Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 CHANNEL ESTMATON USNG EXTENDED KALMAN FLTE WTH SLCED MULT MODULUS BLND EQUALZATON ALGOTHM (SMMA) SANJAY KUMA KVS, D. B. L. MALLESWA Jawahara Nehru Technoogica University, Hyderabad, Eectronics and Teecommunication Engineering Jawahara Nehru Technoogica University, Hyderabad, Eectronics and Communication E-mai: sanjayphd05@gmai.com, bmaeswari@gmai.com ABSTACT Mutipe-nput Mutipe-Output (MMO) systems use mutipe number of antennas on the both sides of transmission and reception to achieve high spectra efficiency. Channe impuse responses are reguary thought to be steady over a bock or packet. These bocks are assumed ike stationary on channes. Though, for communications in a high mobiity and fading channe, the assumption wi cut down the system performance. Here we concentrate on channe estimation for a MMO system with Orthogona Frequency Division Mutipexing (OFDM) transmission technique. The system, estimates the channe matrix at the receiver with Extended Kaman Fiter (EKF). After the estimation, we empoy ow cost OFDM-MMO soft data detector. The soft outputs of soft data detection are fed back to siced muti-moduus agorithm (SMMA) for an improved channe estimation. terativey using EKF and SMMA overa performance has been achieved. Convergence characteristics of EKF-SMMA is simuated using MATLAB and it is shown that it gives better steady-state performance with regard to inter-symbo interference (S) & Bit-error rate. t additionay demonstrates that the researched cacuation shows reduced steady-state misadjustment contrasted with the best reported muti-moduus agorithm (MMA). Keywords: Mutipe-nput Mutipe-Output, Orthogona Frequency Division Mutipexing, Constant Moduus Agorithm, Muti-Moduus Agorithm, Siced Muti-Moduus Agorithm, Extended Kaman Fiters.. NTODUCTON A MMO transmission channe have a arge number of antennas at the transmitter & the receiver end. Utiizing advanced moduation at the transmit antenna & receive antenna for signa processing, MMO channe provides ower deays, greater data rates to mutipath fading (dupicatio, & aso provide support for a number of users ike mobie & broadband communication frameworks contrasted with conventiona frameworks [], [], [3]. Channe estimation is an essentia thing of a receiver as channe response is not change in a particuar time period. Furthermore, space-time coding technique is frequenty empoyed in MMO systems to essen channe fading without giving up bandwidth & getting to be attractive in broadband wireess systems. A system that joins MMO, space-time coding & OFDM can give spectra efficiency & higher data transmission over a fading channe [4], [5]. Basicay, Channe State nformation (CS) makes it at ease to achieve the benefits of MMO technoogy whie reducing the compexity effect incurred through MMO transmission & reception. So, channe estimation remains a significant part in the signa processing stages at the receiver of both the present & the essentia wireess communication systems [6]. S occurs in MMO-OFDM system because of bandwidth imited channes or mutipath propagation. To reduce impact of S, Channe equaization is one amongst the procedures. Adaptive agorithms are utiized to initiaize & reguate equaizer coefficients for unknown channe. Usuay, a primary setting of equaizer weights is accompished through a training sequence before data transmission [7]. Then again, it is essentia to equaize a channe without the support of a piot sequence. t is unfeasibe to transmit a reference piot signa sequence at the time of transmission of signa. This technique, known as bind equaization. This agorithm matches inverse impuse response with regard to the communication medium. So, opening the eye of the communication framework & permitting for a 8
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 correct retrieva of transmitted symbos [8], [9]. Moduus agorithm famiy is presented to enhance S in bind channe. Moduus Agorithm has some important drawbacks in past decades ike poor Signa Error ate (SE) in muti signa & contour variation in coefficients degrades SE & BE. Siced MMA provides improved performance compare with CMA (Constant Moduus Agorithm) & MMA. Because of mutipath symbo interference & power degradation, adaptive fiters are required to fix this probem [0], [], []. Here, SMMA & EKF in MMO channe is modeed & simuated to decrease the mutipath noise & power degradation in the channe. Our objective is to compare the performance of convergence anaysis, error anaysis, & means square with the existing methods CMA, MMA, SMMA & the suggested agorithm EKF-SMMA in ayeigh channe.. LTEATUE EVEW S. Ghazi-Maghrebi et a 03, have discussed about the possibiity to improve OFDM moduation through empoying SMMA equaization. SMMA method