable provide guaranteed solutions for an optimization problem. The proposed methods able to achieve high convergence rate with conventional methods.

Winston et al (2009) discussed about the margin adaptive RA problem for multiuser MIMO-OFDM system. It is imperative to optimize subchannel and power allocations to improve the overall system performance. The non-convex optimization complexity is converted from exponential to linear by Lagrangian dual composition method. The linear beamforming is included at both the transmitter and receiver to reduce the complexity. The approach proposed by Winston et al (2009) gives an optimal solution to reduce the power subject to data rate of the user.

Pischella&Belfiore (2010) focused on optimizing MAD problem by convex method for MIMO-OFDMA system under two cases namely, perfect CSI at the transmitter and statistical CSIT considering power control by distributed convergence.

Ahmedi& Chew (2010) recommended the use of ACO for subchannel and bit allocation in single cell OFDMA system. The overall transmit power at the base station is minimized by the proposed algorithm. The proposed method is able to converge faster at the cost memory.

Ahmed et al (2011) proposed two optimization methods such as Differential Evolution and PSO for dynamic subchannel and bit allocation to minimize the transmit power in multiuser OFDM system. Every user is allocated a minimum of one subchannel even at the bad channel conditions. The margin adaptive RA performance of DE in terms of convergence is better than PSO.

Sharma &Anupama (2011) proposed the use of multi objective Non-dominated Sorting Genetic Algorithm for MIMO-OFDMA systems where two different objectives such as capacity maximization and power minimization are considered for analysis. NSGA-II involves non dominated sorting and crowding distance algorithm to select the parents.

Yang &Alouini (2011) discussed about various multiuser scheduling techniques that can be applied to wireless systems to reduce the power. The suggested methods are Generalized selection multiuser scheduling, OOBS and SBS. Out of the three methods OOBS is a suitable method to increase the ASE for low SNR threshold values .

Annauth&Rughooputh (2012) proposed multi objective PSO to tackle the problems in the multiuser OFDM system for the resource allocation. The two different objectives namely maximizing the capacity and minimizing the power with constraints are considered. Mutation and crowding distance are introduced to improve the performance of PSO. The computational time needed for MOPSO is lower than that of PSO.

Zhou et al (2012) discussed the problem of energy efficient RA for OFDMA systems. It is based on two way relay channel with physical layer network coding. MAD is used to reduce the transmit power consumption and optimal solutions are achieved by the use of convex optimization methods.

Li et al (2013) suggested chunk-based low complexity energy efficient RA for a single cell, multiuser case in OFDMA. This method tends to maximize energy efficiency with the constraint on power and maintaining a balance between spectrum efficiency and energy efficiency.

Chang et al (2013) developed a joint allocation of power, subchannel and phase duration for the user equipment in bidirectional MIMO-OFDM network with the aim of minimizing the energy consumption with multiple decode and forward relay stations. Green RA provides reduced complexity and improved energy conservation by considering the QoS.

#### 2.1.2 RATE ADAPTIVE TECHNIQUES

Several optimization techniques are used for efficient resource allocation in WCS. Goldberg (1989), Mitchell (1996) proposed Genetic Algorithms (GA) to solve single objective optimization problems. Deb et al (2002) proposed the use of multi objective Non-dominated Sorting Genetic Algorithm (NSGA) to solve complex optimization problems with less computational complexity. The suggested approach is computationally fast and has faster convergence rate.

Rhee &Cioffi (2000) suggested an approach to maximize the minimum user's data rate to ensure that all the users get the same data rate or equal share of resources. The channel is assumed to be quasi-static and perfect CSI is known at the BS. The users with bad channel conditions are provided with minimum capacity by means of convex optimization. There is an improvement in spectral efficiency by the suggested low complexity dynamic subchannel allocation method.

Jang et al (2002) discussed on improving the channel capacity of OFDM system by adopting optimal transmit power method. Water filling method is applied over the subchannels in frequency-time domain for power allocation. The performance of frequency-time domain method is found to be better than the frequency domain method in terms of capacity.

Zhang &Letaief (2002) addressed the issue of DRA by means of low complexity algorithm that includes adaptive multiple access control, cell selection in addition to adaptive modulation. To reduce the load and to have uniform traffic density, an adaptive cell selection method is suggested.

Jang & Lee (2003) considered the RAD allocation with constraints on power and Bit Error Rate (BER). Transmit rate adaptation method is used to maximize the data rate of user by proposing two steps of operation which involves the subchannel allocation to the users followed by power allocation for the subchannels. The subchannels are allocated to the users based on the channel gain and power is distributed by water filling method. Equal power allocation is also considered to reduce the computational complexity.

Shen et al (2003) suggested a low complexity optimal method to increase the capacity by considering proportional fairness iteratively to improve the overall system capacity. The performance of this method is found to be better than that of TDMA in terms of capacity.

