Analysis Of Spectral Efficiency With Device toDevice Communications Over Fading Channels
Abstract—In 5G era , the network performance has to be improved in parameters such as network capacity, spectral efficiency ,throughput and reduced delay .Device to Device communication has its ability to enhance the above mentioned with improved system performance ,enhanced user experience, and expanded cellular applications. Device to Device communication enables communication between same user’s devices or with another user’s device without routing through cellular network. For non-Los D2D communication, relay scheme provides an effective utilization of spectrum . Our aim is to analyze the spectral efficiency of relay based D2D communication.NS3 based simulations were used to show the increase in spectral efficiency .

Index terms—
1 Introduction
With the long list of important features such as speed up to 10 Gbit/s,virtually zero latency, 100 times more devices ,faster response time ,very high capacity, more software option to upgrade ,ubiquitous connectivity and wide range of applications 5G is going to change the world. An approximate analysis shows the need for 1000 billion wireless communication devices around the world in 2020 which is accommodated by 5G, using Millimeter waves, Small cell, Massive MIMO, Beam forming and full duplex antennas in base station. The millimeter wave (mm wave) spectrum in 3~300 GHz bands are not reflected by ionosphere and cant propagate and penetrate to long range leading to high outage probability. Device to Device communication compensates the 5G coverage problem by relay based communication. There is a need to provide a trustworthy communication procedure in relay based D2D scheme . The trustworthiness can be induced by using Social Internet-Of-Things (SIOT) architecture in which the devices itself establish social relationships and use the resulting network to find the trusted proximity device which can provide desired service when needed.

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In subjective model for trust evaluation 1, each device calculates the trustworthiness of its proximity devices on the basis of its early experiences and on based on opinion of common friends . The trustworthiness management to isolate almost any intruder nodes in the network for both objective model and subjective model is explained in2.Using SIOT as an application to solve trustworthiness and relay based d2d communication was analyzed in3.In this paper,1) we consider a system model with 7 microcell cell structure.2)Compute trustworthiness of one device communicating with other device. 3) Establish relay based D2D communication 4)Calculate the spectral efficiency and compare it with legacy system.

The rest of the paper is organized as follows. Section II describes our System Model. Section III, we present Trust Calculation Procedure. Section IV gives Relay Based Communication Procedure. Section V deals with Spectral Efficiency Calculation. Finally, Section VI Performance Analysis. Section VII Conclusion

II.System Model
In this paper,we consider a system model with 7 micro cells grouped to 1 macro cell. Each micro cell has 1 enbnode and a total of 1400 user devices distributed in the entire range of 3 km . Figure 1 shows the system model created in ns3 environment .The devices are related by relationships such as Owner Object Relationship (OOR), Parent Object Relationship (POR), Co-Work Object Relationship (CWOR), and Social Object Relationship (SOR)from 4.

Owner Object Relationship (OOR)-established among heterogeneous objects owned by same user (mobile phones, musicplayers, game consoles, etc.).

Parent Object Relationship (POR): established among objects belonging to the same production batch, i.e., usually homogeneous objects originated in the same period by the manufacturer.

Co-Work Object Relationship (CWOR): established whenever objects collaborate to provide a common IOT application (as in case of objects that come in touch to be used together and cooperate for applications such as emergency response, telemedicine, etc.).

Social object relationship (SOR): established when objects come into contact, sporadically or continuously, because their owners come in touch with each other during their lives (e.g., devices and sensors belonging to friends, classmates, travel companions, colleagues).

Each device discover the proximity devices (less than 200 m) using capillary communication (i.e.Wifi) and establish communication edges E = {E1, E2, E3, EM}, where M=700.Using the communication edges, each devices calculates its trustworthiness for communicating with its proximity devices.