was utiized for weight adaptation & to reduce the BE in the OFDM muticarrier moduation. Both anaysis & simuations have demonstrated better performance of SMMA in comparison with east mean square (LMS) & MMA agorithms, in standard channes with additive heat noise & S impairment simutaneousy. t showed that the SMMA equaization was a decent choice for high speed & rea-time appications for instance OFDM based systems. Jenq-Tay Yuan and Tzu-Chao Lin 00, have derived a method for normaized error surface curvatures by utiizing a CMA, MMA, & two bind carrier phase recovery agorithms (CPA) at stationary points by means of arbitrary -D symmetric signa consteations. f any additive noise added in communication channe, then it is not possibe to recover the phase. So, here we are trying to anayze through fiter techniques. G. gnatius et a. 0, have introduced a method for carrying out a powerfu channe estimation for MMO-OFDM frameworks when they experience a fast fading environment. Proposed agorithm modeed the parameters to be assessed utiizing an auto-regressive mode which was executed utiizing Burg Method. The channe estimation has been executed utiizing an EKF. The channe was modeed as L-path parametric ayeigh fat fading. The evauation done based on ayeigh compex ampitudes (CA) & piot frequency offset. 3. POPOSED METHODOLOGY FO CHANNEL ESTMATON n a wireess communication framework, estimation & equaization of the MMO digita communication channes has been of great interest in recent days. Major difficuties are not just to separate these signas, however concurrenty equaize the MMO channe so as to achieve the highest quaity communication. The bind channe equaization technique is one of the effective methods to detach the signas & remove the channe distortion. Equaization method & Bind MMO channe prediction method has gained a ot of interest in mutipe access signa detection, as bind method doesn t gambe on training signas nor require any kind of information of MMO channes & retrieves a the inputs simutaneousy. Current procedures for equaizing the channes do not seect the channe, but directy design an equaizer for the channe. Figure dispays about the bock diagram of bind equaization. Figure : Bock Diagram of Bind Equaization 3. Channe Estimation and Channe Equaization Channe estimation agorithms concede the receiver to estimate channe s impuse response & describe the channe s behavior. To sove the issues of S channe estimation has been empoyed by adaptive channe equaizers. To reduce mean squared error (MSE), maximum ikeihood detectors empoy channe estimates. The channe outcome x (: x ( H( s( + η( = * () 9
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 where η ( is the adaptive noise, H ( is channe matrix, s ( is input signa. Main aim of channe estimation agorithms is to reduce MSE, E[ η ( ] whie using as imited resources as possibe in the evauation process. Major benefits of channe estimation are that it aows coherent demoduation. Coherent demoduation needs the information of the phase of the signa. This can be formuated through utiizing channe estimation methods. Bind equaization is the process of equaizing a channe deprived of training sequence. Bind equaization in digita medium is a fied, which has achieved more interest over the past decades. Main objective of bind equaization is to hep equaizer to match with the impuse reaction of the channe. Efficiency of bind equaization can be cacuated based on convergence rate, Bit Error ate (BE), S & symbo rate. The convergence rate is considered to be most important among other performance methods as it reates to the amount of time that the service woud be interrupted on the network in the course of initiaization, a variation in the features of the channe, or in the event that there is significant interference in the channe being used. SE heps to reate the equaizer s capabiity to produce upon convergence. Therefore, adaptive equaizer must deiver the optima convergencetime without compromising the SE. At bind channe reception an amount of interference is cacuated and it wi reduce with the hep of extended Kaman adaptive fiters. These kind of fiters does not manipuate any previous information regarding channe state, & it can ony be appied in time invariant channe. The channe state mathematica statement is made grounded on the information symbo & driving noise. For unknown channe, the state mode required to improve the unknown parameters by adding information symbo & the channe state. The EKF method appies to the joint estimation of a subcarriers & additionay works in the persubcarrier fashion with a much reduced compexity. Additionay, in the channe estimation, the EKF coud directy give symbo detection. Channe matrix is estimated from equation (). Where P[ n, denotes the piot symbos which is another form of s [ n, as equation () shows. H[ n, = P [ n, X[ n, () Thus, channe state information h[ can be achieved by appying an inverse fast Fourier transform (FFT) to the transfer function H [ n,. h [ = h [ + z [ (3) Here z [ is a compex Gaussian vector whose distribution is N(0, σ z ). The Kaman fiter expoits the state space mode in time/deay domain as shows in equation 4: h [ n + ] = Fh [ + ω [ (4) Here F is M M matrix, M = N T N and ω [ is the M innovation noise vector. f F, σ z, σ are ω known parameters, the estimated channe state parameter h [ can be obtained by expoiting Kaman fitering from the equation (3) and (4). But it is impossibe to discover the significant parameter in advance, so estimated Kaman fitering has been utiized to estimate channe parameters. nnovations noise variance & the channe noise variance is essentia for EKF fitering. But the innovations noise variance cannot be estimated directy due to ω [ not being observed. So we construct an equation (5) to estimate ω [. ω [ = h[ n F[ n h[ n n ] (5) Here in, since h [ n and F [ n can be obtained from the equations mentioned above, we can obtain the innovations noise variance σ ω[ which can be expressed as: L n σ [ = ω [ m] (6) ω LnM = 0 m= The measurement noise variance aso cannot be observed, but estimated. We attain it as beow. z [ = h[ h[ n n ] (7) Here, 30
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 h [ n n ] = F[ n n ] h[ n n ] So the measurement noise variance can be expressed as: L n σ (8) z [ = LnM = 0 m = z [ m] Because h[ can be drawn, we can obtain channe transfer functions in time/frequency domain by FFT as L jk / K H [ n, = h[ e (9) NT = 0 After the estimation of channe matrixh (, MMA is introduced to optimize estimation error ( e MMA ). SMMA, an agorithm for use to digita transmission has been proposed. n SMMA, cost function integrates dispersion constant & sicer output. Severa desirabe features, comprising of mutipe-moduus, symmetry, & (amost) uniformity fufis by SMMA cost function. The SMMA cost function shows a much ower misadjustment compared to other agorithms, for exampe, CMA & MMA. Here the piot symbo considers as the input signa at the receiver end. So, P has been denoted in terms S. Equation () rewritten as Equation (0). x N ( = H( i) s( n i) +η( i= 0 (0) where H ( i) represents Estimated baseband channe form EKF, N is the ength of the equaizer tap weights, x( is compex received signa, s ( is source signa & η ( is additive white Gaussian noise. Equaizer compex tap weight-vector & input-vector are separatey described as W( = [ w( w( w ( )] T 0,,..., L n, X( = [ x(, x( n ),..., x( n L+ ) ] T where T represents T transpose of vector. a( = W ( X( as the channe equaizer output, resut of the decision bock is presented as s ˆ( which is cacuated as the neighbor consteation symbo to a(. The main purpose is to achieve an estimate of the transmitted sequence s( without empoying training signa avaiabe at the receiver, such that s ˆ( = s( n ), where is the buk due to channe-equaizer combined impuse response. Here the equaizer accuratey evauates the received symbo that was transmitted baud times earier. Muti-moduus agorithm permits concurrent joint bind equaization & carrier phase recovery by eiminating the necessity for an adaptive phase rotator to carry out separate consteation phase recovery. Earier many MMA have been deveoped to recover the misadjustment caused by other agorithms ike CMA. Some of the MMA schemes, especiay for MMO consteations, fix the phase offset error without utiizing any rotator toward the equaizer's end stage. Therefore, MMA gives reiabe convergence & does not require rotator in steady state operation. The MMA penaizes dispersion of rea & imaginary parts, u andu, of u( separatey. The MMA, unike the CMA don t observe cross term u u. Here u is in-phase & u is quadrature components. Subsequenty, MMA cost function is not a -D cost function & it is pseudo twodimensiona because it contains u ( and u ( ony. MMA cost function & its parameter are given by [( u ( ) ) ( ( ) ) ] n γ + u n γ J = E () Where E [ ] denotes the statistica expectation. u (, u ( are rea & the imaginary parts of ( u respectivey. γ is dispersion constant for rea parts & γ is dispersion constant for imaginary parts of a transmitted signa, which presented as foowings 4 [ s ( ] [ s ( ] E γ = () E γ = E E 4 [ s ( ] [ s ( ] (3) Where s ( & s ( are rea & imaginary parts of a transmitted signa s(, respectivey. The corresponding MMA weight tap updating agorithm is W( n+ ) = W( + µ e ( X * MMA ( (4) The error function expressed as e MMA ( can be 3