The Fractional frequency reuse method (Song & Li 2003) effectively improves the OFDMA system performance. Utility functions can be applied to calculate the level of users. Optimal subchannel and power allocation is based on utility functions. Capacity is maximized by adding the utilities of all the active users. Utility based RA assures spectral efficiency and fairness.

Holter et al (2004) proposed two multiuser schemes such as, Scan-and-Wait Transmission (SWT) and Switch and Examine Transmission (SET) to maximize the average spectral efficiency and to minimize average feedback load. The proposed schemes are aimed at identifying the acceptable user by functioning in a sequential manner based on a switching threshold for channel quality.

Hoo et al (2004) developed optimal and suboptimal algorithms for multiuser system with Inter Symbol Interference (ISI) under FDMA restriction and proposed weighted sum rate maximization method. The optimal algorithm is accomplished by multilevel water filling.

Wong et al (2004) considered rate adaptive allocation method with fairness and proposed a non-iterative linear subchannel method to improve the capacity with low complexity by relaxing the strict proportional rate constraints.

The performance of low complexity DRA in the downlink of OFDMA systems with fixed or variable rate requirements with fairness is considered. The sum capacity is maximized by imposing proportional rate constraints along with fairness (Shen et al 2005).

Goldsmith (2005) discussed about the capacity in wireless channels with respect to flat fading and frequency selective fading.

Han et al (2005) proposed a fair scheme to allocate subchannel, rate, and power for multiuser access systems. The problem is to maximize the overall system capacity, satisfying the minimum requirement of each user considering fairness. The proportional fairness achieved by the use of Nash bargaining solutions and coalitions.

Mohanram&Bhashyam (2005) suggested a method to maximize the capacity along with fairness. The optimal is obtained by the joint allocation of subchannel and power. Water-filling method is used for power allocation instead of equal power allocation.

Seong et al (2006) proposed a Lagrange dual decomposition method to solve weighted sum rate maximization and sum power minimization. To reduce the complexity in resource allocation, subchannel and power allocations are separately carried out.

Damji& Ngoc (2006) described DRA with interference alleviation technique for the multimedia services in the downlink OFDM. The performance is estimated by QoS and system spectral efficiency. It supports both real time voice and delay tolerant data services in mobile cellular communication system.

One bit channel state information per subchannel is used as feedback information for OFDM system by Rong et al (2006). Two cases are analyzed namely perfect feedback channel and imperfect feedback channel. For the first case three techniques are suggested to improve the system performance such as Adaptive subchannel selection, adaptive power allocation and adaptive modulation selection. Out of the techniques mentioned, the performance of Adaptive subchannel selection is found to be better compared to the other methods when the feedback channel is perfect.

Xu et al (2006) proposed an effective algorithm for subchannel and power allocation to maximize the total system capacity along with proportional rate constraints for MIMO-OFDMA. Capacity is fairly shared by the users and different user rates can be achieved by the use of different proportional rates.

Liu et al (2006) proposed cross layer scheduling scheme for the MAC layer that assigns priorities of connections according to the channel quality, QoS satisfaction and service priority across layers. The users are assigned with weights according to their QOS requirement. According to the weight, the users are provided with good number of subchannels and optimization technique is used to maximize the minimum user capacity.

Yanhui et al (2007) recommended subchannel and bit allocation based on diverse QoS requirements and the class of traffic. Resources are allocated to higher priority users based on the traffic classification thus reducing the outage probability of the users without affecting the system efficiency.

In another novel approach, for subchannel and bit allocation in MIMO-OFDM system Shin et al (2007) used zero forcing beam forming technique to reduce the transmit power and interference among the users. Subchannel allocation is based on semi orthogonal selection to reduce the complexity.

Tang et al (2007) developed low computational complexity algorithms for cross layer based RA which involves optimization of application, physical and MAC layer. The constrained optimization problem is solved by Elitist Selection Genetic Algorithm (ESGA).

Agarwal et al (2008) recommended two low complexity feedback algorithms to achieve optimum performance where the feedback overhead gets reduced by opportunistic feedback method. In the first scheme, contention-based feedback reduction is performed. In the second scheme, collisions are avoided by using sequential methods resulting in a higher performance.

Gunaseelan et al (2008) suggested a method to maximize the spectral efficiency in multiuser OFDM system. The algorithm supports dual services namely Guaranteed Performance (GP) and Best Effort (BE). More number of subchannels is assigned to the GP users than BE users by giving priority to the former.

Suh& Mo (2008) proposed resource allocation for Multicast Services in Multicarrier Wireless Communications to improve the capacity by using the Multiple Descriptions Coding (MDC). Multicast system saturates the capacity when the number of user increases in fading environment. MDC is an advanced level coding technique in which arbitrary combinations of layers can be decoded at the receiver.

Miao &Himayat (2008) discussed utility based resource allocation to improve the system capacity in orthogonal frequency division multiple access system for heterogeneous traffic.

