Abstract—In OFDM system fine-frequency offset and channel state variation will exist continuously due to main few reasons which are Doppler shift, instability of local oscillators, and multipath fading. Thus, fine-frequency offset and channel state variation must be tracked continuously or periodically. Many algorithms have been proposed algorithms for joint frequency tracking and channel estimation aided with OFDM training blocks. In this paper, we propose a study of performance of the channel estimation using LS, MMSE, LMMSE and Lr-LMMSE algorithms in OFDM (Orthogonal Frequency Division Multiplexing) system which, as known suffers from the time variation of the channel under high mobility conditions, using pilot insertion. Index Terms—Channel estimation, frequency tracking, linear minimum-mean-square-error (LMMSE) combiner, INTRODUCTION: ORTHOGONAL frequency division multiplexing (OFDM) has recently received considerable interest for its advantages in high-bit-rate transmissions over frequency selective fading channels it has become increasingly popular during the last decades, mainly because it provides a substantial reduction in equalization complexity compared to classical modulation techniques. In this system, the input high-rate data stream is divided into many low-rate streams that are transmitted in parallel, thereby increasing the symbol duration and reducing the inter symbol interference (ISI).An efficient and accurate channel estimation procedure is necessary for coherent demodulation in OFDM systems. It is also possible to use differential demodulation in OFDM systems for eliminating the need for estimation of channel statistics, however, it has the expense of a 3–4dB loss in signal-to-noise ratio (SNR). The channel estimation technique can be classified into two categories channel estimation algorithm in time domain Another approach is to estimate channel in frequency domain time domain estimators do not require channel statistics and operation SNR, but they should determine the length of channel impulse response in advance The computational complexity is also high owing to the fact that additional IDFT, DFT blocks are required.

The simplest algorithm in frequency domain is the least square (LS) algorithm, which divides the received signal by the transmitted signal in the frequency domain.Generally, the frequency domain channel estimators have been applied to the OFDM receivers because of its simplicity.we have introduced also the estimation of the channel by the minimum mean squared error which as known has a good performance but high complexity. This estimator had demonstrated also a good behaviour in the case of the block - pilot insertion but still performs lower than the LMMSE algorithm. Though a linear minimum mean-squared error (LMMSE) estimator using only frequency correlation has lower complexity than one using both time and frequency correlation, it still requires a large number of operations. We introduce a low-complexity approximation to a frequency-based LMMSE estimator that uses the theory of optimal rank reduction. There are two different types of channel parameter estimators. i) Blind ii) Pilot-aided

a) Comb type b) Block type

Blind channel estimation techniques try to estimate the channel without any knowledge of the transmitted data. This method is helpful in terms of possible savings in training overhead, however they are effective only when a large amount of data can be collected (so that stochastic estimation can be made reliably). This is clearly a disadvantage in the case of mobile wireless systems because of the time-varying nature of the channel. Pilot-aided channel estimation is the other approach in which training sequence consisting of known data symbols (pilots) is transmitted at the beginning of a session and the initial estimation of the channel parameters is performed using the received pilot signal. It has been shown that the pilot-aided channel estimation is the optimum way to estimate the channel when signal-to-noise ratio (SNR) is sufficiently high. Comb type pilot channel estimation, has been introduced to satisfy the need for equalizing when the channel changes even from one OFDM block to the subsequent one. block type pilot channel estimation, has been developed under the assumption of slow fading channel. Even with decision feedback equalizer, this assumes that the channel transfer function is not changing very rapidly.

Channel estimation of OFDM system using low complexity lmmse algorithm

Shobha Shakya Shekhar Sharma SGSITS Indore(M.P.) SGSITS Indore(M.P.) shobhashakya@gmail.com shekhar.sgsits@gmail.com

A dynamic estimation of channel is necessary before the demodulation of OFDM signals since the radio channel is frequency selective and time-varying for wideband mobile communication systems. The estimation of the channel can be based on Least Square (LS) or Minimum Mean-Square (MMSE). The MMSE estimate has been shown to give 10-15 dB gain in signal-to-noise ratio (SNR) for the same mean square error of channel estimation over LS estimate . here we are using a lowrank approximation to linear MMSE by using the frequency correlation of the channel to eliminate the major drawback of MMSE, which is complexity. a linear minimum mean-squared error (LMMSE) estimator Using optimal rank reduction, they develop a low-complexity algorithm which computes an approximated LMMSE estimator. This approximation is limiting the performance at high signal-to-noise ratios (SNRs).

