Mathematical Derivation of MIMO Based MANET to Improve the Network Performance

Transcription

1 Journal of Computer Science Original Researc Paper Matematical Derivation of MIMO Based MANET to Improve te Network Performance Swati Cowduri, Pranab Banerjee and Seli Sina Caudury Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata, India Article istory Received: Revised: Accepted: Corresponding Autor: Swati Cowduri Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata, India Abstract: Te proliferations of researc activities in wireless communication stimulated researcers to develop a new tecnology and a tecnique to enable efficient and purposeful application in mobile ad oc network. Tis new tecnique was developed by invention of MIMO tecnology and its tremendous potential in wireless network. Te advantage of MIMO tecnology is it s ig data rate and improved transmission efficiency in ad oc network, wireless communication, IEEE 80.n (Wi- Fi) and IEEE 80.6e (WiMAX) standards. Mobile ad oc network (MANET) as several significant applications in infrastructure-less wireless network. MIMO tecnology as played a key role to improve te transmission efficiency in MANET. Mobile ad oc network (MANET) and Multiple Input Multiple Output (MIMO) communication bot are very emerging in modern wireless communication system. Main focus of tis researc work is to improve te spectral efficiency of te MANET. MANET and MIMO communication are studied separately to analyze te performance of tese networks. Analysis of tis work can furter elp to implement an integrated network or MIMO based mobile ad oc network. And finally analysis te performance of te integrated network (MIMO- MANET) to improve te spectral efficiency. Keyword: Mobile Ad oc Networks, Multi Input Multi Output (MIMO), Cannel Capacity, Diversity, Space Time Block Code, Spatial Multipleing Introduction Ad oc wireless networking is an efficient tecnique to operate in wireless communication system wic can serve anywere and anytime communication by incorporating routing functionalities into a mobile ost. Tis new paradigm of wireless networking is designed by some portable devices to establis infrastructure less network at any time and dismantle at te end. Tis area of communication and computing is very callenging for computer and communication engineering. Tis designing metod wic can represent wireless ad oc network is called MANET (Paulraj et al., 004; Basagni et al., 003; Clamtac et al., 003). A serious problem in MANET is to ave congestion free transmission in large size networks, wic calls for a system wit improved spectral efficiency. Several classical efforts were made to improve te spectral efficiency witout muc impact. Multiple antennas between te nodes to establis a communication links tat can improve te transmission quality of wireless communication systems in a significant level witout using any etra operational frequency bandwidt (Ali et al., 00; Akyildiz et al., 009; Wu et al., 03a). Because of tis quality te Multiple Input Multiple Output (MIMO) is envisaged for te net generation mobile communication systems (Cen, 006; Papadakis, 0). Multi Input and Multi Output (MIMO) tecnology are integrated wit ad oc nodes at te transmitting and receiving ends of te communication system to improve te spectral efficiency (Faki et al., 009; Wu et al., 0a; 03b). Multi Input Multi Output (MIMO) ad oc network systems are te promising tecniques for improving te data rates particularly in frequency selective fading environments. Utilization of MIMO antenna system can improve te cannel capacity (Wu et al., 0b; Sin and Lee, 004; Teltar, 995). In tis study we present a matematical modelling of te MIMO integrated mobile ad oc network and analyze te performance of tis integrated network. Mobile ad oc networks play an important role in military and civilian application. So, to acieve ig cannel capacity for net generation wireless tecnologies MIMO integrated mobile ad oc network is really a promising approac. MIMO ad oc networks 07 Swati Cowduri, Pranab Banerjee and Seli Sina Caudury. Tis open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license.

