EFFICIENT DATA AGGREGATION TECHNIQUES IN WSNA Project ReportSubmitted ByAbhinav Akash (12000311004)Abhishek Kumar (12000311005)Deepak Kumar (12000311025)Kamal Kr. Sah (12000311039)As a partial fulfillment for the award of the degree of Bachelor of Technology in Electronics and Communication Engineering of West Bengal University of Technology.

Under Supervision ofProf. Rajib Banerjee

Department of Electronics and Communication Engineering.Dr. B.C. Roy Engineering College Durgapur-713206(Affiliated to West Bengal University of Technology) 20th May, 2015

Department of Electronics and Communication EngineeringDr. B. C. Roy Engineering College, Durgapur

Certificate of approval

Date: ___, 2015

The report is hereby approved as a bonafide and creditable project work EFFICIENT DATA AGGREGATION TECHNIQUES IN WSN carried out and presented by Abhinav Akash (12000311004), Abhishek Kumar (12000311005), Deepak Kumar(12000311025), Kamal Kr. Sah (12000311039) in a manner to warrant its acceptance as a prerequisite for award of the degree of Bachelor of Technology in Electronics and Communication Engineering. However, the undersigned do not necessarily endorse or take responsibility for any statement or opinion expressed or conclusion drawn there in, but only approve the report for the purpose for which it is submitted.

(Name of the Supervisor)Prof. Rajib Banerjee

Countersigned

HeadDepartment of Electronics and Communication Engineering

Acknowledgement

This project consumed huge amount of work, research and dedication. Still, implementation would not have been possible if we did not have a support of many individuals and organizations. Therefore we would like to extend our sincere gratitude to all of them.First of all we are thankful to Dr. B.C. Roy Engineering College, Durgapur for their financial and logistical support and for providing necessary guidance concerning projects implementation.We are also grateful to Prof.Rajib Banerjee Sir and Mr.Mrinmoy Chakraborty Sir for provision of expertise, and technical support in the implementation. Without their superior knowledge and experience, the Project would like in quality of outcomes, and thus their support has been essential. We would also like to thanks Dr. Narendra Pathak Sir for all his support.We would like to express our sincere thanks towards volunteer researchers who devoted their time and knowledge in the implementation of this project.Nevertheless, we express our gratitude toward our families and colleagues for their kind co-operation and encouragement which help us in completion of this project.

AbstractAwireless sensor network (WSN) are spatially distributedAutonomous Sensorstomonitorphysical or environmental conditions, such asTemperature,Sound ,Humidity, Pressure etc. and to cooperatively pass their data through the network to a main location. The more modern networks are bi-directional, also enablingcontrolof sensor activity. The development of wireless sensor networks was motivated by military applications such as battlefield surveillance; today such networks are used in many industrial and consumer applications, such as industrial process monitoring and control, machine health monitoring, and so on. These sensors are small, with limited processing and computing resources, and they are inexpensive compared to traditional sensors. These sensor nodes can sense, measure, and gather information from the environment and, based on some local decision process, they can transmit the sensed data to the user.Smart sensor nodes are low power devices equipped with one or more sensors, a processor, memory, a power supply, a radio, and an actuator. A variety of mechanical, thermal, biological, chemical, optical, and magnetic sensors A Wireless Sensor Network (WSN) is a set of sensors that are integrated with a physical environment. These sensors are small in size, and capable of sensing physical phenomena and processing them. They communicate in a multihop manner, due to a short radio range, to form an Ad Hoc network capable of reporting network activities to a data collection sink. Recent advances in WSNs have led to several new promising applications, including habitat monitoring, military target tracking, natural disaster relief, and health monitoring. Studies show that data transmission consumes much more energy than computation. Data aggregation can greatly help to reduce this consumption by eliminating redundant data.

Preface

The basic idea is that single-antenna mobiles in a multi-user scenario can share their antennas in a manner that creates a virtual MIMO system.In the course of the development of cooperative communication, several complicating issues must be addressed, including the loss of rate to the cooperating mobile, overall interference in the network, cooperation assignment and handoff, fairness of the system, and transmit and receive requirement on the mobiles.Hop means the packets of energy that is transmitted from source to destination. Dual hop transmission is a technique by which the channel from source to destination is split into two shorter links using a relay. In this case the key idea is that the source relays a signal to destination via a third terminal that acts as a relay. It is an attractive technique when the direct link between the base station and the original mobile terminal is in deep fade or heavy shadowing or there is no direct link between source and destination. In this project our aim is to analyze the system with multiple relay nodes where source has two transmit antennas and each relay and destination have one antenna. Among the several relays used for the transmission of message from source to destination through relays we have to find the best relay suited for the best transmission in terms of power, BER and outage probability.

