Using Coalition Game Theory Based Cooperative Mimo

Published Date: 02 Nov 2017

Raja Periyasamy [*] , Dananjayan Perumal [**] 

ABSTRACT

The nodes of Wireless sensor networks (WSNs) are limited in power resources. In order to promise the WSN survivability and increase the network lifetime, various energy-efficient schemes have been proposed. Network lifetime is limited due to the radio irregularities and fading effects in wireless channel. The cooperative multi-input and multi-output (MIMO) scheme is utilised to reduce the fading effects in wireless channel. Space-Time Codes (STC) such as space time block code (STBC) and space time trellis code (STTC) are used to achieve maximum diversity for a given number of transmit and receive antennas. In radio fading channel, STC require less transmission energy than single-input single-output (SISO) technique for the same Bit Error Rate and can be employed practically in WSNs. Hence this paper proposes a coalition game formation to select the cooperative nodes for enabling packet transmission using cooperative MIMO. The proposed game enables higher energy savings by allowing nodes to transmit and receive information jointly. The performance of the cooperative MIMO utilizing coalition game 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

Nodes in wireless sensor networks (WSNs) are frequently powered by small batteries. Consequently, improving the energy efficiency in WSNs has always been a primary objective in recent research [1]. Energy efficiency and maximising network lifetime have been the most important design goals for the network due to limited energy of sensor nodes. However, channel fading and radio interfering causes a challenge in design of energy efficient communication protocols for WSN. The multi-input multi-output (MIMO) scheme is utilised for sensor network to reduce the fading effects in wireless channel, [2, 3].

However the MIMO techniques require complex transceiver circuitry and signal processing leading to large power consumptions at the circuit level. However, the direct application of multi-antenna technique to WSN is impractical due to the limited physical size of sensor nodes which can typically support a single antenna [1]. Fortunately some individual sensor nodes can cooperate for the transmission and the reception in order to set up a cooperative-MIMO scheme. Cooperative is a type of MIMO technique where the multiple inputs and outputs are formed via cooperation in a network of single antenna nodes. [4]. Game theoretical techniques have recently been applied in many engineering applications, particularly in wireless communications [6]. The main proposal of this paper is to develop a methodology for sensors to dynamically form optimal collaborative coalitions. Coalition formation game is adopted to choose the cooperative nodes for transmission and reception. The game is formulated such that, the cooperative sensors are dynamically selected based on the residual energy, geographical location of the sensors and sensor distance in a cluster, to reduce the overall energy consumption [7].

2. Cooperative MIMO MAC System Model

Cooperative MIMO transmission model is shown in Fig.1. Considers Nt number of sensors in the transmitting cluster, Nr number of sensors in the receiving cluster and one antenna is placed at one sensor. Within a group, sensor nodes can communicate with relatively low power as compared to inter-group communication. In the sending group, the signals from multiple sending nodes are encoded by space time coding technique and transmitted to the receiving group. At the receiver, space time decoding is used to separate the received signals and extract the original information.

Cooperative sender

Space time coder

Space time decoder

Cooperative receiver

Virtual MIMO

Figure 1 Cooperative MIMO system model

At the beginning of each data transmission, source node sends recruiting request-to-send (RRTS) message to its neighbours for transmission of data packets. The RRTS message is transmitted at a power level lower than that for normal transmission to ensure that only nearby nodes are recruited. The available neighbours will reply with sequential clear-to-send (SCTS) message for the purpose of reducing collision. After recruiting the sending group, the source node sends MIMO RTS (MRTS) to destination node for establishing data transmission link. The destination node recruits receiving group nodes using the same recruiting procedure as that of source node. After the destination node gets SCTS reply, it sends broadcast messages to selected receiving neighbours to recruit them and help in receiving MIMO data. If the receiving group does not have enough nodes, the MIMO CTS (MCTS) control message will notify the source to retransmit. Otherwise, after receiving MCTS from destination node, the source node starts data transmission [6,7].

2.1 Energy Consumption

Consider a cooperative MIMO scenario with Nt senders group and Nr receivers group. The energy consumed for an unsuccessful transmission and for a successful transmission from sending group to the receiving group using STBC MIMO MAC is calculated to analyse the overall energy consumption in a hop [8]. The energy consumption for an unsuccessful transmission attempt is

eucoop = 2emcps +(Nt-1)escts+ebs+edata+(Nr-1)ecol (1)

and the energy consumption for a successful attempt is

escoop = eucoop + eack (2)

where

emcps is the energy consumed for MIMO control packets

errts is the energy consumed for sending RRTS

escts is the energy consumed for sending SCTS

ebs is the energy consumed by the source node group to send data

edata is the energy consumption for data

ecol is the energy consumed by destination or sink node to collect the data

eack is the energy consumed for sending ACK

Total energy consumption for single-hop transmission in cooperative MIMO system in-terms packet error probability (pp) of 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 reduces the occurrence of retransmissions which in turn reduces the packet delays. The transmission delay of complete transmission [1] that is successful using cooperative MIMO transmission is given by