2 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. present an interesting and important role in future application and epected to be implemented in modern communication system because of its iger spectral efficiency, iger transmission rate and increasing information efficiency. Te performance analysis of tese networks needs to be addressed properly and become an important area on researc nowadays. Te nodes of MIMO ad oc networks are cooperative in nature and communicate to eac oter troug multipat routing and multiop communication rely on implicit trust among temselves. Te lack of fied infrastructure and central concentration (base station) make it difficult to apply te different control mecanisms tat are used in mobile communication. Design of efficient and reliable cannel mecanism and quality of service provisioning is a callenging issue to improve te spectral efficiency of te integrated network. Te paper as been organized as follows. In section, MIMO integrated mobile ad oc network model is described. Arcitectural model for a single node is also described to design te node wit MIMO cannel. Section 3 introduces diversity and multipleing tecnique for te designing aspect of te network. Te cannel capacity or performance of te MIMO integrated network cannel is analyzed in section 4. Simulated result and discussion is given in section 5 followed by a conclusion in section 6. MIMO Ad oc Network Model Te cannel model of MIMO integrated mobile ad oc network is sown in Fig. considering all te ad oc nodes consist of N T number of transmitting and N R number of receiving antennas. Ten te input-output relation of te network can be written as: Y =. X + W () Were: y y Y = and X =.. yn R NT and te element is a N T N R matri tat ave a comple Gaussian distribution. W is te additive wite Gaussian noise vector wit zero mean and C w is covariance matri covariance. Te block diagram of a MIMO integrated mobile ad oc node is sown in Fig.. In Fig. all te ad oc nodes in te network consist of multiple inputs multiple output antenna system. Signal transmitted from transmitted nodes reaces to te receiving nodes by MIMO cannel. Tere are two aspect of designing of MIMO ad oc network one is to improve te reliability of te system to transmit same data across te different propagation (spatial) pats. Tis is called spatial diversity or simply diversity. And second one is to improve te data rate of te network by placing various parts of te transmitting data on different propagation pats (spatial-multipleing). Spatial diversity and spatial multipleing sceme is used to improve reliability and transmission rate of multipleantenna cannels. Multipleing and diversity tecnique of MIMO cannel is sown in Fig. 3. Te first part of above figure describe ow to provide te replicas of te transmitted signal at te receiver consuming minimum power, bandwidt, decoding compleity and oter resources. And te second part of te figure is sows ow te replica of te transmitted signal is sent to te receiver wit minimum probability of error. Te main objective is to send two or more copies of te signal troug independent fades. Errorcorrecting codes are used ere to reduce te amount of redundancy (Wang and Giannakis, 004; Kettani and Zaarov, 00; Blum, 003). Te transmitted signal from mobile ad oc networks propagate troug multiple pats and arrive at te receiver from different directions wit different propagation delays in eac node, due to use of multiple antennas. Te signal received by any receiving node consists of multiple numbers of signals aving randomly distributed amplitude, pase and angle of arrival. As a result te signal received by te receiving node is distorted or faded. To mitigate fading effect of te signal different diversity tecniques are used. To obtain diversity, te signal is transmitted troug multiple (ideally) independent fading pats e.g., in time, frequency or space and combined constructively at te receiver. Multiple-Input-Multiple-Output (MIMO) system accomplises spatial diversity by aving several transmitting and receiving antennas. Diversity is a bandwidt efficient metod to mitigate te fading effect (Wam and Dubey, 000; Merzakreeva et al., 0; Riawi and Louet, 007). Tis tecnique uses multiple cannels to improve te signal to noise ratio in te presence of fading. Not only using multiple antennas diversity can also be acieved by coding te signal over bot space and time (or frequency). STBC and are te tecnique tat combines coding, modulation and signal processing to acieve transmission diversity. STBC sceme supports linear decoding compleity for Maimum Likeliood (ML) decoding. STBC is used for two transmitting antenna were as Ortogonal Space Time Block Code (O-STBC) is a generalized form of arbitrary number of transmitting antennas. It maintains te equity of linear Maimum Likeliood decoding wit full transmission diversity. O-STBC, QO-STBC (Quasi Ortogonal Space time Block Code) acieve full transmission diversity due to low decoding compleity and iger code rate.