III.Trust calculation procedure
The trustworthiness Tij of i device2 communicating with j is calculated using a function of social relationships, CentralityRij,history of previous direct transactions and indirect transactions of common neighbours ,
Centrality: It represents how much pjis central in life of pi and not in entire network This aspect helps to prevent malicious nodes that buildup a lot of relationships to have high values of centrality. The number of neighbors of i node is represented as Ni and kijbe number of common friends of i and j, then centrality is given as follows,

Direct opinion: The direct opinion based on its own experience is given by,

Nijis total number of transaction between i and j, this equation shows even if Nij=0, long term opinion and short term opinion are considered with different weights. Also when Nij is not null the relationship factor and the computational capabilities are considered again, with a weight that decreases as Nij increases. The long and short -term opinions are computed as

Where number of transaction in long term opinion Llong is 50 and number of transaction in short term opinion Lshort is 5
is the feedback factor in transaction . A feedback system allows to improve the performance by evaluating the previous service pi received from by the provider pj.

is the transaction factor 1 based on relationships which indicates the relevance of transaction between pi and pj. It avoids nodes to build up their trustworthiness with small transactions and then become malicious for an important one.
Fij is relationship factor2 that depends on relation between pi and pj . It represents a unique characteristics of the SIoT. And finally a static characteristics of the objects ,the computational capability 2, namely its intelligence Ij is taken into account. Because a smart object is expected to have more capabilities to cheat leading to not accurate transactions.

e.g. Trusting a sensor over a smart phone in temperature value computing is not appropriate.

Table 1:Transaction factor tabular column podu.

Table 2:Relationship factor tabular column poduTable 3:Computational tabular column poduIndirect opinion:The indirect opinion is given by,
When i device asks opinion about j device to k device ,it first weighs k device with credibility value and then considers k device direct opinion about j device .

The credibility is calculated as,
Table 4:Subjective model parameters tabular column podu (refer trust calculate panrathuku oru paper print eduthenla athu)
IV. Relay based communication procedure
Consider our system with 1400 nodes .Each device communicates with proximity device within range of 200 m and establish communication edges .Then the device compute those devices trust value utilising their edges. If the trust value is greater than the threshold value , then it forms social edges and establishes social communication edges. Now the device makes relay request and sends data to a device with trustworthiness greater than threshold value and also greater than the trust value of other relay responses. When the device itself is a relay, it broadcast relay services to the remaining nearby devices, aggregate data from them and send.
Relay communication algorithm:
1:if distance between two nodes i and j ,
2: Establish communication edge
3: if then
4: Establish social edge
5: Establish social communication edge
6: end if
7:end if
8: if device is not a relay then: Broadcast relay request to nearby devices
9: if relay response >0
10: Check for all responses
11: if and and i j k then
12: Send data to relay node using
13: end if
14:else go to step 1
15: else
16: The device broadcast relay services to nearby devices
17: Aggregate data from nearby devices and send
V .Spectral efficiency calculation.

From spectral efficiency ,it is possible to obtain the minimum bandwidth necessary to transmit predetermined information rate or the maximum information rate that can be supported by a given bandwidth. In D2D communication data transmission between devices takes place without routing through a cellular network which provides hop gain. Also it enables reuse of resources between D2D users and cellular network users providing resource reuse gain. Thus the spectral efficiency and network throughput can be increased.

The spectral efficiency ,according to Shannon theorem is
In legacy system ,spectral efficiency is
In relay based communication, the spectral efficiency is
The signal to noise plus interference ratio for legacy system is,
Where g is Antenna gain ,P is Device transmission power and is additive white Gaussian noise for 60 GHz and is interference from N other devices .So to increase spectral efficiency ,SINR needs to be increased for which interference from number of devices has to be reduced.
Thus, the SINR in relay scheme is .

The number of devices aggregated using relay scheme using total of K relays is given by,
Where is number of devices in proximity of relay .

Relay based communication depends on trust value and trust is a function of relationship . Consider a set of total possible owners of size , from which the probability of one device having the same owner as another becomes ,if there are total manufactures , is size of co-workers then, social networks then .

The total probability of trustworthy devices is and is number of different relationships
Also the data rate in legacy system and relay scheme when b is bandwidth can be computed as ,

VI . Performance analysis and results

Figure 1b shows system model scenario with 1400 user nodes, 7 eNB nodes ,a server node and a gateway node ,in which proximity devices less than 200 m are communicating with relay based communication system.

Figure 2a. shows the Capacity gain Vs Number of devices .There is sharing of spectrum resources between cellular and D2D users. Thus resulting in capacity gain .This shows that the relay based D2D communication provides coverage to approximately 800 additional devices over 1400 devices.

Figure 2a. show Vs Number of devices Vs Number


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