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 e MMA ( u ( ) + j u( ( u( ) ( = u ( γ γ (5) MMA cost function can be cacuated as the summation of two -dimensiona cost functions, that heps to decrease dispersion of u & u around second contours. So the MMA is suitabe to take advantage of the symbo statistics on specific kinds of signa consteations, for exampe, non-square & very dense consteations. Though CMA provides accurate convergence & is capabe of reducing inter-symbo interference (S) eve to a significanty ow eve, it suffers from phase error when the signa consteations become very arge. Hence, in steadystate operation the compexity increases with the receiver because of the requirement to a rotator at the output of the equaizer. The traditiona MMA aso has some compications with dense consteations. Therefore, SMMA agorithm has been proposed to increase the performance of MMA by decreasing the mismatch vaues. Since the proposed agorithm is devised by integrating the siced symbos in the dispersion constants, it is known as SMMA. The SMMA cost function penaizes dispersion of rea & imaginary parts of u( separatey, which is presented as foowing J S MMA = E c c ( u ( ) ˆ ( ) ) + ( ( ) ˆ( ) ) n a n u n a n γ γ (6) The corresponding SMMA tap updating agorithm is * W ( n + ) = W ( + µ emma ( X ( (7) Where µ a step-size parameter & asterisk is represents compex conjunction. The error e MMA ( function is given by e SMMA c c ( sˆ ( ) ( )) ( )( ˆ n u n + j u n s( u( ) ( = u ( γ γ (8) c [ u ( ] sˆ ( γ. SMMA update mechanism is aware of the dispersion of u( away from the neighbor symbo s ˆ( in some statistica sense. SMMA produce faster convergence & offers the potentia of mutipe tap equaizer impementations. 4. COMPUTE SMULATONS The simuation system appies to a MMO-OFDM system. The subcarrier number is 64, the ength of FFT is 6, and the moduation scheme is OFDM. The computationa difficuty of the LMS method is ower than the EKF method. Though the EKF method is more compex than the LMS method, the EKF method has better performance than LMS one. Hence, the choice of different methods is a trade-off between good performance and ow computationa compexity. Figure and Figure 3, represents the BE vs EbNodB and MSE vs iteration respectivey. As Figure 4 and 5 shows, the EKF-SMMA method has better convergence than existing method. esuts showed that performances of the proposed EKF- SMMA method is better than those of the SMMA, MMA, and the CMA methods at 64 OFDM symbos. Though it has highest computationa difficuty, the EKF method is sti used to estimate channe because of its highest performance. 5. ESULT AND DSCUSSON n this segment, a detaied anaysis of the proposed system has done & makes use of BE curves to prove the vaidity & study the system in a detaied manner. Curves are potted for MMA & SMMA for different cases. The sub-section 5. describes the overa experimenta set-up & the simuation used. n the section 5.. & 5.., a detaied anaysis of the system has been made. 5. Experimenta Set Up & Simuation Where c represents a positive constant (c ). Here we can notice that SMMA update is simiar to the MMA. When c=0, the SMMA reduces to MMA. Since we use equaizer & the sicer output, the SMMA forces u ( and u ( to ie on the point contours. Point contours c is described as sign [ u ( ] sˆ ( γ & sign The proposed channe estimation of MMO-OFDM system based on EKF-SMMA is impemented in MATLAB Version 8..0.604 (03a). The system on which the technique was simuated was having 4 GB AM with 64 bit operating systems having i5 Processor. For assessment of the proposed method, a randomy generated signa has been used. 3
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 The Bit Error occurs when the received bits of the data sequence over a communication medium differs from the transmitted signas. The system considered ayeigh noise channe for BE comparison. Here, we consider ayeigh channe as a communication medium. methods varies between 0-5dB and 0-5dB. This shows that wherever the signa reception fais, EKF-SMMA achieves peak position when compared to existing methods due to the identification of channe matrix through EKF. 5. Effects on The Performance of the Proposed System n this section, the ength of the user input data N has been varied, to assess the performance of the system. The ayeigh channe has been considered in a cases. BE curves for both the MMA & SMMA have been potted. BE Vs Eb_N0_dB, MSE Vs iteration, Convergence Vs iteration. Figure shows the anaysis of BE over EbN0dB of different methods such as CMA, MMA, SMMA and Proposed EKF- SMMA. When we consider the vaue of EbN0dB ranging from 4dB to 38dB it can be inferred that SMMA attains better BE when compared with CMA and MMA. Aternativey, EKF-SMMA achieves better BE even than SMMA ranging from 5dB to 35dB. This is due to the proposed method consist of the EKF in SMMA which predicts the channe matrix (H) instead