IndexSerial No.ContentPage No.

1.Abbreviations and Notation Used

9

2.Introduction

10-15

3

Types of WSN

16-17

4Characteristics of a WSN

18-20

5Architecture of a WSN

20

Motivation

6Contiki-Brief Review

21-22

7Proposed model

23

8Working Model

24-26

9Results

27-28

10Limitations

29-32

11

33-34

12

35

13Conclusions

36-38

14REFERENCES

39-40

List of Figures

1. Figure describing cooperative communication (page no: 11)

2. Figure describing Detect and Forward method (page no: 12)

3. Figure describing Amplify and Forward method (page no: 13)

4. Figure describing coded cooperation (page no: 14)

5. Figure describing Relaying Architectures (page no: 15)

6. Figure describing relaying network (page no: 28)

7. Figure describing modulation BPSK (BER vs SNR) (page no: 37)

8. Figure describing modulation QPSK (BER vs SNR) (page no: 38)

9. Figure describing outage probability vs SNR (page no: 38)10.

Abbreviations and Notation Used

Bit error rate, amplify and forward, multiple input multiple output, decode-and-forward, probability density function (pdf), coded cooperation, amplify and forward and detect and forward.

IntroductionWireless sensor networks (WSN) have drawn the attention of the research community in the last few years, driven by a wealth of theoretical and practical challenges. This growing interest can be largely attributed to new applications enabled by large-scale networks of small devices capable of harvesting information from the physical environment, performing simple processing on the extracted data and transmitting it to remote locations. Significant results in this area over the last few years have ushered in a surge of civil and military applications.

As of today, most deployed wireless sensor networks measure scalar physical phenomena like temperature, pressure, humidity, or location of objects. In general, most of the applications have low bandwidth demands, and are usually delay tolerant. More recently, the availability of in expensive hardware such as CMOS cameras and microphones that are able to ubiquitously capture multimedia content from the environment has fostered the development of Wireless Multimedia Sensor Networks (WMSNs) i.e., networks of wirelessly interconnected devices that allow retrieving video and audio streams, still images, and scalar sensor data. With rapid improvements and miniaturization in hardware, a single sensor device can be equipped with audio and visual information collection modules.

Types of WSN

Detect and Forward.1. Amplify and Forward.2. Coded Cooperation.

Detect and Forward Methods: In decode and forward method a cooperating node first decodes signals received from a source and then relays or retransmits them. The receiver at the destination uses information retransmitted from multiple relays and the source (when available) to make decisions. It should be noted that it is possible for a cooperating node to decode symbols in error resulting in error propagation. Perfect regeneration at the relays may require retransmission of symbols or use of forward error correction (FEC) depending on the quality of the channel between the source and the relays. This may not be suitable for a delay limited networks

Fig 2

Amplify and Forward: Each user in this method receives a noisy version of the signal transmitted by its partner. As the name implies, the user then amplifies and retransmits this noisy version. The base station combines the information sent by the user and partner, and makes a final decision on the transmitted bit. Although noise is amplified by cooperation, the base station receives two independently faded versions of the signal and can make better decisions on the detection of information. In this method each cooperating node receives the signals transmitted by the source node but do not decode them. These signals in their noisy form are amplified to compensate for the attenuation suffered between the source-to-relay links and retransmitted. The destination requires knowledge of the channel state between source-to-relay links to correctly decode the symbols sent from the source. This requires transmission of pilots over the relays resulting in overhead in terms of additional bandwidth. Additionally sampling, amplifying, and retransmitting analog values is a nontrivial task for real-time implementation.

Fig 3

Coded Cooperation: The users divide their source data into blocks that are augmented with cyclic redundancy check (CRC) code. In coded cooperation, each of the users data is encoded into a codeword that is partitioned into two segments, containing N1 bits and N2 bits, respectively. It is easier to envisionthe process by a specific example: consider that the original codeword has N1 + N2 bits; puncturing this codeword down to N1 bits, we obtain the first partition, which itself is a valid (weaker) codeword. The remaining N2 bits in this example are the puncture bits. Of course, partitioning is also possible via other means, but this example serves to give an idea of the intuition behind coded cooperation. In the first frame the users transmit their own N1 bits and if they decode each other N1 bits then they will transmit each other N2 bits and The users act independently in the second frame, with no knowledge of whether their own first frame was correctly decoded. Four cases arise and they are as follows:-

1. Both users cooperate.2. User 1 co-operate and user 2 doesnt.3. User 2 co-operate and user 1 doesnt.4. Both users dont cooperate.