Tao et al (2008) discussed about resource allocation for delay differentiated trafﬁc in multiuser OFDM systems. Adaptive allocation of subchannel and power in multiuser OFDM system is focused on homogeneous traffic to maximize the sum rate of the entire user with non-delay constrained data traffic while maintaining individual basic rates of delay constrained traffic with total power constraint. Optimal power allocation over subchannels follows a multi-level water filling principle.

Gao& Cui (2008) proposed low complexity algorithm for subchannel, power and bit allocations in OFDMA system for uplink transmission. The proposed method involves two steps such as, Initial Subchannel Allocation to maintain fairness among users and Residual Subchannel Allocation to increase the capacity.

Tang et al (2008) proposed the integration of PHY, MAC and application layers RA. Instead of ESGA, a low complexity Elitist Selection Adaptive Genetic Algorithm (ESAGA) is proposed by varying the probabilities of mutation and cross over based on population diversity.

Malathi&Vanathi (2008) considered Orthogonal GA for adaptive resource allocation to maximize the minimum user capacity in MIMO-OFDM system. The orthogonal crossover operation is involved in GA to improve the capacity of the system. The performance of OGA is found to be better than the static allocation methods.

To solve the subchannel allocation problem in wireless OFDMA, Chatzifotis et al (2009) proposed the use of Ant Colony Algorithm (ACO) to achieve optimal solution within short period of time to improve the system capacity. Time interval is based on the number of ants involved in the system. If more number of ants is used in the system, the execution time taken has been more but better solution is possible.

Zhou et al (2009) described the GA based cross layer RA for the downlink OFDM system with heterogeneous traffic to maximize the weighted sum capacity. The RA involves both physical and MAC layers. The heterogeneous traffic considered is Voice over Internet Protocol (VoIP), Variable Bit Rate (VBR) and Best Effort (BE) services.

Sharma &Anupama (2009) proposed genetic algorithm based resource allocation in OFDMA with proportional rate constraint. The power allocation is based on water-filling algorithm. The proposed algorithm combines the characteristic of both deterministic and GA to maximize the throughput and maintaining the proportionality among the users in OFDMA. The computational complexity is found to be slightly higher than that of the existing algorithms.

Sadr et al (2009) proposed two suboptimal algorithms for ARA in OFDMA system with fixed or variable rate constraints. The first algorithm provides preference to the user with high sensitivity which is determined by the variance between the subchannel gains to perform subchannel allocation. The second algorithm is focused towards maximizing the minimum user capacity by adapting power allocation based on water-filling method.

The total capacity improvement with fairness has been addressed by Da &Ko (2009) for MIMO-OFDMA systems. The proposed algorithm considers fairness as the main factor. It involves subchannel rearrangement. Here the subchannels are rearranged among the users with most fairness gain and least capacity loss. A Tradeoff-Factor (TF) is introduced for subchannelexchange to have a fair resource allocation. The scheme with maximum TF value used in strict fairness scenario reduces the system capacity. There should be tradeoff between fairness and capacity. The capacity obtained by this method is better than static allocation methods like TDMA and FDMA.

Zhang & Leung (2009a) proposed a greedy Max-Min algorithm for resource allocation in cognitive radio. The proposed low complexity method maximizes the overall capacity, by maintaining the interference within the threshold limit.

Zhang & Leung (2009b) suggested a Greedy max-min algorithm for resource allocation in CR system. A low complexity algorithm is employed to maximize the overall achievable rate by CR, while keeping interference within specified thresholds. The algorithm maximizes the overall bit rate achievable by CR while keeping interference to PU within tolerable range utilizing spectrum holes efficiently. Max-min algorithm provides a solution that is close to optimal.

Ji et al (2009) considered the problem of scheduling and RA for multiuser video streaming over downlink OFDM channels. Scalable video coding is combined with OFDM to derive the benefits of both the methods. Gradient based scheduling and RA algorithms provide importance to cater the needs of different users by calculating the weights of video contents, dead line requirements and transmission history.

Nam et al (2009a) discussed the use of SBS scheduling method involving a threshold based allocation of power to increase the ASE and also to increase the effective number of acceptable of users. By this power allocation scheme, the average BER increases slightly which was still below the target BER and hence acceptable.

Nam et al (2009b) proposed two multiuser scheduling schemes namely OOBS and SBS aiming to improve ASE while maintaining the BER performance. From the performance of the two schemes, the average feedback load is slightly reduced without any significant degradation in average spectral efficiency. It is observed that OOBS scheme provides a better BER performance and a slightly higher ASE. Also, SBS scheme has a minimum BER and ASE loss but AFL is significantly reduced.

Efficient resource allocation algorithm for Cognitive OFDM systems is proposed by Wang (2010) in which secondary users could use the spectrum as long as the interference introduced to primary user is under threshold limit.

