Coalition Game Theory Based Cooperative

Published Date: 02 Nov 2017

The nodes of Wireless sensor networks (WSNs) are limited in power resources. Hence various energy efficient schemes have been proposed to enhance the survivability of WSN’s network lifetime. In wireless channel, network lifetime is reduced due to radio irregularities and fading effects. To reduce these fading effects, cooperative multi-input and multi-output (MIMO) scheme is used. Maximum diversity in transmit and receive antennas for a given number is attained by Space-Time Codes (STC) such as space time block code (STBC) and space time trellis code (STTC). In radio fading channel, energy transmission will be less in STC than single-input single-output (SISO) for the same bit error rate (BER). Hence STC can be deployed practically in WSNs. This paper proposes a coalition game formation for selecting the cooperative nodes for making transmission using cooperative MIMO. The proposed game enables higher energy savings in the nodes by jointly transmitting and receiving information. Utilizing coalition game, the cooperative MIMO’s performance is evaluated in terms of energy consumption and packet delay.

Key Words

Cooperative MIMO, Coalition Game, Space Time Block Code, Space Time Trellis Codes, WSN

1. Introduction

Small batteries are often used to power nodes in wireless sensor networks (WSNs). Therefore the prime objective is improving the energy efficiencies in WSNs [1]. To enhance the network lifetime and increasing energy efficiency, efficient energy scheme has to be provided to the sensor nodes of the network. The main challenge in the design of energy efficient communication protocols for WSN is channel fading and radio interfering. Fading effect in wireless channel is optimized by using multi-input multi-output (MIMO) scheme in sensor network [2, 3].

There is large power consumption at the circuit level since MIMO technique requires complex transceiver circuitry and signal processing. Directly applying multi-antenna technique to the sensor node is impossible since limited physical size of sensor nodes typically support a single antenna [1]. Setting up of cooperative MIMO scheme is supported by some individual sensor. Cooperative MIMO technique is one where multiple inputs and outputs are formed using cooperation among the single antenna nodes [4, 5]. Now-a-days Game theoretical techniques have been applied in many engineering fields and particularly that too in wireless communications [6]. The main aim of this paper is to develop cooperative MIMO scheme by using coalition game for effective transmission and reception in the cooperative communication. The formulated game helps to select the cooperative sensors dynamically based on the residual energy, geographical location and distance in a cluster thereby reducing the overall energy consumption [7].

2. Cooperative MIMO MAC System Model

Fig.1 shows the cooperative MIMO transmission model. Let nt be the number of sensors in transmitting cluster, nr be the number of sensors in the receiving cluster. The sensor nodes can communicate within a group relatively low power as compared to inter-group. The signals from multiple sending nodes from sending group are encoded by space time coding (STC) technique and transmitted to the receiving group. Space time decoding technique is utilized to separate the received signals and extract the original information at the receiver end.

Cooperative sender

Space time coder

Space time decoder

Cooperative receiver

Virtual MIMO

Fig 1 Cooperative MIMO system model

Source node sends recruiting request-to-send (RRTS) message to its neighbours at the beginning of each data transmission for transmitting data packets. Thus RRTS message is transmitted at lower power level than the normal transmission to ensure that only nearby nodes are recruited. Inturn the available neighbours will reply with sequential clear-to-send (SCTS) message in order to reduce collision. The transmission link is established between the source and destination nodes by the source node group sent by MIMO RTS (MRTS) after recruiting the sending group. The destination node follows recruiting procedure as the source node in recruiting the receiving group nodes. After getting SCTS reply by destination node, it sends broadcasting message to selected receiving neighbours to recruit them and help in receiving MIMO data. MIMO CTS (MCTS) control message sends and notify the source node group to transmit the data to the receiving group, therefore the source nodes start the data transmission after receiving MCTS from destination node [6.7].

2.1 Energy Consumption

Let us assume a scenario containing nt transmitters and nr receivers group in cooperative MIMO transmission. In MIMO MAC protocols the energy consumed for an unsuccessful and successful transmission from sending to the receiving group is determined to compute the overall energy consumption in a hop [8].