Fig 4

Dual hop transmission is a technique by which the channel from source to destination is split into two shorter links using a relay. On the other hand diversity technique is an effective technique to mitigate the severe form of interference that arises due to the multi path propagation of wireless signal gain without increasing the expenditure of transmission time or bandwidth. In cellular, the ad-hoc network when one user is transmitting information to a remote terminal, other users nearby also receive it and transmit the signal to the destination. This process results in multiple copies of same signal from independent fading paths at the destination and brings diversity. Depending on the nature and the complexity of the relays cooperative transmission system can be classified into two main categories; regenerative and non regenerative systems. In regenerative systems, relay fully decodes the signal that went through the first hop. Then retransmits the decoded version to the second hop. This is also referred to as decode- and forward or digital relaying. On the other hand, non regenerative systems use less complex relays that just amplify and forward the incoming signal without performing any sort of decoding. It is called amplify and-forward or analog relaying signal. If many relay stations transmit signal to destination then it also needs synchronization of carrier phases among several transmit receive pairs which will increase the complexity of receiver as well as cost. Choosing the minimum number of relays for reducing cooperation overhead and saving energy without performance loss is an important concern. There are various protocols proposed to choose the best relay among a collection of available relays in literature.

Relaying Architectures

Fig 5Fig.5 shows various relaying architectures that reduce to commonly used channel models in the absence of cooperation. At the heart of cooperative communication is the classical relay architecture as shown in Fig. 5 (a), which is also called the three body problem. In the figure S is the source, R is the relay and D is the destination terminal. The source broadcasts the signal to both the relay and destination. The relay then retransmits the information to the destination. When the destination is unable to hear the source, the architecture reduces to the case of cascade multi hop communication. When the source and the relay cooperate to transmit information simultaneously to the destination this reduces to a multiple access channel as shown in Fig. 5 (b). When the relay and the destination cooperate this reduces to a broadcast problem as shown in Fig. 5 (c). Fig 5 (d) shows a simple case of multi branch relaying using two parallel branches of relays. When the relays near the source and the relays near the destination cooperate the case reduces to a simple cluster-to-cluster communication with interference as shown in Fig. 5 (e). This can be viewed as the nodes at the source cluster broadcasting and the nodes at the receiver in multiple-access mode. In this paper our aim is to analyze the system with multiple relay nodes where source has two transmit antennas and each relay and destination have one antenna. In the second hop, before transmitting signal to destination the best relay is selected based on the instantaneous channel conditions of two hops. This technique can save the transmission power of the network. It also reduces the decoding complexity at receiver side and at the same time achieves diversity gain. However this intermediate relay shall increase the maximum distance between source and destination also increase the spectral efficiency.Rules for cooperation:Partner selected such that both partners get higher mutual information.Cooperation time is allocated similarly for both partners.For a given pair of partners, time allocation is chosen to maximize the minimum rate.

Advantages and Disadvantages of Cooperative Communications

The key advantages of cooperative communications can be summarized as follows:

Cooperative Diversity Gain : Cooperative communications exploit space and time diversity in wireless networks in a distributed manner to improve system performance. The benefits of cooperative diversity can be translated into reduced transmission power, higher throughput, better transmission reliability or larger network coverage.

Balanced Quality of Service (QoS) : In traditional systems, users at the edge of the network coverage or in shadowed areas with poor channel conditions may suffer from capacity limitations. However, cooperative relaying can be used to overcome this discrepancy and hence give more balanced QoS to all users.

Infrastructure-less Network Deployment : Cooperative communications ease the rollout of a system that has no infrastructure available prior to deployment. For instance, in disaster-struck areas, relaying can be used to facilitate communications even though cellular systems or other existing communication systems are out of order.

Higher Energy Efficiency and Extended Network Lifetime : Cooperative transmission is also utilized to improve energy efficiency and extend the lifetime of networks composed of battery-operated nodes, e.g., sensors in a WSN. It has been shown that cooperative transmission schemes with multiple collaborative nodes can greatly improve network lifetimes by reducing the forwarding traffic loads of energy-depleting nodes.