Mitran et al (2010) considered resource allocation for an OFDM based CR with fixed users from point to multipoint network. The secondary users are allowed to transmit on any sub channels and interference to primary users is kept below a critical threshold.

Gheitanchi et al (2010) considered a low complexity PSO based resource allocation in adaptive multi carrier cooperative communications (MCCC). PSO with virtual particles is considered for centralized optimization and trained PSO for distributed optimization for single- and cross-layer subchannel allocation in MCCC technique.

Chakravarthy& Reddy (2010) recommended the use of resource allocation combined with scheduling in OFDMA system. Two approaches namely PSO based resource allocation and Credit based scheduling are used to satisfy the QoS requirements in WiMax. The proposed method is found to improve the sum capacity and fairness and is suitable for video –on – demand services.

Zhao et al (2010) proposed two algorithms based on Ant Colony Optimization (ACO) for resource allocation. The first one is to improve the throughput based on ACO and the second is to maintain proportional fairness among the users.

Vasileios et al (2010) recommended fairness aware user selection and resource allocation for the downlink of MISO-OFDMA system over a frequency selective channel. Suboptimal efficient algorithm is developed using zero forcing beamforming method. Fairness is maintained in addition to maximizing the sum data rates of users.

Almalfouh&Stuber (2011) considered the RA problem in OFDMA based CR Networks to maximize the throughput. The Resource Allocation is a Mixed-integer non-linear programming problem. The proposed algorithm provides near optimal performance and it reduces the computational complexity. The Proposed Algorithm starts with initial power allocation step and then subchannel allocation to maximize CR network throughput while satisfying transmit power budgets and PU interference protection threshold.

Aggarwal et al (2011) discussed joint scheduling and resource allocation for OFDMA systems with imperfect channel state conditions to maximize the sum capacity and good put. The non-convex optimization problem that arises when multiple users time-share a single OFDMA subchannel is converted into convex optimization problem and solved using dual optimization approach. When only a single user is allowed per subchannel at a time the mixed integer optimization problem that arises can be solved in a similar way for most situations.

Choi et al (2011) investigated RA in MIMO-OFDMA with and without adaptive modulation for co-ordinate multipoint. To reduce interuser interference, linear pre and post processing techniques are used.

Sharma &Anupama (2011) proposed the use of novel GA that combines the characteristic of both deterministic and GA to maximize the throughput and maintain the proportionality among the users in MIMO-OFDMA. Two point crossover operation is performed and mutation operation is randomly performed over the entire population. The performance of the proposed algorithm is comparatively good in terms of low computational complexity and high system capacity.

PSO and GA can be combined to improve the performance of OFDM system. The hybrid optimization technique proposed by Yi et al (2011) involves the standard PSO operation followed by GA in the updation of particles position and velocity. It combines PSO and GA for the subchannel and power allocation. Hybridization yields better performance than normal PSO and resource allocation is considered for three different scenarios namely MCSPF, MPF and MMC with different objectives.

Chen et al (2012) discussed RA problem in OFDM to maximize the user apparent QoS. A heuristic algorithm called bound relaxation technique with fix and drop operation is proposed to enhance the system performance in terms of QoS while achieving fairness between the users.

Kwan Ng et al (2012) formulated dynamic RA and scheduling for MIMO-OFDMA system with full duplex and hybrid relaying as a non-convex and combinational optimization problem. The different data rate required for delay sensitive and non-delay sensitive users are considered. Iterative distributed algorithm for subchannel and power allocation is considered. Optimal solutions are obtained with minimum number of iterations and performance gains obtained by full duplex MIMO relaying are better than half duplex relaying.

Goyal et al (2012) recommended a cross layer based fair resource allocation for multiuser OFDM based on scheduling. The scheduling is based on the weight of the packets determined by MAC layer. The method maximizes the weighted sum capacity along with fairness among the users.

Sharma et al (2012) applied customized particle swarm optimization technique for subchannel allocation in downlink OFDMA system. The subchannels are allocated to the users based on the channel gain and power allocation is performed by Water-filling method. The proposed algorithm is found to function well for discrete particle positions compared to standard PSO method which is suitable for continuous particle positions.

Two Adaptive resource allocation schemes for OFDM have been proposed by Rahman et al (2012).The first one is the combination of Genetic Algorithm and Fuzzy Rule Based System (FRBS) assisted adaptive coding and the second one is water filling and FRBS assisted adaptive coding. Out of the two methods, GA and FRBS assisted adaptive coding performance is found to be better than the others.

Wang et al (2012) studied the resource allocation problem for OFDM based cognitive radio systems with proportional rate constraints. The interference caused by the secondary user to the primary user should be below a threshold value. The channel gain and the interference level together predicts the maximum capacity of each subchannel with less complexity.

Chen & Yuen (2013) designed a competent RA for multiuser MIMO Cognitive Radio Network (CRN) with QoS requirement. Imperfect channel condition is assumed and optimal solution achieved by using the Heuristic algorithm. The RA strategy can resolve amount of feedback and mode of transmission based on the delay requirements.

