Adaptve Modulaton and Codng for Utlty nhancement n VMIMO WSN Usng Game Theory R. Vall and P. Dananjayan mparments. The data transmtted from the sensor nodes s hghly susceptble to error n a wreless envronment whch leads to hgher packet loss and thereby ncreases the transmt power. rror Control Codng (CC) s used to mprove the system performance and s shown that CC saves energy as compared to uncoded data transmsson []. To mtgate the fadng effects n wreless channel, dversty technques can also be used. Mult-Input Mult-Output (MIMO) scheme technology has the potental to enhance channel capacty and reduce transmsson energy consumpton partcularly n fadng channels []. Another way to combat fadng s the use of adaptve modulaton whch allows a wreless system to choose the hghest order modulaton dependng on the channel condtons whle ensurng that no harmful nterference s caused to other nodes []. Adaptve approaches result n better effcency by takng advantage of the favourable channel condtons as compared wth non-adaptve methods whch requre a fxed margn to mantan acceptable performance when the channel qualty s poor,. After the physcal layer set the optmal modulaton level, t wll adjust the transmsson power to stablze at the mplct optmal transmsson power by the feedback based power control scheme. So actually the optmzaton of modulaton level and transmsson power s jontly consdered. An approach to adjust the transmsson power of a node n WSN s based on game theory whch has ts roots n economcs [] and there has been a growng nterest n applyng game theory to study wreless systems [- ]. Game theory nvolves a set of competng players lookng to maxmze ther own utlty, based upon certan actons they can take. When the users have no knowledge a pror about what others are smultaneously dong, e.g., n a dstrbuted system, the game s non-cooperatve, as users have no nformaton on the bass of whch they could cooperate. Non-cooperatve game theory was frst proposed as an effcent framework to formulate the power control problem for wreless data networks wthout centralzed control, e.g., n ad hoc networks []. Gao Peng et al., have proposed a non-cooperatve power control game for Adaptve Modulaton and Codng (AMC) and analysed []. But here the energy of the nodes has not been taken nto consderaton whle desgnng the game. In ths paper, a non-cooperatve power control game for adaptve modulaton and codng n VMIMO WSN consderng the resdual energy of the nodes s analysed. The rest of the paper s organzed as follows. System model s conferred n Secton II. Game theoretc approach for WSN s dealt n Secton III. The power control game for adaptve modulaton s also formulated n ths secton. Smulaton Abstract The prmary component of resource management n wreless sensor network (WSN) s transmtter power control snce the sensors are tny, low cost battery powered devces. The adverse mpacts caused by rado rregulartes and fadng ncrease the energy consumpton and thereby reduce the WSN lfetme. An effcent power control technque s mportant to sustan system qualty and effcency of wreless sensor networks n such fadng condtons. To reduce the fadng effects n wreless channel, mult-nput mult-output (MIMO) scheme s utlsed for sensor network. Ths paper proposes a power control soluton for Vrtual MIMO (VMIMO) WSN usng game theoretc approach. The game s formulated as a utlty maxmzng dstrbuted power control game n VMIMO WSN consderng the resdual energy of the nodes along wth adaptve modulaton. The proposed algorthm adapts to the changes n channel condton and selects the approprate modulaton and transmts usng the optmal transmsson power. Smulaton results show that the game wth prcng provdes maxmum utlty by consumng lesser power. Index Terms Adaptve modulaton and codng, game theory, utlty, wreless sensor network. I. INTRODUCTION Wreless sensor network (WSN) are a network composed of tny, mcroelectronc devces capable of sensng, low power computng and wreless communcatons. Due to the very lmted network bandwdth, power and processng capacty, WSN presents remarkable challenges n the felds of wreless networkng, communcatons and sgnal processng. Whle a large number of research efforts have been spent on networkng and dstrbuted sgnal processng n order to reduce power consumpton, there are few research efforts on energy effcent wreless communcatons schemes specfcally desgned for WSN. WSN provdes an attractve low-cost technologcal soluton for a wde range of remote sensng and envronmental montorng applcatons []. Due to the large number of wreless sensors n the network and the severe constrants n the system, the wreless communcatons schemes for WSN should be cost effectve and energy effcent. Transmsson power s accountable for up to % of the total energy consumpton for off-the-shelf sensor nodes []. Therefore energy conservaton s very crucal for WSNs, both for each sensor node and the entre network to escalate the network lfetme. In a WSN, each node transmts ts nformaton over the ar and s prone to fadng and other Manuscrpt receved January, ; revsed Aprl,. The authors are wth Adhparasakth ngneerng College, Melmaruvathur,Taml Nadu, Inda (e-mal: vall.r@pec.edu, pdananjayan@ pec.edu). DOI:./IJCT..V.