II SYSTEM DESCRIPTION

The OFDM system based on pilot channel estimation is given in Fig. 1. The binary information is first grouped and mapped according to the modulation for signal mapping. Then pilots will be inserted to all sub-carriers uniformly between the information data sequence or with a specific period. Yet, IDFT block is used for transforming the data sequence of length N{X(k)} into time domain signal {x(n)} as follow: x(n) = IDFT{X (k)} n = 0,1, 2...., N −1

=∑ ���������� � �����

Fig: 1 Baseband OFDM system Following IDFT block, guard time, which is chosen to be Larger than the expected delay spread, is inserted to prevent Inter-symbol interference. This guard time includes the cyclically extended part of OFDM symbol in order to eliminate inter carrier interference (ICI). OFDM symbol resulting from this succession is the follow:

�����=� ��� � ��,� � ���,��� � 1����� � 0,1, ……� � 1 !

Where Ng is the length of the guard interval. Then, the OFDM symbol �"(n) will pass through the channel which is expected to be frequency selective and time varying with Rayleigh fading and an Additive White Gaussian Noise AWGN w(n) . The received signal is given by: #"��� � �"(n) h(n)+w(n)

Wherever h(n) is the channel impulse response which can be represented as follow

$���=∑ $%&��%�� ��'(�� )*+',-�. � /%�

Where r is the total number of propagation paths, hi is the complex impulse response of the ith path, fDi is the ith path Doppler frequency shift, l is the delay spread index, T is the sample period and i t is the ith path delay normalized by the sampling time. at the receiver, after passing to discrete domain through S/P block, guard time is removed and the expression of y(n) is given by #���� For �0 1 � 1 � � 1 Y(n)=#��� � �0� n=0,1,2,.....N-1 Then y(n) is driven to the DFT block and given by: Y (k) = DFT{ y(n)} k = 0,1, 2,..., N -1

1�2 #���

��1

��0��3�

25��� �

If we assume that the guard interval is longer than the length of channe1 impulse response- there is no inter-symbol interferencebetween OFDM symbols- the demultiplexed samples Y (k) can be represented by Y(k)=x(k)h(k)+W(k) k=0,1,.....N-1 After that, the received pilot signals Yp(k) are extracted from Y (k)and so the channel transfer function H(k) the transmitted data samples X(k) can be recovered by simply dividing the received signal by the channel response:

x(k) = #���6′���

H’(k) is the estimate of H(k) CHANNEL ESTIMATION SCHEME: channel estimation symbols are transmitted regularly and all sub-carriers are employed as pilots. If the channel is invariable during the block, there will be no error in the channel estimation as the pilots are sent at all carriers. Y=Xh+n Where y is the received vector, X is a matrix containing the transmitted signalling points on its diagonal, h is a channel attenuation vector, and n is a vector of i.i.d. complex, zero mean Gaussian noise with variance 89: In the following we present the LMMSE estimate of the channel attenuations h from the received vector y and the transmitted data X. We assume that the received OFDM symbol contains data known to the estimator - either training data or receiver decisions The complexity reduction of the LMMSE estimator consists of two separate steps. In the first step we modify the LMMSE by averaging over the transmitted data, obtaining a simplified estimator. In the second step, we reduce the number of multiplications required by applying the theory of optimal rank-reduction. Low complexity LMMSE channel estimation LMMSE CHANNEL ESTIMATOR: The LMMSE channel estimator tries to minimise the mean square error between the actual and estimated channels $;<<=� � >$#>##�1y R@AisthecrosscorelationandRAAistheautocorrelation

The LMMSE estimator can be expressed as:

ℎ;<<=� = >ℎℎ[>ℎℎ + 8�2(XYH)−1]−1ℎ;=

where

ℎ;= = �−1T = U#0�0#1�1 …… .