Zhou et al (2013) mentioned the user grouping method called OFDM-Interleave Division Multiple Access (OFDM-IDMA) to get the best possible capacity and assign the subchannels to the users based on the corresponding channel conditions.

Leith et al (2013) developed low complexity weighted sum rate maximization algorithm with proportional rate constraints for both uplink and downlink systems. The users are selected based on a weighted channel SNR ranking combined with water filling for power allocation.

Wang et al (2013a) discussed about joint subchannel and power allocation to enhance the security of the physical layer in cooperative OFDMA systems. The power is initially equally distributed among the subchannels and later the power allocation is based on alternative ascending clock auction mechanism.

Guruacharya et al (2013) discussed RA of macrocells overlaid with femtocells in a cellular system. Leader follower game model known as Stackelberg game is used to improve the performance of the system with macro BSs as the leader and femto access points as followers. Analysis is also done by adding QoS constraint enforced on the leader. The performance of the Leader follower game model is found to be better than Nash equilibrium.

Zhang et al (2013) investigated QoS aware scheduling problem for downlink cooperative OFDMA system. The work concentrates on joint allocation of subchannel, power and relay selection with required QoS. A Two level decomposition method is suggested to solve the mixed binary integer nonlinear programming. The algorithm is used either with amplify and forward relays or with decode and forward relays.

Ye et al (2013) developed a combined optimization method for subchannel and power allocation for adaptive resource allocation. The resource allocation algorithm is based on the subchannel exchange and tradeoff is maintained between fairness and sum capacity. Even when malicious users exist the algorithm can maintain minimal user capacity.

Singhal et al (2014) concentrated on RA for edge cell users to benefit in terms of capacity and QoS. The split handoff scheme significantly improves the network performance with respect to hard hand off in terms of system capacity, QoS guarantee and traffic load balancing.

Sharma &Anpalagan (2014) proposed the use of Artificial Bee Colony algorithm (ABC) along with selection mechanism based on Deb (2000) to improve the system capacity with proportional constraints for OFDMA system. Two methods are suggested for DRA wherein the first method uses ABC for subchannel allocation. The use of ABC in the second method is to jointly perform subchannel and power allocations. The sum capacity is improved and near optimal solutions achieved by both the methods at the cost of slight increase in computational complexity.

## CHAPTER 3 RESOURCE ALLOCATION IN MULTIPLE INPUT MULTIPLE OUTPUT - ORTHOGONAL FREQUENCY DIVISION MULTIPLE ACCESS SYSTEM USING GENETIC ALGORITHM.

### 3.1 INTRODUCTION

The advent of Multiple Input Multiple Output (MIMO) technology is used to provide high data rate reliable wireless communications. MIMO-OFDM systems are multiplexing the users in both space and frequency domains. Multiple antennas increase capacity, transmission range reliability and suppress interfering signals. By increasing the number of receive and transmit antennas the throughput of the channel can be increased linearly with every pair of antennas added. OFDMA allows multiple users to simultaneously transmit on different subchannels per OFDM symbol. OFDMA and MIMO are combined to improve the system capacity. Da &Ko (2009) proposed subchannel exchange method for the allocation of resources to improve the system capacity and also considers fairness among users by the use of Trade off Factor (TF). Capacity improvement is achieved using Genetic Algorithm approach for resource allocation in MIMO-OFDM system. This chapter deals with GA based adaptive resource allocation in MIMO-OFDMA system.

### 3.2 SYSTEM MODEL

The downlink system model of MIMO-OFDMA with ‘K’ users, sharing a bandwidth of ‘B’ having ‘N’ subchannels is shown in Figure 3.1.

[Abbildung in dieser Leseprobe nicht enthalten]

**Figure 3.1 Downlink MIMO-OFDMA system model**

The following assumptions are made during the analysis:

- No subchannel is shared by different users.

- The system suffers from slowly time varying frequency selective fading channel.

- Perfect CSI of all the users are available at the BS.

BS receives the channel state information through the feedback channels from all the mobile users. The resource allocation information is forwarded to the MIMO-OFDM transmitter. The transmitter loads each user’s data onto its allocated subchannels. The resource allocation scheme is updated as soon as the channel information is collected and also the subchannel and bit allocation information is sent to each user for detection, through a separate channel.

The system consists of ‘K’ users, sharing ‘N’ subchannels with total transmit power[Abbildung in dieser Leseprobe nicht enthalten]. The objective is to maximize the total system capacity and concern about fairness between the users within the power budget. Assume that each user has Mr receiving antennas and the BS has Mt transmitting antennas. For user k (k=1, 2…, K) on subchannel n (n=1, 2…, N), the channel state matrix is [Abbildung in dieser Leseprobe nicht enthalten]with dimension of Mr X Mt.

