# Performance Comparison of Channel Estimation Technique using Power Delay Profile for MIMO OFDM

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3 International Journal of Electrical and Computing Engineering diagonal elements are leakage powers of for all i. so that the distortion of W can be eliminated as =T = E {.. (6) PDP at the (p,q) th antenna port on the th OFDM symbol estimated using the received sample vector, = T and T ( ) PDP ESTIMATION IN PRACTICAL MIMO- OFDM SYSTEMS: The sample vector received is given as [ ] )+.. (7) [ ] is the sample vector of implemented PDP estimation with l th entry [ { [ ] [ ] (12) [ ] = [ ] and. The implemented technique estimates the average of residual noise at the zero-taps of, to reduce the effect of residual noise. The zeo-tap is detected at the l th entry of as T ( ), and {.. (13) T ( ) assume is an effective noise by AWGN. Then the sample average of received sample vector [ ] is given by [ ] [ ] (8) =, N is the total number of samples for PDP estimation which is given as N PQ. = the number of pilot symbols at the th subcarrier in a time slot. To obtain the accurate PDP N must be sufficiently large. Since and It is difficult to obtain such a large number of samples at the receiver in a practical MIMO OFDM system. With an insufficient number of samples, the PDP can be approximated as. However PDP accuracy with insufficient samples is improved by reducing the effective noise as follows [ ]. (9), is a residual noise vector, which entry has a zero-mean with N samples the error of PDP estimation can be calculated as ( ( ) ) (10) Since,, [ ], (11) is threshold value for detecting zero-tap. At zero-taps the average of residual noise is estimated as (14) is the number of detected zero-taps. The PDP estimate at the l th tap after reducing the residual noise, can be expressed as, {.. (15) The frequency-domain channel correlation in the LMMSE channel estimator is obtained using the estimated PDP in (15). PERFORMANCE ANALYSIS: With imperfect PDP in (15) the LMMSE channel is estimated as. (16) by taking first columns of DFT matrix which is X matrix is obtained. = is expressed as the estimated PDP. The for the l th element is defined as {. (17) From matrix inversion lemma, is converted as A = A -A A. (18) B ( ) A F p ( ). 67

4 Then, the coefficient matrix for LMMSE channel estimation with can be rewritten as (19) length is increasing the MSE also increases the interference get increases. In figure 5, graph shows is the coefficient matrix for wiener filtering, and A A + ( ).. (20) With imperfect PDP the error covariance matrix of LMMSE channel estimation can be obtained as ( ) =( +. (21) Fig 4: Graph plotted between MSE and channel length using implemented MMSE and 1D LS method. [ ] Using the error covariance matrix the frequency domain MSE of the implemented method is = (22) RESULTS AND DISCUSSION: The simulation results obtained in MIMO OFDM system with two transmit and receive antennas. The simulated graph shows the channel estimation by taking different parameters. The simulated graphs show the MSE performance of LMMSE technique using estimated PDP. Fig 5: Graph plotted between MSE and mobile equipment speed using implemented MMSE and 1D LS method. Fig 3: Graph plotted between MSE and SNR using implemented MMSE and 1D LS method. In figure 3 the graph shows the relation between MSE and SNR. As the MSE is decreasing then the SNR is increasing i.e., as the mean square error is reducing the signal level is increasing which leads to increase in SNR ratio. In figure 4, graph plotted between MSE and channel length. As the channel Fig 6: Graph plotted between MSE and number of samples using implemented MMSE and 1D LS method. 68

5 VOL. 59, NO. 1, JANUARY how the MSE varies with the mobile equipment speed. As the mobile is moving fast then it experiences a fast fading in multipath channel which increases the MSE. In figure 6 as the number of samples increases the MSE decreases. CONCLUSION: The simulated graphs show the comparison between the implemented method using LMMSE technique and 1D least square technique. The implemented technique using LMMSE gives less mean square error compared to the 1D least square method. Implemented algorithm holds good, as the number of samples increases also observed from the result. The implemented technique effectively reduces the spectral leakage and residual noise. The performance of LMMSE channel estimation approaches that of wiener filtering using the implemented PDP estimate. [7] J. K. Cavers "An analysis of pilot symbol assisted modulation for Rayleigh fading channels", IEEE Trans. Vehicular Techn., vol. VT-40,Nov [8] J. Choi and Y. Lee, Optimum pilot pattern for channel estimation in OFDM systems, Wireless Communications,IEEE Transactions on, vol. 4, No. 5, September [9] T. Cui and C. Tellambura, Power delay profile and noise variance estimation for OFDM, IEEE Communication. Lett., vol. 10, Jan [10] H. C. Won and G. H. Im, Iterative cyclic prefix reconstruction and channel estimation for a STBC OFDM system, IEEE Commun. Lett.,vol. 9, Apr REFERENCES [1] Kala Praveen Bagadi, Prof. Susmita Das, MIMO-OFDM Channel Estimation using Pilot Carries, International Journal of Computer Applications ( ) Volume 2 No.3, May [2] Young-Jin Kim and Gi-Hong Im, Pilot- Symbol Assisted Power Delay Profile Estimation for MIMO-OFDM Systems IEEE Commun LETTERS, Vol. 16, no. 1, jan [3] H. Taub, D. L. Schilling, G. Saha, Taub sprinciples of Communication Systems. Tata McGraw Hill, [4] s.s Ghorpade, S.V.Sankpal, Behaviour of OFDM system using Matlab simulation, International Journal of Advanced Computer Ressearch Volume-3 No.2, june [5] Qun Yu, Ronglin Li, Research on Pilot Pattern Design of Channel Estimation,Journal of Automation and Control Engineering, Vol. 1, No. 2, June [6] Kun-Chien Hung and David W. Lin, Senior Member, IEEE, Pilot-Based LMMSE Channel Estimation for OFDM Systems With Power Delay Profile Approximation IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, 69

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