results are gven and dscussed n Secton IV. Fnally, conclusons are drawn n Secton V. II. SYSTM MODL A two dmensonal plane s consdered and s assumed to have N nodes n the network area A. All nodes reman statonary after deployment. The energy of the all nodes s lmted and own same ntal energy except the snk node. The maxmum energy of a node s gven as m. nergy consumed n the transmsson s proportonal of bytes transferred and dstance. The sensor node has power control capablty and s capable of transmttng at varable power levels dependng on the dstance to the recever. The node power control range s [s mn, s max ], where s max s the maxmum transmsson power. Nodes are locaton unaware.e. they are not equpped wth any Global Postonng System (GPS) devce. The source node through local communcaton broadcasts the data to M t actve nodes whch compose the dstrbuted antenna array. The actve nodes are a subset of the total cluster nodes. At ths step each actve node encodes the transmsson sequence accordng to Space Tme Block Codng (STBC) as f each node were a dstnct transmt antenna element n the centralzed antenna array. Ths set of M t cooperatve sensor nodes, communcates wth the destnaton composed of an actve set of M r cooperatve sensor nodes. The destnaton receves data through an M t x M r MIMO channel. Space tme codng schemes are used to mprove the performance of MIMO WSN combatng the channel fadng and nterference. The code provdes the full dversty over fadng channels and mproves the qualty of sgnal transmsson. Of the space tme codng schemes, STBC s more sutable for wreless sensor network wth low encoder/decoder complexty. STBC operates on a block of nput symbols producng a matrx output whose column represent tme and rows represent antennas []. They are optmal over all untary codes wth respect to the unon bound on error probablty. Modulaton schemes can be adjusted for the wreless module of the node. In WSNs snce depleton of battery resource has a drect mpact on the network lfetme, the power control should take nto account the resdual energy of the nodes. By consderng the nodes resdual energy, those nodes wth mnmum resdual energy can be used less frequently, thus prolongng lfetme of the node and hence the network. The Sgnal to Interference Nose Rato (SINR) consderng the th node s gven as, hs m ( ) N m hjs j + N j=, j j SINR = γ = G G =W / R s the processng gan W s channel bandwdth, R s the data rate s resdual energy of the th node j s resdual energy of the j th nterferng node s s the transmsson power of th node () s j s the transmsson power of j th nterferng node m s maxmum energy of th node h s the path gan N s the nose spectral densty III. GAM THORTIC MODLLING Nowadays use of game theory n the vast majorty of scence and applcatons has ncreased consderably [], []. The game s defned as a trple G =[N,{S, M },U ] where N s the set of players, whch may be a group of nodes or an ndvdual node n wreless sensor networks. They are the man decson makers of the game. A set of actons, avalable for the player to make a decson. Here each node selects modulaton type m M and the correspondng s S. The payoff {u, u,.., u }resulted from the strategy profle. Payoff functon expresses the level of ncome or utlty that can be got from the game by the players and s a functon of the strategy of all the players. ach node represents a player, where each player n can adjust ts transmt power [s mn -s max ] to maxmze ts ndvdual utlty functon u. However, the wreless envronment s nherently nterference lmted, whch results n nteractons between nodes. Varous utlty functons can be consdered, but durng condtons of mutual nterference, these are nvarably dependent upon