Hk,n can be decomposed through SVD as,

[Abbildung in dieser Leseprobe nicht enthalten] (3.1) where[Abbildung in dieser Leseprobe nicht enthalten]is the singular value of[Abbildung in dieser Leseprobe nicht enthalten]in descending order, [Abbildung in dieser Leseprobe nicht enthalten] and [Abbildung in dieser Leseprobe nicht enthalten]are the corresponding left and right singular vectors, respectively. The SISO channel denoted by [Abbildung in dieser Leseprobe nicht enthalten] is referred as the dominant eigen channel for user k on subchannel n.

In a system with K users and N subchannels, there are KN subchannel allocations, since it is assumed that no subchannel can be used by more than one user.

The optimization problem considered by Da & Ko (2009) is given in Equation (3.2) with the corresponding constraints from Equation (3.3) to Equation (3.5).

[Abbildung in dieser Leseprobe nicht enthalten] (3.2) where ‘B’ is the Bandwidth of the system and ‘N’ refers to the number of subchannels. [Abbildung in dieser Leseprobe nicht enthalten] in Equation (3.2) gives the corresponding SNR, where [Abbildung in dieser Leseprobe nicht enthalten] is the allocated power of user ‘k’ on subchannel ‘n’ and [Abbildung in dieser Leseprobe nicht enthalten] is the channel gain of user and [Abbildung in dieser Leseprobe nicht enthalten] is the set of subchannels assigned to user k. with constraints

Abbildung in dieser Leseprobe nicht enthalten

The channel to noise gain of the ith eigen channel for kth user on nth subchannel is defined in Equation (3.6)

Abbildung in dieser Leseprobe nicht enthalten

where[Abbildung in dieser Leseprobe nicht enthalten]is the singular value of[Abbildung in dieser Leseprobe nicht enthalten]in descending order, N0 is the noise power.

The relation between [Abbildung in dieser Leseprobe nicht enthalten] and [Abbildung in dieser Leseprobe nicht enthalten]are given by

Abbildung in dieser Leseprobe nicht enthalten

for k= 1,2,….K users and n= 1,2,….N subchannels.

The dominant channel to noise gains of all users and subchannels is given in Equation (3.8)

Abbildung in dieser Leseprobe nicht enthalten

The total data rate of all the users is calculated using Equation (3.10)

Abbildung in dieser Leseprobe nicht enthalten

### 3.3 SUBCHANNEL EXCHANGE ALGORITHM

The subchannel allocation algorithm is suboptimal because equal power distribution is assumed in all the subchannels. Two separate stages of subchannel allocation and power allocation are considered to reduce the complexity of the system. The steps involved in subchannel allocation are,

1. Determine the number of subchannels to be initially assigned to each user.

2. Assign each user the first subchannel based on scheduling principle. User with less preassigned number Nk of eigen channels has more priority to choose the first subchannel.

3. Assign the subchannels to the users according to the number estimated in Step 1.

4. Allocate the remaining subchannels if any to users with the objective of enhancing the total system capacity.

5. Rearrange subchannels among the users to ensure fairness by means of Tradeoff factor (TF).

**Step 1 **

In the initial step, the number of subchannels for each user is determined as in Figure 3.2.

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.2 Parameter Initialization**

where [Abbildung in dieser Leseprobe nicht enthalten]are the sets of user and subchannel indices. [Abbildung in dieser Leseprobe nicht enthalten]is the data rate of user k, [Abbildung in dieser Leseprobe nicht enthalten] denotes equal power allocation across all eigen channels [Abbildung in dieser Leseprobe nicht enthalten]is the set of subchannels allocated to user k, [Abbildung in dieser Leseprobe nicht enthalten] is the number of subchannels needed for kth user, [Abbildung in dieser Leseprobe nicht enthalten] is the number of unallocated subchannels available from the total number of subchannels N and [Abbildung in dieser Leseprobe nicht enthalten]=1 if subchannel n is allocated to user k.

**Step 2**

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.3 First subchannel allocation**

Second step, as given in Figure 3.3 is to assign each user the unallocated subchannel that has the maximum gain for that user. The user with minimum number of required eigen channels has the higher preference to select the first subchannel. The user that has chosen the subchannel is removed from the user index and the respective subchannel is also removed from the subchannel index. The rate for kth user is found using channel gain of nth subchannel for the kth user.

**Step 3**

The user with the minimum amount of subchannels at that instance has more priority to choose one subchannel at a time. The user with least subchannels to its preferred proportion can get more subchannels by selecting the subchannels with good channel conditions. The priority based subchannel allocation is given in Figure 3.4

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.4 Priority based subchannel allocation**

The user having the minimum value for the ratio of instantaneous rate (achieved rate) to the required rate is given the priority to select the subchannel. If the number of required subchannels is non zero, the steps indicated in Figure 3.2 are performed.