Reduced Costs : Cooperative communications provide more cost effective solutions in many cases. For example, in cellular networks, it has been shown that the cost of providing a given level of QoS to all users in the cell is generally lower with the help of cooperative communications.

On the other hand, there also exist a few major disadvantages in cooperative systems as listed below.

Extra Relay Traffic and Interference : Extra resources in the form of frequency channels, time slots or orthogonal codes need to be allocated for relaying traffic. In addition, without smart power allocation schemes, cooperative relaying will certainly generate extra interference, which potentially causes deterioration of system performance.

Complex Schedulers : In cooperative systems, not only the traffic of different sources but also the relayed traffic needs to be scheduled. Therefore, more sophisticated scheduling is required. The complexity of scheduling mechanisms increases significantly when there are multiple users with multiple participating relays in the network.

Increased End-to-End Latency : Cooperative communications typically involve the reception and decoding of a data packet before it is re-transmitted by relays. With regard to delay-sensitive services, such as voice and increasingly popular multimedia services, the extra latency introduced by relaying may become detrimental.

Increased Overhead : The functioning of a cooperative system requires access control, synchronization, scheduling, additional security, etc. All these requirements certainly induce an increased overhead in comparison with traditional communication systems.

Classification of Cooperative Systems

From the perspective of implementation, cooperative systems can be classified according to different ways of utilizing relays. Here, we list a few factors that affect the realization of a particular cooperative system, as shown in Fig. 6

Fig 6

Literature Survey

The performance of cooperative communication has been compared using the three classes of signalling described in the introduction part. The hybrid version of detect-and forward is superior to the simple version of detect and forward. In comparing the three cooperative transmission schemes, both amplify-and forward and hybrid decode-and-forward are not very effective at low SNR. This is due to the fact that their signalling is equivalent to repetition coding, which is relatively inefficient at low SNR. Coded cooperation, however, has graceful degradation and performs better than or as well as a comparative non cooperative system at all SNRs. In addition, coded cooperation generally performs better than other cooperative methods for moderate to high SNR. An important question is how partners are assigned and managed in multi-user networks. In other words, how is it determined which users cooperate with each other, and how often are partners reassigned? Systems such as cellular, in which the users communicate with a central base station, offer the possibility of a centralized mechanism. Assuming that the base station has some knowledge of the all the channels between users, partners could be assigned to optimize a given performance criterion, such as the average block error rate and outage probability for all users in the network. In contrast, systems such as ad hoc networks and sensor networks typically do not have any centralized control. Such systems therefore require a distributed cooperative protocol, in which users are able to independently decide with whom to cooperate at any given time. There are various protocols proposed to choose the best relay among a collection of available relays in literature. It was proposed to choose the best relay depending on its geographic position, based on the geographic random forwarding protocol. In different paper the author proposed opportunistic relay based on the instantaneous channel conditions.

Table 1 shows a synopsis of most of the related literature found on cooperative communication followed by a summary and brief discussion open issues on the topic. Table 1 Reference

Characteristics

[1] [2]Describes the channel capacity lower bounds of physically degraded relay channels for different random coding schemes.

[3] [5]Extension of work in [1] to includechannel quality, multiple relays andasymptotic (w.r.t. # of relays) performance.

[6] [8]Analyze performance of a cooperative space-time relay based communication system along with error detection coding. Both diversity and coding gains areanalyzed. Performance with adaptive modulation is presented. Signalling schemes and performance withheterogeneous nodes each with different number of antennas is also considered.

[9] [11]Derive analytical expressions for outage probability and average symbol error rate for multi hop relay system. Also discuss optimal power allocation strategies over multiple hops.

[12]Analyze outage probability of a cooperative network with a certain node distribution. This is compared to the case when there is no cooperation.

Motivation

Cooperative communications presents many new challenges to researchers along with the numerous advantages. Relay functionality at the cooperating node is of foremost concern for the realization of cooperative communication. This problem has received large attention of researchers, and signicant progress has been made in this area. Another main concern in cooperative communication is the sharing of network resources (potential relays) among users and to investigate resource allocation schemes. While many key results have been obtained in this eld, several issues remain unexplored. The optimal assignment of partners (relays) in the multiuser network is one area that demands attention. Further, which criterion for optimality should be considered is another pertinent issue. Both, centralized and decentralized schemes are required to be developed for the network depending on its topology and demands. Furthermore, most of the cooperative systems produced so far are based on some very strong assumptions (e.g., synchronization among cooperative nodes and presence of perfect channel state information etc) which must be relaxed to come up with systems with practical constraints.