3 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. Fig.. MIMO ad oc network model Fig.. Block Diagram of MIMO based Mobile ad oc node Fig. 3. MIMO wit diversity and multipleing

4 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. Space Time Block Code (STBC) Diversity STBC diversity tecnique for MIMO antenna system is consider in Fig. 4. Space time diversity is done period of time and te decoding will be - period of time: y n ' = = ' + y n Y () were, ij is te pat gain between te j t transmit antenna and i t receive antenna. If te symbols y and y from above set of equations are comple conjugated ten: y = + + n y = + + n * y = + + n y = + + n * (8) Te above equation is for first time period. Second time period te equation will be: Y y n * = = * y + n (3) y n y n = + y n * * y n (9) Y and Y represents received OFDM symbol at first and second time period. Bot te equation can be easily combined and arranged to produce result: Wic can be rewritten as: y = ef + n (9i) y n y n Y = = + y n y n (4) At te receiver, Maimal Ratio Combining wit Maimal Likeliood decoder tecnique is used: ~ = y (0) ef We can isolate and by simply multiplying te matri Y by inverse of. Since tis matri is not square, we need to use te Moore-Penrose inverse + to solve our equation: y ~ y = ~ * y * y () ( ) + = (5) y _ y ( ) * = y * y (6) To improve reliability of MIMO cannel Space time block coding sceme is implemented. A simplest transmit diversity tecnique (*) is Alamouti STBC coding wic is sown in Fig. 5. For two receive antennas, te received symbols are: Finally, Maimum-Likeliood (ML) decoder received te combined symbols and estimates te transmitted symbols. If in te transmission pat is severely faded te ML decoder recovers te transmitted symbols troug oter propagation pats. Alamouti code is used only for two antennas. For multiple transmit and receive antennas STBC ortogonal transmission matrices can be constructed based on urwitz-radon (R) teory. Ortogonal designs of antennas as on: Ortogonal designs of 4 4 antennas as on: () y = + + n y = + + n y = + + n y = + + n (7) (3)

5 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. Fig. 4. STBC for MIMO system Fig. 5. MIMO system wit Alamouti coding and ML decoding Ortogonal designs of 8 8 antennas as on: (4) Te code can be noted as in tis sceme C(n, k, T), were m is number of transmitting antennas, k symbols and T is time slot. Te code rate is represented as k T. Te transmission matri of four numbers of transmit antennas for / rate code C(4,4,8) is represented as: (5) And for 3/4 rate code C(4,3,4) represented as: (6) In tis way, transmission matri of ½ and ¾ rate code for 4,8,6, numbers of transmit antenna can be generated. To obtain te codes for oter number of transmit antennas like 3,5,6,7,. One or more numbers of column can be eliminated from te transmission matri of previous codes, keeping te column ortogonality remain same. In tis way te transmission matri of any sets of antennas is generated and te after tat te codeword are modulated by different modulation tecnique. OFDM is a modulation as well as multipleing sceme. To improve transmission rate multipleing is necessary in designing of MIMO cannel. Te transmitted signal is divided into some narrow bands sub stream and modulated by PSK, QAM (for eample). A comparative study is done for 6-PSk, 3-PSK and 6- QAM, 3-QAM modulation to estimate Bit Error Rate (BER) sown in Fig. 6a and 6b.