the user SINR. The SINR n turn depends on the transmt powers of all users n the network. Usng the standard notaton n the game theory lterature, we denote the transmt power vector of users other than user n by s -. The utlty functon consdered for VMIMO WSN s gven as M R u ( s,γ ) = η = M R f ( γ ) () eff,mch sym codng = where M sym s the number of bts of each symbol that can be modulated n the n th type scheme of modulaton and codng f s schemes (MCS), R codng s the codng effcency. the effcency functon whch ncreases wth expected SINR. The effcency functon whch s the functon of SINR, s gven as f ( γ ) = (- p ) F () where p e s the bt error rate (BR) correspondng to the type of modulaton used F s the sze of the packet Hgher order modulaton rates are able to offer much hgh data rates and hgher levels of spectral effcency for the rado communcatons system, but ths comes at a cost. The hgher order modulaton schemes are consderably less mmune to nose and nterference. Hence many rado communcatons systems now use dynamc adaptve modulaton technques. Dynamc modulaton technque sense the channel condtons and adapt the modulaton scheme to obtan the hghest data rate for the prevalng channel condtons. As sgnal to nose rato decrease, errors ncrease thereby ncreasng the number of retransmsson and reduce the throughput. By changng to a e
utlty lower order modulaton scheme the lnk can be made more relable wth fewer data errors and retransmsson. The AMC [] selects approprate MCS accordng to the change of channel condton n order to maxmze the effectve modulaton and effcency. The nodes teratvely decde ts transmsson power level by maxmzng ts utlty functon. The deal AMC s gven by ( ) η eff,amc = max η eff,mc,η eff,mc...η eff,mcn () The nodes teratvely decde ts transmsson power level by maxmzng ts utlty functon. The non cooperatve nature of the game means that, an attempt to maxmze the utlty consumes maxmum power, snce utlty monotoncally ncreases wth power. Ths wll also create excessve nterference, leadng to performance degradaton. The soluton to ths problem s to ntroduce prcng, whch nduces a degree of cooperaton among players, brngs an mprovement n system performance by penalzng the selfsh nodes and enables the nodes to communcate wth a relatvely low and stable transmsson power. Prcng accounts for the energy consumed / draned by the sensor node wth usage of resources. If the strategy of the th node s to transmt at sgnal power s S the prcng ncurred s a functon of s. The class of prcng functons consdered s lnear and s a monotoncally ncreasng functon of transmt power. The prcng functon s gven by, where z s the prcng constant. The utlty wth prcng s gven by m K = zhs () c u (s,γ )= u (s,γ )- K () Power Control Game based on nergy Consder node s transmttng data to the snk node. Node broadcasts the data to the cooperatve nodes. The cooperatve nodes then communcate the data to the destnaton. The non-cooperatve game s an teratve procedure, where at each teraton, the players select the strategy that maxmzes ther utlty functon. In other words, a system adapts the most approprate MCS accordng to the state of channel condton. Ths utlty functon s very mportant n non-cooperatve power control game. The frst step n the game s to determne the threshold SINR. The SINR target requrement s determned based on the modulaton type when employng an adaptve modulaton scheme. ach node selects modulaton type m M accordng to the change of SINR n order to maxmze the power effcency and network lfetme []. The pseudocode of the procedure explaned s gven n the algorthm mentoned below. Algorthm Requre: S = {s, s,..,s max } M={, QAM, QAM, QAM Select the cooperatve nodes for