**Step 4**

The fourth step assigns the remaining unallocated subchannels to the users in order to maximize the overall system capacity. This method increases the overall capacity by maintaining the proportional fairness. The residual subchannel allocation steps are mentioned in Figure 3.5. The unallocated subchannels are chosen from the subchannel index and it follows the steps given in Figure 3.2 for allocation.

Abbildung in dieser Leseprobe nicht enthalten

**For** select the first subchannel index n from[Abbildung in dieser Leseprobe nicht enthalten] **[Abbildung in dieser Leseprobe nicht enthalten]**

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.5 Residual subchannel allocation**

**Step 5**

The subchannels are reorganized among user with most fairness gain and least capacity loss. The [Abbildung in dieser Leseprobe nicht enthalten]value is the root mean square of [Abbildung in dieser Leseprobe nicht enthalten] It is defined to compare proportional fairness among users, where [Abbildung in dieser Leseprobe nicht enthalten]is the normalized rate proportion of user k.

Abbildung in dieser Leseprobe nicht enthalten

The value in Equation (3.11) shows the overall proportional deviation of all the users from their desired proportions. The proportional fairness is high when [Abbildung in dieser Leseprobe nicht enthalten]value is less. Absolute fairness is achieved when [Abbildung in dieser Leseprobe nicht enthalten] A Tradeoff-Factor (TF) is used to manage the number of subchannel exchanges. The subchannel reorganization is described in Figure 3.6.

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.6 Subchannel reorganization**

If there are any unfair allocations among the users, Drms ≠ 0 and TF>0. While maintaining fairness, capacity loss occurs. The value of [Abbildung in dieser Leseprobe nicht enthalten] is calculated for all users and ‘e’ is chosen to guarantee minimum capacity loss. Among the two selected users, the excessive subchannels are swapped. It is an iterative exchange process to increase the fairness among the users by slight reduction in capacity.

### 3.4 SUBCHANNEL ALLOCATION BASED ON GA

Genetic algorithm (GA) is a heuristic search technique derived from natural evolution. Genetic algorithms belong to the larger class of Evolutionary Algorithms (EA), which generate solutions to optimization problems using selection, crossover and mutation. It is a suitable method for solving both constrained and unconstrained optimization problems. The steps performed by GA are as follows,

- The algorithm starts with random set of solutions called population.

- In each step (generation) new population is achieved from the old one.

- New individuals are created by crossing old ones (parents). Based on the fitness values the individual can become a parent.

- The mutation is performed after cross over which produce children for the next generation.

The OFDM system consists of K Users (k = 1, 2. . . K) and N subchannels (n = 1, 2 . ., N). The system assigns a subset of N subchannels to a user and determines the number of bits/symbol per each assigned subchannel on downlink transmission.

1. Initialization: Generate population of chromosomes, where each bit of all the chromosomes is randomly picked from 1 to K.

2. Fitness evaluation: Update power allocation for each chromosome by using the subchannel allocation presented by the chromosome and utilizing the corresponding power and subchannel allocation of each chromosome, obtain the fitness value of each chromosome based on Equation (3.2).

3. Elitism: Find Nelite chromosomes with the highest fitness values and copy them directly into the next generation.

4. Crossover: Pick two chromosome parents from the current generation to create chromosome children for the next generation. Using those parents, single point crossover is done

5. Mutation: Perform mutation over the new generation with the probability of 0.01.

6. Repeat Steps 2, 3, 4 and 5 until the maximum generation limit Ngen.

### 3.5 FAIRNESS

TF is used to control the number of subchannel exchanges. In each loop, subchannels between two selected users with most unfair proportions are exchanged. This step is an iterative exchange process, which can enhance fairness at the cost of losing certain amount of capacity.

The performance of the algorithm in maintaining the proportions are calculated using,

Abbildung in dieser Leseprobe nicht enthalten

[Abbildung in dieser Leseprobe nicht enthalten]can have the maximum value as 1 and is considered to be the fairest case, where all the users would achieve the same data rate. [Abbildung in dieser Leseprobe nicht enthalten], Fairness lies between 0 and 1 and [Abbildung in dieser Leseprobe nicht enthalten] is the proportional rate constraint for the kth user.

### 3.6 SIMULATION PARAMETERS

The proposed GA for capacity improvement in MIMO-OFDMA system is designed using MATLAB 7.1 on a PC with Core 2 Duo processor operating at 2.53 GHz. Simulations are carried out using the parameters specified in Table 3.1.

**Table 3.1 Simulation parameters**

Abbildung in dieser Leseprobe nicht enthalten

### 3.7 RESULTS AND DISCUSSION

The performance of GA is compared with subchannel exchange method in terms of sum capacity and fairness. The algorithm used for comparison is also designed for MIMO-OFDMA system using MATLAB 7.1 on a PC with Core 2 Duo CPU operating at 2.53 GHz.