6 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. (a) (b) Fig. 6. (a) SER vs SNR curve using (b) SER Vs SNR curve using PSK modulation QAM modulation Fig. 7. BER Vs SNR at different coding tecnique It is found tat BER can be minimized by using iger order modulation tecnique. Furter reducing of BER in significance level Trellis Coded Modulation (TCM) combines wit STBC wic is sown in simulated result (Fig. 7). After Modulation, Multipleing (MIMO-OFDM) is done. Transmitted data rate can be improved after te implementing multipleing. Te main objective up to tis work is to minimize te BER or increase te signal rate. If te transmitted signal rate is increased ten cannel capacity of te cannel will automatically increase, wic effect te improvement of spectral efficiency of te network. Signal generated from STBC encoder is modulated and ten modulated data transmit via MIMO cannel. Capacity Analysis Capacity of te cannel is represented by maimum mutual information. Te mutual information I(X; Y) is te amount of uncertainty of difference between te entropies of te cannel input and output, were X and Y transmitted and receiving signal tus: ( ) ( ) ( ) ( ) I( X, Y ) = X X Y Y Y = X (7) Were: NR NT y j ( Y / X ) = P( i, y j ) log P (8) j = i= i

7 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. And: n ( ) ( j ) log ( j ) Y = P y P y (9) j= Mean square value of X is S and noise is N, ten: Y S N = + (0) I(X,Y) is maimum wen (Y) is maimum: ma Y log e S N ( ) = π ( + ) () Real valued random vector X consists of N i.i.d, Gaussian random variable. Covariance matri: X = {( µ )( µ ) T } () C E X X were, µ = 0: Under te condition X is known.x is a constant mean. ence te conditional entropy: ( Y ) = (. + W ) = ( ) X W X X = ( Y ) N.log ( π e) + log det ( Cw ) Capacity of te cannel per vector transmission is: C = Ima X, Y =.log log det N e + C.log ( ) log det ( ) N π e + Cw log det (. = Cy Cw ) log det (.. T = C Cw ) C w + log det (.. T = I N C Cw ) + γ log det. = I + N ( ) ( π ) ( y ) (5) (6) X N e C X ( ) = log ( π ) + log det ( ) (3) CN T, N = log R det eye NT, NT + SNR * * ( ( ) ) (7) Te mutual information of te cannel wit Rayleig fading environment is sown below: (, ) ( ) ( Y ) ( ) (. W ) I X Y = Y Y X X = + X (4) Putting te value of Y from equation (): γ were, CC w = ; γ is signal to noise ratio. N R Simulated Result and Discussion Cannel capacity of te MIMO system wit different sets of antennas can be evaluated sown in Fig. 8. Fig. 8. Cannel capacity at different sets of antennas

8 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. Fig. 9. Number of antennas Vs spectral efficient at different SINR If we increase te number of antennas it is observed tat te cannel capacity is increases. MIMO cannel capacity can be obtained by spatial multipleing of transmitted data and space time coding at te transmitter. Finally te spectral efficiency of te network is sown in Fig. 9 by varying te number of antennas. It is concluded tat spectral efficiency cannot be increases indefinitely by increasing te number of antennas. Spectral efficiency is optimized by te number of antennas for a fied SNR. Conclusion Design of efficient and reliable cannel mecanism and quality of service provisioning is a callenging issue to improve te spectral efficiency of tis network. Te main aspects of designing a MIMO cannel are diversity and multipleing tecnique. Space Time Block Code (STBC) diversity sceme wit Trellis Coded Modulation (TCM) and MIMO-OFDM multipleing scemes is implemented to minimize Bit Error Rate (BER). Minimize BER can improve te signal transmission wic affect te improvement of cannel capacity of te cannel. Improvement of cannel capacity can improve te spectral efficiency of te integrated network. But te spectral efficiency of te network can t be increases indefinitely. Optimization of spectral efficiency is done for different number of antennas. Acknowledgement We tank OD, ETCE Dept of Jadavpur University and Principal, Tecno India Batanagar to continue and complete tis researc work. Autor s Contributions Swati Cowduri: Done all te researc work (simulation results) and contributed to te writing of te manuscript. Pranab Banerjee: Contribute te idea of te researc work. Seli Sina Caudury: Organized te researc work and ceck language of te manuscript. Etics Tere is no conflicts of interest regarding te publication Matematical Derivation of MIMO Based MANET to Improve te Network Performance. References Akyildiz, I.F., Z. Sun and M.C. Vuran, 009. Signal propagation tecniques for wireless underground communication networks. Pys. Commun. (Elsevier) J., : Ali, S., K. Al-Omari and P. Sumari, 00. An overview of Mobile Ad oc Networks for te Eisting Protocols and Applications. J. Applic. Grap Teory Wireless Ad oc Networks Sensor Networks, : Basagni, S., M. Conti, S. Giordano and I. Stojmenovic, 003. Ad oc Networking. st Edn., IEEE Press Wiley, New York. Blum, R.S., 003. MIMO capacity wit interference. IEEE J. Selected Area Commun., : Cen, B., 006. MIMO Communication in ad oc networks. IEEE Trans. Signal Proc., 54: Clamtac, I., M. Conti and J.J.N. Liu, 003. Mobile ad oc networking: Imperatives and callenges. Ad oc Networks, : 3-64.