Energy consumption for an unsuccessful transmission is

eu= emrts+ emcts+(nt-1)escts+ebs+edata+(nr-1)ecol (1)

and the energy consumption for a successful transmission is

es= eu+ eack (2)

where

emrts is the energy required to send MIMO RTS

emcts is the energy required to send MIMO CTS

errts is the energy required to send RRTS

escts is the energy required to send SCTS

ebs is the energy used by the source node to transmit the data

edata is the energy consumption for data transmission between sending and receiving group

ecol is the energy consumed by destination or sink node to collect the data from cooperative receiving group

eack is the energy consumed in transmitting ACK

In cooperative MIMO systems, the total energy consumption for one-hop transmission in-terms packet error probability (pp) is given by

(3)

Packet Transmission Delay

Packet transmission in cooperative MIMO may increase the packet delays. However, the reduction in the packet error probability with cooperative MIMO MAC protocol reduces the occurrence of retransmissions which in turn reduces the packet delays. The duration of transmission attempt [1] that is successful using cooperative MIMO transmission is given by

(4)

and the duration for an unsuccessful transmission is

(5)

where

trts is the time required to transmit RTS

tbr is the time required for recruitment message sent by the destination node

tcts is the transmission time for the CTS

tbs is the transmission time required for the source node to send the data packet to its cooperating nodes

tdata is the transmission time for the data

tcol is the transmission time for the cooperating receiving nodes to send the data to the destination

tack is the transmission time for the ACK

twait is the duration for which sender waits for an ACK

The total expected packet delay for cooperative MIMO MAC is given by

(6)

2.3 Space Time Coding Scheme

Space time coding schemes is used for combating the channel fading and interference to improve the performance of cooperative MIMO in WSN. The code provides the full diversity over fading channels and improves the quality of signal transmission. To improve the reliability of data-transfer, STBC [2, 3] code is used by MIMO for transmitting copies of a data stream crosswise a number of antennas and to utilize the various received version of data. The copies of received signal are used to extract the original data using the STC decoding at the receiver side. Consider the encoder structure of space time trellis coded quadrature phase shift keying (QPSK) modulation [16] with nt transmit cooperative nodes. The m binary input sequences c1,c2,…,cm are fed into the encoder, which consists of m feed forward shift registers.

3. Coalition Game Formation

Energy-efficiency is a key issue in a WSN due to the severe energy constraints. It is not clear that MIMO transmission achieves better energy-efficiency compared to the SISO transmission scheme, due to the additional overhead in terms of data communications. Hence to decide which transmission scheme either SISO or MIMO is suited as a paramount important at this juncture. In addition, the peculiar characteristic of sensor networks is that they can cooperate on some joint task i.e.it has spirit innately. In order to achieve the above mentioned design, coalition game theory provides a set of analytical tools suitable for such a problem. To analyze the behaviour in decentralized and self-organizing networks, Game theory is used.

Game Theory consists game consists of

a set of players N = { 1, 2,...,n};

an indexed set of possible actions A = A1× A2× ... × An, where Ai is the set of actions of player i (for 0 < i= n );

a set of utility functions , one for each player. The utility function u assigns a numerical value to the elements of the action set A; for actions x, y ∈ A if u(x) ≥ u(y) then x must be at least as preferred as y.

In a coalitional game (N,) with N players, the coalition value or utility of a coalition is determined by a characteristic function  :2N→ R which applies to coalitions of players.

The game is modeled as (N, , S)

where

N is the set of players, {1,2…..,n} and

 is the characteristic function based on the network energy and S is the partition of N, S N.

The coalition formation is done using the merge and split algorithm [2]. In the coalition formation phase, iteration of arbitrary merge and split rule is repeated until termination to form coalitions between the node. A coalitional game provides a cost value for each of the 2N possible coalitions. In general, this amount of information is not easy to analyze directly. Characteristic function of the system is modeled based on the network lifetime and is given by

(7)

where ,is the utility of the node within the coalition Sj , is the number of sensor nodes in S and

eMIMO is the energy consumption.