(4)

and the time delay for an unsuccessful attempt is

(5)

where

trts is the transmission time for the RTS

tbr is the transmission time of a recruitment message sent by the sink node

tcts is the transmission time for the CTS

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

tdata is the transmission time for the data transmission

tco is the time required by 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 are used to improve the performance of MIMO WSN combating the channel fading and interference. The code provides the full diversity over fading channels and improves the quality of signal transmission. STBC [2,3] codes are used for MIMO systems to enable the transmission of multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data-transfer. Space-time coding combines all the copies of the received signal in an optimal way to extract as much information from each of them as possible. In STTC, 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

Game theory can be used to analyze behaviour in decentralized and self-organizing networks. Game theory typically models the nodes as players and choice of strategies of self-interested players, in order to capture the interaction of players in an environment such as a communication network. A 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}

 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]. During the coalition formation phase, the nodes form coalitions through an iteration of arbitrary merge and split rules repeated until termination. 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

In the coalition game formation phase, the nodes form coalitions through an iteration of arbitrary merge and split rules repeated until termination.

3.1 Utility Function

The objective is to reduce the total energy consumption in the network, so the utility function need to be define in which it reflects the energy consumed for data transmission and signal interference [13].

(10)

When applying w to a node j, Ej is the power used for message transfer by j and j is the signal to interference and noise ratio (SINR) for j. In addition, R is the rate of information transmission in L bit packets in the WSN. 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 power emax given as

e = {e1, e2….eM+1} (11)

The game is played by having all the nodes simultaneously pick their individual strategies. This set of choices results in some strategy profile s s’, and is called as the outcome of the game.

4. Results and Discussions

The analysis of the proposed game is carried out using MATLAB 10.0. 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 are 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)

32

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

Energy co of Uncoded MIMO and MIMO with STC schemes using Coalition Game

The energy consumption for various diversity orders (2ï‚´2, 3ï‚´3 and 4ï‚´4) with the uncoded system for the proposed MAC protocol is shown in Fig.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 Fig.2 the energy consumption is 16% lesser when 4 ï‚´ 4 cooperative nodes are used at transmit and receive clusters. This reduction in energy consumption is due to higher diversity gain of cooperative MIMO systems.

Figure 2 Energy consumption of uncoded scheme for fixed group size MIMO configurations

4.1.1 Energy Analysis of Cooperative MIMO with STBC Scheme using Coalition Game

The energy consumption of various diversity orders (22, 33 and 44) are presented for the STBC based cooperative MIMO scheme using coalition game is shown Fig.3. When comparing the performance of the STBC with the uncoded scheme shown in Fig.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. The increase in cooperative group size by 33 and 44 will give better performance in STBC coded scheme. Moreover, the maximum number of cooperative nodes used for simulation is restricted to four as further increase of it introduces hardware complexity and cost of the system.

Figure 3 Energy consumption with STBC scheme for fixed group size MIMO configurations

4.1.2 Energy Analysis of Cooperative MIMO with STTC Scheme using Coalition Game

The energy consumption of different cooperative nodes (2×2, 3×3 and 4×4) at transmit and receive cluster using STTC scheme is evaluated in Fig.4. The energy characteristics obtained are similar to that of STBC cooperative MIMO MAC protocol. 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 by 33 and 44 13% and 25% when compared with STBC coding Irrespective of the coding technique used the improvement in energy consumption is noticed clearly with increase in cooperative sending and receiving group sizes. This is due to the diversity gain of coding schemes.

Figure 4 Energy consumption with STTC scheme for fixed group size MIMO configurations

Delay Analysis of Uncoded MIMO and MIMO with STC scheme using Coalition Game

The delay incurred for various transmit and receive group sizes (22, 33 and 44) are plotted in Fig.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 with uncoded scheme has fewer data retransmissions and 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 Analysis of Cooperative MIMO MAC with STBC Scheme using Coalition Game

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

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

4.2.2 Delay Analysis of 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 Fig.7. The delay incurred 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 evident from the results (Fig.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

Energy Analysis of Cooperative MIMO MAC with STBC, STTC and Uncoded Scheme

Fig.8 demonstrates the energy comparison of the 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 analysis of 4x4 cooperative group size for STBC, STTC coding and uncoded scheme

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

The delay incurred by the cooperative MIMO MAC protocol is due to transmission of RTS, CTS, ACK and data between the sending and receiving group. Fig.9 illustrates the delay responses of a 4 x 4 cooperative MIMO configuration for STBC, STTC and uncoded schemes. It is vivid 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 analysis of 4x4 cooperative group size for STBC, STTC coding and uncoded scheme

5. Conclusions

MAC protocol utilising cooperative MIMO transmission in wireless sensor network has been explored to enhance the network lifetime. The cooperative MIMO is created with the group of transmitting and receive group antennas by using coalition game. The performance of the cooperative MIMO MAC system with coalition game is evaluated for various orders of diversity (2×2, 3×3 and 4×4) with uncoded scheme STBC and STC and in terms of energy and delay. Simulation results prove 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 from the reduction in SER and diversity gain of higher order MIMO configurations. The performance of the cooperative MIMO MAC with STC scheme using coalition game is reduced the energy consumption of the nodes to increase the network lifetime.