communcaton Determne threshold SINR for k= to N ter do Perform resdual energy check Compute current SINR based on resdual energy usng eqn (). f current SINR Threshold SINR Select approprate AMC end f stmate the transmt power from eqn. () or () Transmt wth optmal power end for IV. SIMULATION RSULTS AND DISCUSSION MATLAB acts as a smulaton platform n ths work. In the area of m m, random spread of sensor nodes wth maxmum energy of J s consdered. The smulaton parameters consdered are gven n Table I. TABL I: SIMULATION PARAMTRS Smulaton Parameters Descrpton Network area m Transmt power {s mn:s max} :mw Channel Bandwdth MHz Nose spectral densty - Path loss component Modulaton technques, -QAM, -QAM, -QAM Code rates /, /,/, /, /, /, / Number of transmt and receve antennas -QAM -QAM -QAM xmimo,, Fg.. Utlty of the game usng transmt and receve antennas for a codng effcency of /. The modulaton and codng scheme wth hgher utlty needs a hgher SINR to operate. Fg. shows the utlty of the game wth energy check for codng effcency of /. AMC works by measurng and feedng back the channel SINR to the transmttng node, whch then chooses a sutable MCS from the strategy set to maxmze the utlty. modulaton s adapted durng worse channel condtons. It s manfested from fgure that, for MIMO confguraton the game wthout prcng provdes an utlty of. bts/s, for a SINR of db and codng effcency of /. Hgher order modulatons
utlty utlty utlty utlty utlty wth hgher codng rates are adapted when the channel condton mproves. If the current SINR s greater than db and less than db -QAM s adapted. It s obvous from the fgure that at a SINR of db, the game provdes an utlty of.bts/sec whereas at a SINR of db, the game wthout prcng gves an utlty of. bts/s. Consderng -QAM, t s apparent that at a SINR of db and a codng effcency of /, game wthout prcng provdes a utlty of.bts/s. -QAM -QAM -QAM xmimo -QAM -QAM -QAM xmimo Fg.. Utlty of the game wth prcng usng transmt and receve antennas for a codng effcency of /. Fg.. Utlty of the game usng transmt and receve antennas for a codng effcency of /. From Fg. t s evdent that, for MIMO confguraton the game wthout prcng provdes an ncrease n utlty by %, for a SINR of db and codng effcency of /. It s further observable from the fgure that at a SINR of db, the game provdes an utlty of.bts/sec whereas at a SINR of db, the game wthout prcng gves an utlty of. bts/s. Consderng -QAM, t s apparent that at a SINR of db and a codng effcency of /, game wthout prcng provdes a utlty of.bts/s. -QAM -QAM -QAM xmimo Fg.. Utlty of the game usng transmt and receve antennas for a codng effcency of /. Fg. gves the utlty of the game takng nto account transmt and receve antennas. From ths fgure t s observed that, for MIMO confguraton the game wthout prcng provdes an ncrease n utlty by % compared to x MIMO scheme, for a SINR of db and codng effcency of /. An ncrease n utlty by % and % s obtaned for -QAM and -QAM respectvely. On adaptng -QAM, t s notceable that at a SINR of db and a codng effcency of /, game wthout prcng provdes a utlty of.bts/s. -QAM -QAM -QAM xmimo Fg.. Utlty of the game wth prcng usng transmt and receve antennas for a codng effcency of / -QAM -QAM -QAM xmimo Fg.. Utlty of the game wth prcng usng transmt and receve antennas for a codng effcency of / Fgs. - gve the utlty of the game wth prcng for, and MIMO confguraton. Consderng the MIMO scheme the game wth prcng provdes an utlty.bts/sec for a SINR of db thereby provdng % ncrease n utlty. An ncrease n utlty by.% and % s obtaned for the -QAM and -QAM consderng the game wth prcng. -QAM provdes a utlty of. bts/sec. On comparng and MIMO schemes wth prcng an ncrease n utlty by around % s acheved.