The frequency selective multipath channel is modeled as consisting of six independent Rayleigh multi paths with an exponentially decaying profile for downlink MIMO channel between any couple of transmitting and receiving antennas. The performance metrics viz., sum capacity and fairness are tabulated. The GA based resource allocation in MIMO-OFDM system is compared with subchannel exchange method for various Tradeoff Factor (TF) values and also with TDMA. The performance based on sum capacity using GA with various values of TF and TDMA for K=16 and N=64 are tabulated in Table 3.2 and the corresponding graphical representation is shown in Figure 3.7

For the case, when TF=0, which means a no subchannel exchange case, achieves higher capacity among other TF values. However, the capacity obtained for the different TF values are less than the capacity by GA. In addition, larger TF value leads to reduced capacity. The system capacity increases with the increasing number of users, which is due to the multiuser diversity. The performance of TDMA scheme is low when compared to various values of TF factor and GA. At the end of simulation, there is 3.9% capacity improvement in GA when compared to TF=0, 4.9% with TF=5, 5.1% with TF=10, 5.3% with TF=24 and 11.5% with TDMA. Hence, the proposed GA based method achieves higher capacity than the zero subchannel exchange and subchannel exchange methods.

**Table 3.2 Sum capacity vs user number**

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.7 Sum capacity vs user number**

**Table 3.3 Fairness Index vs number of users**

Abbildung in dieser Leseprobe nicht enthalten

The performance based on fairness to the number of users with GA is compared with existing method for 16 users and 64 subchannels are tabulated in Table 3.3 and the corresponding graphical representation is shown in Figure 3.8. The maximum fairness is achieved when TF=24 compared to other methods. Fairness achieved by GA is low compared with TF schemes.

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.8 Fairness vs number of users**

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3.9 N ormalized rate proportions vs user index**

Figure 3.9 shows the normalized capacity distribution between the users with[Abbildung in dieser Leseprobe nicht enthalten][Abbildung in dieser Leseprobe nicht enthalten][Abbildung in dieser Leseprobe nicht enthalten]Capacity achieved by GA is better than that of the other methods.

Resource allocation scheme using GA with flexible controllability on capacity, fairness has been investigated with proportional rate constraints for the MIMO-OFDMA systems. The scheme based on subchannel allocation with maximum TF value achieves almost ideal fairness with a small capacity loss. The scheme based on GA achieves higher capacity, but increased capacity with the reduction in fairness among the users.

## CHAPTER 4 CONCLUSION AND FUTURE WORK

The Wireless Communication Systems (WCS) are expected to provide high data rate needed for voice, file transfer, web browsing, wireless multimedia, teleconferencing, and interactive games. Resource allocation plays a vital role in wireless communication systems. To support more number of users in WCS, it is necessary to allocate the limited resources efficiently. For downlink scenario, the base station has to perform effective resource allocation with the limited bandwidth to improve the system performance to accommodate more number of users. Hence, there is a need to develop proficient algorithm for capacity improvement, overall transmit power reduction and fairness among users. It can be achieved by the use of various optimization techniques for resource allocation to improve the performance of OFDMA and MIMO-OFDMA systems.

### 4.1 CONCLUSION

Resource allocation scheme using GA with flexible controllability on capacity, fairness has been investigated with proportional rate constraints for the MIMO-OFDMA systems in chapter 3. Experimental evaluation of the proposed GA revealed a capacity improvement of 3.9%, 5.3% and 11.5% with TF=0, TF=10 and TDMA methods respectively. The RA scheme based on GA achieves higher capacity at the cost of reduction in fairness among users.

### 4.2 SCOPE FOR FUTURE ENHANCEMENTS

The present work is based on the assumption that CSI is known at the base station. Resource allocation can be carried out with imperfect CSI conditions. Multiple cell wireless environments can be considered instead of single cell system. But adjacent channel interference becomes a problem. The interference due to adjacent cells has to be considered. Several scheduling concepts can be combined with resource allocation to improve the performance of the system

The latest research is more focused on resource allocation in Cognitive Radios where two types of users are utilizing the resources, namely primary (licensed users) and secondary (unlicensed) users. It is a challenging task to assign the limited resources for CR systems. The different optimization algorithms used in the present work can be applied to resource allocation in Cognitive Radio.

In addition to the multiple objectives viz., capacity, transmit power and fairness, BER can be added as another objective to enhance the capacity in high data rate transmission system. The multi objectives can be optimized using different combinations of optimization algorithms. Their combinations can be used to develop an effective rate adaptation algorithm or power adaptation algorithm to improve the system performance in the case of OFDM, OFDMA and MIMO-OFDMA system.

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## Details

- Pages
- 58
- Year
- 2016
- ISBN (Book)
- 9783668359345
- File size
- 840 KB
- Language
- English
- Catalog Number
- v346329
- Institution / College
- Mahalingam College of Engineering and Technology
- Grade
- Tags
- optimization techniques resource wireless communication systems