The energy consumption of the sensor node which takes part in MIMO communication is given by

(8)

where, e0 is the residual energy of the node and P is the optimal energy consumption of the node decided from the iterations

e0 = ei - eMIMO (9)

where

ei is the initial energy of the node and eMIMO is the energy consumption of the node in the previous round

3.1 Utility Function

To minimize the energy consumption in the network, the utility function is to be defined which should show the energy consumed for data transmission and signal interference [13].

(10)

Equation (10) shows w is a function of ej and j, where ej represents the energy utilized for data transfer and j represents signal to interference and noise ratio (SINR). R represents the rate of information transmitted in L bit packets. The existence of energy strategy sets e1,e2,….ent+1 for the nodes 1,2,….(nt+1) is assumed. These sets consist of all possible energy levels ranging from the minimum transmit energy emin to maximum transmit energy emax given as

e = {e1, e2….eM+1} (11)

The collation game is played by all the nodes simultaneously picking up their individual strategies. These set of choices results in some strategy profile s s’, and it is called as the outcome of the game.

4. Results and Discussions

MATLAB 10.0 is used to validate the proposed game. The parameters considered for simulation is summarised in Table 1. The performance of proposed game based cooperative MIMO MAC protocol with coded and uncoded schemes was evaluated in terms of energy consumption and packet delay from source to the destination node for the traffic conditions in the network.

Table 1

Simulation parameters

Parameter (unit)

value

Time for transmitting RTS (ms)

36

Time for transmitting CTS (ms)

31

Time for transmitting ACK (ms)

32

Time for transmitting data (ms)

6

Energy consumed for transmission of RTS,CTS,ACK (J)

0.027

Energy consumed for transmission of data (J)

0.2

Number of transmit and receive antenna

2,3,4

Analysis of Energy usage for uncoded and coded MIMO schemes using Coalition Game

Energy consumption for different diversity orders (2ï‚´2, 3ï‚´3 and 4ï‚´4) with the uncoded system for the proposed cooperative MIMO MAC protocol is shown in Figure 2. For lesser cooperative sending and receiving group sizes, symbol error rate (SER) increases at low signal to noise ratio (SNR), which in turn results in multiple retransmissions, thereby resulting in higher energy consumption of sensor node. As the SNR increases, reduction in SER decreases energy consumption. It can be seen from the Figure 2, the energy consumption in 4 x 4 is 16% lesser than 2 ï‚´ 2 cooperative nodes at 5 SNR(dB). This reduction in energy consumption is due to higher diversity gain of cooperative MIMO systems.

Figure 2 Energy utilized by uncoded scheme for fixed group size MIMO configurations

4.1.1 Analysis of Energy usage by Cooperative MIMO with STBC Scheme

The energy consumed by various diversity orders (22, 33 and 44) are presented for the STBC coded cooperative MIMO scheme using coalition game is shown Fig.3. By comparing the performance of the STBC with the uncoded scheme shown in Figure 2, it is observed that there is a significant reduction in energy consumption because of diversity gain of coded MIMO system. The energy consumption with 4×4 diversity order is 14% lesser than that of 22 MIMO configuration. Better performance in STBC coded scheme increases with cooperative group size of 3x3 and 4x4. However the maximum number of cooperative nodes is restricted to four since further increase in size causes hardware complexity.

Figure 3 Energy usage by STBC coded scheme for fixed group size MIMO configurations

4.1.2 Analysis of Energy usage by Cooperative MIMO with STTC Scheme

The energy consumption of different cooperative nodes (2×2, 3×3 and 4×4) at transmitter and receiver cluster using STTC scheme is shown in Figure 4. The characteristics of energy utilized in cooperative MIMO are similar to that of STBC scheme. The 2×2 MIMO configuration consumes 39% and 42% more energy compared to 3×3 and 4×4 MIMO system with STTC respectively. Cooperative MIMO with STTC coding consumes lesser energy in cooperative group size of 33 by 13% and 44 by 25% when compared with STBC coding. The diversity gain of coding schemes improves the efficiency of energy consumption by increasing cooperative transmitting and receiving group sizes.