Objectives

A list of potential topics, which are very important issues in cooperative system design, are given below.

1. Resource Allocation: Once the multiple access schemes are determined in a system, each source and relay node can be allocated with different resources in terms of time, frequency, number of codes, etc. To design a contention-based cooperative transmission protocol, effective resource allocation can be achieved by employing a smart back off mechanism.2. Power Adjustment: Different levels of transmission power can be allocated to source and relay nodes to optimize different performance criteria according to channel conditions. The achieved optimal performance will be strongly affected by the availability of feedback from a receiver back to its transmitter. There is a trade-off between performances and overhead that needs to be balanced with regard to resource allocation in cooperative systems.3. Relay Selection: In cooperative communication networks with multiple potential relays, we need to determine which relay(s) to cooperate with. The decision can be made based on average or instantaneous relay channel conditions. In a distributed wireless network without a central controller, relay selection is a fairly challenging task in the cooperative scheme design.4. Mobility of Relays: In a planned cooperative system, it is possible to allocate optimal relay positions while planning. Whereas in mobile networks, the mobility of the relays is also an important factor to consider. The relay mobility will strongly impact the complexity and the performance of a cooperative system.5. Traffic Scheduling: In cooperative networks, both original traffic from users and extra relayed traffic need to be scheduled. In certain situations, the relayed traffic requires higher priority over the original traffic, and in other cases, it is the other way around. In addition, there are packets from different relays with the same information that need to be dealt with in coordinated way. Traffic scheduling and medium access control in traditional networks are already complicated, and these issues introduced by cooperative communications add considerable extra complexity.6. Cooperative Networking: The application of cooperative communications needs to be extended to multi-hop scenarios. However, a lot of challenges will be confronted in a cooperative multi-hop network. Questions like how to explore cooperative diversity from the routing layer, or how to combine routing with the underlying cooperative systems, need to be answered. Therefore, it is imperative to have a carefully designed cross layer solution in cooperative networking, because any gains due to cooperation at the physical layer can dissipate rapidly if not handled properly at the medium access and higher layers.7. Backward Compatibility: Most cooperative systems are proposed independently without considering the compatibility with the existing communications systems. This certainly hinders the applicability of cooperative communications in real life. Hence, it is of pragmatic importance to design cooperative communication systems while keeping the compatibility to the current hardware and protocols. This implies that instead of searching for a general cooperation solution, cooperative schemes should be tailored for specific application scenarios.8. Performance Evaluation: There are different approaches to evaluate a novel cooperative scheme. Firstly, the benefits of cooperative communications can be demonstrated through theoretical analyses in terms of Signal-to-Noise Ratio (SNR) benefits, outage probability and coverage extension. Secondly, the performance of cooperative schemes such as transmission reliability and network throughput can be illustrated through simulations using simplified network scenarios. Thirdly, the correctness and the feasibility of a proposed cooperative protocol can be verified through formal methods. Most proposed cooperative systems focus on the theoretical analysis and network simulations. However, in order to know the real performance of a cooperative system and promote the application of cooperative communications in reality, the evaluation has to be carried out by implementing test beds and measuring the performance in real-life.

Our main objective in this project is to study various existing schemes for relay allocation in cooperative communications and to develop novel approaches for the same. Among the n relays for the transfer of message from source to destination we have to find the best relay suited for this communication on the basis of performance which includes less power with high performance, End to end BER and Outage probability, with the aim of maximizing the sum throughput in a multiuser cooperative wireless network.