9 Swati Cowduri et al. / Journal of Computer Science 07, ( ):. DOI: /jcssp.07.. Faki, K., J.F. Diouris and G. Andrieu, 009. Transmission strategy of MIMO mobile ad oc network. EURASIP J. Wireless Commun. Networking. DOI: 0.55/009/8098, Kettani,. and V. Zaarov, 00. MIMO ad oc network performance in te presence of co-cannel interference. Proceedings of te International Conference on Computer Researc and Development, (CRD 0), pp: Merzakreeva, A., O. Leveque and A. Oezguer, 0. ierarcical beamforming for large one-dimensional wireless networks. Proceedings of te IEEE International Symposium on Information Teory, Jul. -6, Cambridge, MA. Papadakis, G.I., 0. Performance consideration of MIMO-based ad-oc network. Proceedings of te Military Communication Conference, 7-0 Nov, pp: DOI: 0.09/MILCOM Paulraj, A.J., D.A. Gore, R.U. Nabar and. Bolcskei, 004. An overview of MIMO communication a key to gigabit wireless. Proc. IEEE, 9: DOI: 0.09/JPROC Riawi, B. and Y. Louet, 007. Gaussian and flat fading cannel influences on PAPR distribution in MIMO OFDM systems. Proceedings of te European Wireless Conference, (EWC 07), Paris, pp: -5. Sin,. and J.. Lee, 004. On te capacity of MIMO wireless cannels. IEICE Trans. Commun., E87-B: Teltar, E., 995. Capacity of multi antenna Gaussian cannels. Eur. Trans. Telecommun., 0: Wam, L. and V. Dubey, 000. Bit error probability of OFDM system over frequency selective fast Rayleig fading cannels. IEEE Electronics Lett., 36: Wang, Z. and G.B. Giannakis, 004. Outage mutual information of space-time MIMO cannels. IEEE Trans. Inform. Teory, 50: Wu, Y., R..Y. Louie, M.R. McKay and I.B. Collings, 0a. Generalized Framework for te Analysis of Linear MIMO Transmission Scemes in Decentralized Wireless Ad oc Networks. Accepted IEEE Trans. Wireless Commun.,: Wu, Y., R..Y. Louie and M.R. McKay, 0b. Impact of training on te transmission capacity of wireless ad oc networks. Proceedings of te IEEE International Conference on Acoustics, Speec and Signal Processing, Mar. 5-30, IEEE Xplore Press, Kyoto, pp: DOI: 0.09/ICASSP Wu, Y., R..Y. Louie and M.R. McKay, 03a. Analysis and design of wireless ad oc networks wit cannel estimation errors. IEEE Trans. Signal Processing, 6: Wu, Y., R..Y. Louie and M.R. McKay, 03b. Impact of training on multiple-antenna communications in wireless ad oc networks. Proceedings of te Asilomar Conference on Signals, Systems and Computers, Nov. 3-6, IEEE Xplore Press, Pacific Grove, pp: DOI: 0.09/ACSSC