V. CONCLUSION An energy effcent adaptve modulaton and codng for power control n VMIMO-WSN usng game theoretc approach takng nto account the resdual energy of the nodes has been analysed. The game s desgned such that, approprate modulaton and codng s selected based on the current channel condton. The utlty of nodes resdual energy check for, and MIMO schemes are compared. The maxmum utlty s obtaned as the order of dversty ncreases. Wth the ncluson of prcng the nterference among the nodes due to the optmzng behavour of a partcular node s suppressed. Further the outcome shows that employng hgher order MIMO confguraton wth prcng acheves the best response for the sensor nodes. [] D. Goodman and N. Mandayam, Power control for wreless data, I Personal Communcaton Magazne, vol., no., pp. -, Apr.. [] P. Gao, D.-X. Meng, N. Cheng, S.-C. Lang, and G.-F. Tu, Non-cooperatve power control game for adaptve modulaton and codng, The Journal of Chna Unverstes of Posts and Telecommuncatons, vol., no., pp. -, June. [] V. Tarokh, H. Jafarkhan, and A. R. Calderbank, Space-tme block codes from orthogonal desgns, I Transactons on Informaton Theory, vol., no., pp. -,. [] S. Sengupta, M. Chatterjee, and K. A. Kwat, A Game theoretc framework for power control n wreless sensor networks, I Transactons on Computers, vol., no., pp. -, February. [] R.Vall and P. Dananjayan, nergy effcent adaptve modulaton for power control n WSN usng game theoretc approach, n Proc. Internatonal Conference on Informaton and Communcaton Technolgy, Chenna, th Decemebr, pp. -. RFRNCS [] F. Akyldz, W. Su, Y. Sankarasubramanam, and. Cayrc, A survey on sensor networks, I Communcatons Magazne, vol., no., pp.-, August. [] D. Lymberopoulos, A. Lndsey, and Savvdes, Characterzaton of the rado sgnal strengh varablty n -D I.. networks usng monopole antennas, n Proc. Thrd uropean Workshop on Wreless Sensor Network, Zurch,, pp. -. [] S. Chouhan, R. Bose, and M. Balakrshnan, A framework for energy consumpton based desgn space exploraton for wreless sensor nodes, I Transacton on Computer-Aded Desgn of Integrated Crcuts and Systems, vol., no., pp. -, July. [] S. Cu, Andrea. J. Goldsmth, and A. Baha, nergy effcency of MIMO and cooperatve MIMO technques n sensor networks, I Journal on Selected Areas n Communcatons, vol., no., pp.-, August. [] A. J. Goldsmth and S.-G. Chua, Adaptve coded modulaton for fadng channels, I Transactons on Communcatons, vol., no., pp. -, May. [] D. Fudenberg and J. Trole, Game theory, MIT Press, Cambrdge, MA,. [] C. U. Saraydar, N. B. Mandayam, and D. J. Goodman, ffcent power control va prcng n wreless data networks, I Transactons on Communcaton, vol., no., pp. -, August. [] M. Hayajneh and C. T. Abdallah, Dstrbuted jont rate and power control game-theoretc algorthms for wreless data, I Communcaton Letter, vol., no., pp., August. [] A. B. MacKenze and S. B. Wcker, Game theory n communcatons: Motvaton, explanaton, and applcaton to power control, n Proc. I Global Telecommuncatons Conference, San Antono, TX, USA, November, pp.. R. Vall receved B. degree n electroncs and communcaton engneerng from Madras Unversty, Chennan and M. Tech degree n and Ph.D. n from Pondcherry Unversty. She has ffteen years teachng experence. She s currently workng as an assocate professor n the Department of Informaton Technology at Adhparasakth ngneerng College,Melmaruvathur, Inda. She has publshed several papers n Internatonal Journals and Internatonal Conferences. She has vsted Malaysa to present a paper n an Internatonal Conference. Her research nterests nclude computer networks, wreless ad hoc and sensor networks. P. Dananjayan receved Bachelor of scence from Unversty of Madras n, Bachelor of Technology n and Master of ngneerng n from the Madras Insttute of Technology, Chenna and Ph.D. degree from Anna Unversty, Chennan. He s workng as professor n the Department of lectroncs and Communcaton ngneerng, Pondcherry ngneerng College, Pondcherry, Inda. He has been as vstng professor to AIT, Bangkok. He has more than publcatons n Natonal and Internatonal Journals. He has presented more than papers n Natonal and Internatonal Conferences. He has guded Ph.D. canddates and s currently gudng Ph.D. students. Hs research nterests nclude spread spectrum technques, wreless communcaton, wreless adhoc and sensor networks.