Proposed Model

We are considering a wireless dual hop network where a number of relay nodes are placed randomly and independently according to some distribution. The direct link between source and destination may be blocked by some obstacles. The relays can communicate with both end points. In our model the sources equipped with two transmit antennas and each relay node has a single antenna which can be used for both transmission and reception. All transmissions are assumed to be half duplex and therefore a relay station cannot transmit and receive at the same period. During the first hop source broadcasts symbols, the relays listen and during the second hop relay forward the decoded version of the received signal to destination. Figure 1 shows the channel model. We are assuming the channel remains constant during the two hops with Rayleigh fading. We are applying OSTBC at the source. No channel information is available at source. So no power or bit loading is performed at source. Each transmission antenna of source is assumed to use the same transmission power s2 = P/t , where P is the total transmission power of the base station and t is the number of antennae at base station. In this paper we are considering t =2. For two transmit antenna, there exists a rate one OSTBC defined by the transmission matrix X , X= (1) Where x1 and x2 are a pair of complex symbols to be transmitted and * denotes the complex conjugate. We assume there are r relays and number of transmit antennae at source is 2. So the channel matrix for the first hop is given by Hsr = (2) where the element hij denotes the channel gain between the ith relay and the jth transmission antenna of source, i=1,2,... r = and j = 1,2. We assume that each element of Hsr is independent and identically distributed complex Gaussian random variable with zero mean and 1 variance. We observe each row of Hsr represents the channel coefficient between source and relay. So the channel matrix for each relay can be represented i = for i = 1,2.....r (3) And for the second hop gi is the individual relay to destination fading amplitude.

Fig 7

The above given figure is the proposed model of our project. We have a source having two antennas, r relays having single antenna and the destination having single antenna.

Performance Analysis

Let si and id denote the total channel power from source to ith relay and ith relay to destination respectively. Here, si and id describe the quality of the wireless path between source to relay and destination to relay. si is calculated by relay i by the following equation. si = |hi1|2+ |hi2|2 . . . (4)And id = |gi|2 is the fading amplitude from relay to destination. Since the two hops are both important for end to end performance, each relay calculates corresponding hi based on the two decision rules. Rule1: hi = min{ si , id } .... (5) Rule 2: hi = 2/(1/ si + 1/ id) ........ (6)The relay i that maximizes function hi is one with the best end to end path between initial source to destination. After being selected as the best relay it relays signal to destination. In this project it is assumed the destination have perfect channel information available for decoding the received signal.End to End BER AnalysisIn the half duplex two hop protocol during the first time slot, the source transmits while all the relay nodes listen and during the next time slot the best relay is selected based on equations 5 and 6, then it transmits to destination .The selected relay is most opportunistic among all pairs for relaying signal to destination. The end to end SNR through this selected relay i is given by = maxi = 1,2,...r(min(si , id)) ....... (7)where si and id are the instantaneous SNR of the S-R and R-D link, respectively.The selection of the best relay is done by order statistics. The first step is to obtain the weaker link between the first hop and the second hop of each relay node. The weak link is ordered and the one with the largest SNR is selected as the candidate relay to perform detection and forward to destination. We assume the S-R and R-D link have the same average channel gain. The probability density function of can be obtained as..f() = 2rf(*)(1-F(*))(2F(*)-F(*)2)r-1 ........(8)where f(*) = 1/ * exp(-*/ * ) and

F(*) = 1 exp(-*/ * )Are the pdf and cdf of Rayleigh distributed random variable respectively. Finally the pdf of can be obtained as f() = r[exp(-*/ (* /2) )/ * /2{1- exp(-*/ (* /2)}r-1] ........(9)and through the binomial expansion, we further can writef() * exp(-i(2 */ * )) ..........(10)The pdf obtained in equation (10) can be employed for evaluating the error performance of this relaying scheme with any modulation techniques.

Outage ProbabilityThe mutual information between the source and relay nodes i= 1,2,r in the first hop can be given byIi1 = 1/2 log(1+ i1SNR) ........(11)With i1 = (|hi1|2 + |hi2|2)/2. i1 is exponential distribution with parameter =1/2 and the mutual information in the second hop of this corresponding relay is given byIi2 = 1/2 log(1+ i2SNR) ........(12)The probability density function of i1 and i2 are in order as followsf(i1, 1) = 1e i1 1 ...........(13)f(i2, 2) = 2e i2 2 ...........(14)So the capacity of the network for relay i is the minimum of the mutual information of this two hopC(i) = min(Ii1 , Ii2). .............(15) We are selecting the best relay based on end to end channel condition. So the maximum capacity of the entire network depends on the mutual information of the best relay. The mutual information of the best relay can be given byI = max(min(Ii1 , Ii2)) where i = 1,2,....r ........(16)I = max(min(1/2 log(1+ i1SNR), 1/2 log(1+ i2SNR))). ..........(17)So the network capacityC() = I

The outage probability Pout which can be defined as the probability that instantaneous capacity C () fall below outage capacity Cout. Pout = Pr( C() < Cout ) (18) Pout = pr(max(c( i)< Cout)) (19) Due to the independent channel assumption it given by Pout = piout (20) with piout = pr(c( i)