of utiizing random channe matrix or generated channe matrix which has been used by the previous methods. The BE difference is 0.5 db. Figure 3 dispays that, MSE in CMA is not stabe throughout the iterations but vice versa in the other methods. This shows that, whenever the received strength is ow, MSE is notaby high and whenever the received strength is high, MSE is notaby ow. MSE is mosty ow and even no error can be found after the 5th iteration in terms of EKF-SMMA. Figure : Comparison between BE and Eb No db Figure 3: Comparison between MSE and iteration Figure 4 presents that the convergence deviation is notaby high between EKF-SMMA and the existing methods. We can aso observe that in the initia set of iterations, the best fitness vaues of both EKF-SMMA and MMA are amost simiar but when it is crossed around 5th iteration (approximatey) EKF-SMMA shows a drastic minimization. This expains us that the strength of received signa from EKF is notaby high. Figure 5 expains the convergence error between EKF-SMMA and the existing methods. t can be witnessed that proposed and existing Figure : Convergence Anaysis of MMO-OFDM 33
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 Figure 3: Comparison between Convergence and MSE 6. CONCLUSON We have introduced EKF-SMMA for the bind equaization of OFDM signas that essens a cost function which is composed of equaized and siced symbos. Steady-state mis-adjustment anaysis was done to compare existing and proposed technique. The outcomes of the anaysis and simuations show the benefit of using the proposed BE over the traditiona muti-moduus BE associated with the conventiona SMMA, MMA & CMA. The experiment based on simuation showed that the EKF-SMMA shows a superior efficiency in contrast with the MMA, yieding a better BE, without compromising the convergence rate. EFENCES: [] J. Haifang and S. Yin, An efficient iterative DFT-based channe estimation for MMO- OFDM systems on mutipath channes, Proceedings of Third nternationa Conference on Communications and Networking, China, 008, pp. 45-49. [] N. Daryasafar, A. Lashkari, and B. Ehyaee, Channe estimation in MMO-OFDM systems based on comparative methods by LMS agorithm, JCS nternationa Journa of Computer Science, Vo. 39, No. 0, 0, pp. 777-779. [3] Z. J. Wang, Z. Han, and K. J. Liu, A MMO- OFDM channe estimation approach using time of arrivas, EEE Transactions on Wireess Communications, Vo. 4, No. 3, 005, pp. 07-3. [4]. aissawinda,. G. P. Astawa, Y. Moegiharto, A. Zainudin, and. D. Agusaim, Channe Estimation Design of MMOOFDM systems Using MMSE for EEE 80.n WLAN Standard, European scientific journa, Vo. 0, No. 6, 04, pp. 37-46. [5] M. mani and H. Bakhshi, Training Based Channe Estimation in MMO-OFDM Systems, Communications and Network, Vo. 4, No. 0, 0, pp. 54-60. [6] M. Cicerone, O. Simeone, and U. Spagnoini, Channe estimation for MMO-OFDM systems by moda anaysis/fitering, EEE Transactions on Communications, Vo. 54, No., 006, pp. 06-074. [7] J. Siew,. Piechocki, A. Nix, and S. A. Armour, A Channe estimation method for MMO-OFDM systems, Proceedings of the London Communications Symposium, 00, pp. 0-04. [8] H. Minn and N. A-Dhahir, Optima training signas for MMO OFDM channe estimation, EEE Transactions on Wireess Communications, Vo. 5, No. 5, 006, pp. 58-68. [9] K. P. Bagadi, and S. Das, MMO-OFDM channe estimation using piot carries, nternationa Journa of computer appications, Vo., No. 3, 00, pp. 8-88. [0] J. Du and Y. Li, MMO-OFDM channe estimation based on subspace tracking, Proceedings of the 57th EEE Semiannua on Vehicuar Technoogy Conference, 003, pp. 084-088. [] Md M. ana, Md K. Hosain, Adaptive Channe Estimation Techniques for MMO OFDM Systems, nternationa Journa of Advanced Computer Science and Appications, Vo., No. 6, 00, pp. 34-38. [] S. Kumar and Dr. B. L. Maeswari, Channe Estimation Using Extended Kaman Fiter and Adaptive Maximum Likeihood Estimator in MMO-OFDM System, nternationa Journa of Appied Engineering esearch, Vo. 0, No., 05, pp. 3086-3088. [3] S. Ghazi-Maghrebi, B. H. B. Naeeni, and M. Lotfizad, Achieving Better Performance of SMMA Agorithm in the OFDM Moduation, Journa of nformation Systems & Teecommunication, Vo., No., 03, pp. 9-7. 34
Journa of Theoretica and Appied nformation Technoogy 005-06 JATT & LLS. A rights reserved. SSN: 99-8645 www.jatit.org E-SSN: 87-395 [4] Jenq-Tay Yuan, and Tzu-Chao Lin, Equaization & carrier phase recovery of CMA & MMA in bind adaptive receivers, EEE Transactions on Signa Processing, Vo. 58, No. 6, 0, pp. 306-37. [5] G. gnatius, K. V. U. Murai, N. S. Krishna, P. V. Sachin, and P. Sudheesh, Extended Kaman Fiter based estimation for fast fading MMO channes, Proceedings of nternationa Conference on Devices, Circuits and Systems (CDCS), 0, pp. 466-469. 35