#� − 1�� − 1W

X

Is the LS estimates of h. 89: is the variance of the additive channel noise the LMMSE channel estimator can be represented as

ℎ;<<=� = >ℎℎ Y>ℎℎ + Z[�> \]

−1ℎ;=

WhereZ is a constant depending on the type of modulation In the case of 16-QAM transmission, β = 17/9. The error covariance matrix Ree of the LMMSE estimator can be represented by

>�� = >ℎℎ − �>ℎℎ (>ℎℎ + Z[�> \)

−1 >ℎℎ^ (1)

we can see that LMMSE channel estimation requires knowledge of the channel frequency correlation and the operating SNR LMMSE channel estimation needs the matrix inversion and complex multiplication in an efficient implementation. Thus, the main drawback of LMMSE channel estimation is that it has a very high complexity owing to the matrix inversion. Now we take the optimal rank reduction of the estimation of eq. (1) using the singular value decomposition (SVD). SVD of the channel correlation matrix is given by >__=DΛbc Where D is a matrix checking to have orthonormal columns d�, d,: de, …………d �� and Λ designs a diagonal matrix which contains the singular values .� ≥ .�g ≥ .: ≥. �� ≥ 0on its diagonal We can write eq.(1) ℎh=D∆bcℎhjk

Where ∆ is a diagonal matrix containing the values -l� .l

.l + Z[�>

The best rank -p approximation of the estimator of eq (1)

ℎmn = o (Δm 00 0)o

6ℎ;=q

Where ∆r is the upper left p× p corner of∆

SIMULATION RESULTS: The OFDM system parameters used in our simulation are presented in Table 1

Parameters Specifications FFT SIZE 1024 Number of active carriers

256

Pilot Ratio 1/8 Guard interval 256 Guard type Cyclic extension Bandwidth 17.5 Signal constellation 16 QAM Channel model Rayleigh fading

Table 1: simulation Parameters We evaluate the performance of the proposed scheme in Fig: 1 we have carried out the result of Lmmse channel estimation algorithm which shows the improved BER performance over without channel estimation. In fig: 2 we can see that when the FFT size is very high, we remark that the three algorithms converge .for the good performance of lr-lmmse we need to keep the FFT size high.

Fig: 1 channel estimation Vs no channel estimation

Fig: 2 BER Vs SNR for FFT size=1024 using LS, LMMSE, Lr-LMMSE algorithms with a 16 QAM modulation CONCLUSION: In this paper, we proposed a simple and low-complexity approach for the estimation of time varying OFDM channels using different algorithm. LMMSE algorithm is convenient to both comb – pilot insertion and block-pilot insertion for the estimation of OFDM channel since it gives a good enhancement of the BER versus SNR and a good MSE. The difficult task in this simulation is the size of FFT which take more simulation time. REFRENCES:

[1] Aleksandar Jeremic´, Timothy A. Thomas, Arye

Nehorai,“OFDM Channel Estimation in the Presence of Interference” IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 52, NO. 12, DECEMBER 2004

[2] John Proakis, Digital Communications, McGraw-Hill, 1989.

[3] Sinem Coleri, Mustafa Ergen,Anuj Puri, Ahmad Bahai “A Study of Channel Estimation in OFDM Systems” IEEE 56TH VEHICULAR TECHNOLOGY CONFERENCE

[4] Y. Li, Pilot-Symbol-Aided Channel Estimation for OFDM in Wireless Systems, in IEEE Transactions on Vehicular Technology, vol. 49, no.4,July 2000

[5] O. Edfors, M. Sandell, J.-J. van de Beek, S.K. Wilson, and P.O. Brjesson, OFDM channel estimation by singular value decomposition, IEEE Transactions on Communications, vol. 46, no. 7, pp. 931-939, July 1998.

[6] Yinsheng Liu, Zhenhui Tan, Haibo Wang, Kyung Sup Kwak, “Joint Estimation of Channel Impulse Response and Carrier Frequency Offset for OFDM Systems” IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 9, NOVEMBER 2011

[7] Morelli, M., and Mengali, U ”A comparision of pilot- aided channel estimation methods for OFDMsystems” IEEE trans signal process IEEE trans 2001,49,pp.3065-3073

0 5 10 15 20 25 30 35 4010

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0 2 4 6 8 10 12 14 16

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lrlmmsezf

[8] J.-C. Lin, “Least-squares channel estimation for mobileOFDM communication on time-varying frequency- selective fading channels,” IEEE Transactions on Vehicular Technology, vol. 57, no. 6, pp3538–3550, 2008

[9] Book of “OFDM system for wireless communication “ by Ramji prasad

.