Figure 4 Energy usage by STTC coded scheme for fixed group size MIMO configurations

Analysis of Delay in uncoded and coded MIMO schemes using Coalition Game

The delay incurred for various transmit and receive group sizes (22, 33 and 44) are plotted in Figure 5 using uncoded scheme. The packet delay keeps decreasing at low SNR with the increase in the number of receiving cooperative nodes. The decrease in delay is due to lesser SER and fewer retransmissions in the system. In the cooperative group size 4×4 has fewer data retransmissions which results in 3% lesser packet latency than 22 system.

Figure 5 Packet delay of uncoded scheme for fixed group size MIMO configurations

4.2.1 Delay in Cooperative MIMO MAC with STBC Scheme using Coalition Game

The delay performance with STBC scheme for different transmitting and receiving group sizes (2ï‚´2, 3ï‚´3 and 4ï‚´4) are described in the Figure 6. The delay keeps reducing with the increase in the diversity order due to fewer packet retransmissions. It is vivid from the figure 6 that the STBC based cooperative MIMO MAC scheme with diversity order of 2ï‚´2 incur a increase in delay of about 70 % and 82% over 3ï‚´3 and 4ï‚´4 MIMO system.

Figure 6 Packet delay in STBC coded scheme for fixed group size MIMO configurations

4.2.2 Delay in Cooperative MIMO MAC with STTC Scheme using Coalition Game

The delay analysis of STTC based cooperative MIMO MAC protocol for various orders of diversity (2×2, 3×3 and 4×4) is illustrated in Figure 7. The delay in the transmission of data reduces with the increase in the number of cooperative nodes both at transmitter and receiver clusters by exploiting coding and diversity gain. It is clear from the results (Figure 7) that 2×2 STTC based cooperative MIMO MAC scheme incurs larger delay of about 83% and 93% over 3×3 and 4×4 MIMO system respectively.

Figure 7 Packet delay of STTC coded scheme for fixed group size MIMO configurations

Analysis of Energy in Cooperative MIMO MAC with Coded and Uncoded Scheme using Collation Game

Figure 8 shows the energy comparison of 4x4 MIMO system with STBC, STTC and uncoded schemes. In coded scheme the number of packet retransmissions decreases and results in lesser energy consumption. It is obvious that STTC offers 63% lesser energy consumption and STBC consumes lesser energy by an amount of 60% than uncoded scheme. This is due to the fact that STBC provides better diversity gain and lesser hardware complexity than STTC scheme.

Figure 8 Energy usage of 4x4 cooperative group size for coding and uncoded scheme

4.4 Analysis of Delay in Cooperative MIMO MAC with STBC, STTC and Uncoded Scheme

In cooperative MIMO MAC protocol, the delay incurred is due to transmission of RTS, CTS, ACK and data. Figure 9 shows the delay responses of a 4 x 4 cooperative MIMO configuration for STBC, STTC and uncoded schemes. It is clear that STBC and STTC offers better performance in terms of delay over uncoded scheme by providing better diversity gain for transmission of data packets from the source to destination cluster.

Figure 9 Delay of 4x4 cooperative group size for coding and uncoded scheme

5. Conclusions

To enhance the network lifetime in wireless sensor network, cooperative MIMO transmission utilizing MAC protocol is analysed. The cooperative MIMO was created using the group of transmitting and receiving group antennas by using coalition game. The MIMO MAC protocols performance for various orders of diversity (2×2, 3×3 and 4×4) is evaluated with coalition game with uncoded scheme STBC and STC and in terms of energy and delay. Simulation results proves that 4×4 MIMO configuration with STC coded schemes performs better and consume lesser energy and delay for packet transmission than uncoded scheme. Due to the hardware complexity of STTC encoder, the STBC scheme is preferred for this cooperative MIMO scheme. This results in the reduction of SER and diversity gain of higher order MIMO configurations. The performance of the cooperative MIMO MAC with STBC scheme using coalition game reduced the energy consumption of the nodes and thereby the network lifetime is increased.