PILOT DESIGN FOR SPARSE CHANNEL ESTIMATION IN OFDM

LMMSE CHANNEL ESTIMATION FOR BLOCK PILOT INSERTION IN OFDM SYSTEMS UNDER TIME VARYING CONDITIONS11Need for channel estimationIn all communication the signal goes through a medium (called channel) and the signal gets distorted or various noises are added to the signal while the signal goes through the channel. To properly decode the received signal without much errors we have to remove the distortion and noise applied by the channel from the received signal. To do this, we have to figure out the characteristics of the channel that the signal has gone through. The technique to characterize the channel is called 'channel estimation'.2PROBLEMS FACEDDue to inefficient channel estimation, signal transmission face losses.Inefficient channel estimation leads to non inclusion of significant parameters of channel that affects the signal.High Bit Error Rate and low Signal to Noise Ratio at receiver. 3SOLUTIONWe require an efficient channel estimator.This paper proposes 2 channel estimators: LMMSE and Lr-LMMSE with later having slightly better performance than former.

4INTRODUCTIONChannel estimation methods based on the pilot insertion can be divided into two classical pilot models: 1] Block-type and 2] Comb-type model. The first model refers to that the pilots are inserted into all the subcarriers of one OFDM symbol with a certain period. For comb type, part of the sub-carriers are always reserved as pilot for each symbol.

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Fig. 1. (a) Block-type arrangement. (b) Comb-type arrangement.OFDM (Orthogonal Frequency Division Multiplexing) system suffers from the time variation of the channel under high mobility conditions.Here we look into the performance of the channel estimation using LS, LMMSE and Lr-LMMSE estimators in OFDM.These channel estimations give a simple and low-complexity approach for the estimation of time varying OFDM channels.6SYSTEM MODELThe system model based on pilot channel estimation is depicted in Figure.

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TRANSMITTER SIDE:The binary information is mapped. Pilots are inserted to all sub-carriers uniformly.From the IDFT block is used for transforming the data sequence of length N{X(k)} into time domain signal {x(n)} as follow:

(1) where N is the DFT length. The guard interval is inserted to avoid inter-symbol interference.8

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RECEIVER SIDE:At the receiver, after passing to discrete domain through S/P block, guard time is removed. Then y(n) is driven to the DFT block and given by:

(4)The relation between the resulting Y(k) to H(k) = DFT{h(n)}, is given by:(5) where I(k) denotes the inter-carrier interference and W(k) = DFT{w(n)}.10

After passing through the DFT block, the pilot signals are extracted and cross the channel estimation block. The estimated channel H(k) for the data sub-channel is obtained and the transmitted data is estimated by:

(6)Finally, the binary information data is restored back in the signal de-mapper block.11

CHANNEL ESTIMATION SCHEMEModel: Block - type pilot insertionEstimation schemes: LMMSE, Lr-LMMSE estimatorsAssumptions: 1] Inter symbol interference is dropped by guard interval, then we can write Y(k) as :(7) Where Y:received vector, X: matrix containing transmitted signalling points on its diagonal, h: channel attenuation vector, n: vector of zero mean, Gaussian noise with variance .2] Received OFDM symbol contains data known to the estimator - either training data or receiver decisions.

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LMMSE Estimator

The LMMSE estimate of the channel attenuations h, in (7), from the received data y and the transmitted symbols X is:(8) where (9) is the least-squares (LS) estimate of h, is the variance of the additive channel noise, and the co-variance matrices are: (10) , (11) , (12) 13

The LMMSE estimator is of considerable complexity: A matrix inversion is needed every time the training data in X changes. We reduce the complexity of this estimator by averaging over the transmitted data i.e., we replace the term in (8) with its expectation .Here where I is the identity matrix. Defining the average signal-to-noise ratio as: (13) We obtain a simplified estimator as: (14) where .Because X is no longer a factor in the matrix calculation, no inversion is needed when the transmitted data in X changes.

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Furthermore, if and SNR are known before hand or are set to fixed nominal values, the matrix needs to be calculated only once. Under these conditions the estimation requires N multiplications per tone. To further reduce the complexity of the estimator, we proceed with low-rank approximations in the next section.

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Optimal Low -rank ApproximationThe optimal rank reduction of the estimator in (14), using the singular value decomposition (SVD), is obtained by exclusion of base vectors corresponding to the smallest singular values . We denote the SVD of the channel correlation matrix

Where U is a matrix checking to have orthonormal columns and designs a diagonal matrix which contains the singular values on its diagonal. This allows the estimator in (14) to be written:

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Where is a diagonal matrix containing the values on its diagonal. The best rank -p approximation of the estimator in (14) then becomes . Where p is the upper left p p corner of .17

SIMULATION RESULTSThe OFDM system parameters used are:

18PARAMETERSSPECIFICATIONSFFT size128, 256, 512, 1024, 2048Number of active carriers256Pilot ratio1/8Guard interval256Guard type Cyclic extensionBandwidth 17.5 KHzSignal constellation16-QAMChannel modelRayleigh Fading

19FIG 1: BER Vs SNR for FFT size= 128 using LS, LMMSE, Lr-LMMSE algorithms with a 16 QAM modulation

FIG 2: BER Vs SNR for FFT size= 256 using LS, LMMSE, Lr-LMMSE algorithms with a 16 QAM modulation

For LS, LMMSE, Lr-LMMSE estimator 20

FIG 3: BER Vs SNR for FFT size= 512 using LS, LMMSE, Lr-LMMSE algorithms with a 16 QAM modulation

FIG 4: BER Vs SNR for FFT size= 1024 using LS, LMMSE, Lr-LMMSE algorithms with a 16 QAM modulation

21FIG 5: BER Vs SNR for FFT size= 2048 using LS,LMMSE, Lr-LMMSE algorithms with a 16 QAM modulationINFERENCES:When the FFT size is inferior or equal to 1024, it is observed that the LMMSE algorithm still performs well in terms of low bit error rate especially when then the SNR is superior to 5 dB.Also by increasing the FFT size, the BER increases.LMMSE algorithm performs well with slowly time varying channel i.e with block pilot insertion.When the FFT size is very high, the LMMSE algorithm cannot estimate the channel completely but just in some values of SNR (less than 15 dB).The three algorithms converge for SNR when it is above 20 dB but the Lr- LMMSE estimator behaves a little better than both LS and LMMSE.CONCLUSIONA simple and low-complexity approach for the estimation of time varying OFDM channels using the three algorithms LS, LMMSE and Lr-LMMSE in the case of block-pilot insertion.The low rank estimator is shown to be a robust estimator to changes in the channel characteristics.

22REFERENCES[1] Aida Z, Ridha B , LMMSE channel estimation for block pilot insertion in OFDM systems under time varying conditions, Mediterranean Microwave Symposium (MMS), Pages:223-228, 2011 [2] J.-C. Lin, Least-squares channel estimation for mobile OFDM communication on time-varying frequency- selective fading channels, IEEE Transactions on Vehicular Technology, vol. 57, no. 6, pp. 35383550, 2008.

[3] O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson, and P. O. Borjesson, OFDM channel estimation by singular value decomposition, IEEE Transactions on Communications, vol. 46, no. 7, pp. 931939, 1998. 2324THANK YOU24