DCT based Channel Estimation in OFDM using MMSE and LS

DCT based Channel Estimation in OFDM using MMSE and LS

Sowmya Sreenivasan

Department of Electronics and Communication Christ University Faculty Of Engineering, Bangalore- 560075, Bangalore, India

Sujatha. S

Department of Electronics and Communication Christ University Faculty Of Engineering, Bangalore- 560075, Bangalore, India

Abstract Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technique and it has the ability to handle frequency-selective fading due to multi-path, without complex equalization filters. In this paper, a channel estimation scheme based on channel impulse response is presented. Channel estimation method based on the Discrete Cosine Transform (DCT) using phase shifted pilot sequences for MIMO-OFDM systems. With reasonable design and phase shifted pilot sequences for each transmitter antenna, the DCT- based channel estimation method can achieve highly efficient and accurate estimation without sacrificing much system overhead. When compared to DFT the channel is assessed using Minimum Mean-Square Error (MMSE) and Least-Squares (LS) channel estimators.

KeywordsChannel estimation, MIMO-OFDM, discrete cosine transform (DCT), phase shifted pilot sequences, discrete Fourier transform (DFT)

1. INTRODUCTION

   It is one of the main challenges which are faced in wireless OFDM systems. There are several approaches for channel estimation in OFDM system subcarriers. Channel estimation techniques for OFDM based systems can be divided into two main types: blind and non-blind. In the blind channel estimation approach it exploit the statistical behavior of the received signals and require a large amount of data. Then in the non-blind channel estimation methods the information of previous channel estimates or some portion of the transmitted signal are available to the receiver to be used for the channel estimation. But the issues of DCT based channel Estimation in OFDM is that the response of the channels in the network rapidly changes due to the mobility of receivers, transmitters or due to the scattering objects. [1].Yen-Hui Yeh et al., [2] have proposed two discrete cosine transform (DCT)-based pilot-symbol-aided channel estimators, which can mitigate the aliasing error and high-frequency distortion of the direct discrete Fourier transform (DFT)-based channel estimators when the multipath fading channels have non-sample-spaced path delays. These estimators are based on the property of channel frequency response and the concept of interpolation in transform domain. Both proposed estimators outperform the conventional DFT based channel estimators. The advantage of these estimators is that they have the advantage of easy and convenient realization by existing efficient DCT/IDCT hardware and software.Feifei Gao et al., [3] have proposed two maximum-likelihood joint frequency offset and phase offset estimators considering non-circular transmission of DCT-OFDM. The phase offset can be estimated only if the transmitted symbols are non-circular. The advantages of these

   offset estimators are the frequency offset estimation range increases from only one subcarrier spacing to its maximum. Second, the frequency offset and phase offset estimation is not only more accurate, but also more robust to the amount of the redundancy per block.Bin Jiang et al., [4] have proposed a 2-D DCT-based channel estimator for OFDM systems with virtual subcarriers in mobile wireless channels. This approach can well approximate the optimal MMSE channel estimation with the low-complexity implementation. The advantage of this approach is that it can deal with the spectral leakage, which results in an irreducible error floor and also the DFT- based filtering or interpolation in time-domain which has performance degradation for system with high Doppler frequency. OFDM is a promising candidate for high date rate wireless communications for its many advantages, notably, its high spectral efficiency, robustness to frequency selective fading, as well as the feasibility of low-cost transceiver implementations. The multi-input multi-output (MIMO) system , has the potential to obtain a diversity gain to mitigate the fading effect and to improve the system capacity, in order to meet the high data rate requirements from wireless applications. Hence, the combination of DCT with OFDM technology provides a promising candidate for next generation fixed and mobile wireless systems [5]. For wideband wireless communication, it is necessary to dynamically estimate the channel before demodulating the MIMO-OFDM signals, since radio channel is frequency selective and time-dependent. For OFDM channel estimation based on pilot, it can be classified as preamble method and PSAM method (Pilot Symbol Assisted Modulation or comb- type pilot method) in accordance with the difference of insertion position of pilots [6]. Since the conventional preamble assisted channel.

   Figure 1: OFDM

2. CHANNEL ESTIMATION

   To examine the state of channel, we consider the following

   h h0 ,

   p ,

   hn1

   DFTn (g)

   T

   T

   (5)

   assumptions. Let s(x) be the transmitted input symbols and

   s(x) be the received output symbols. Assume, g(x) as the

   The vector N is equivalent to,

   channel impulse response and N(x) represents the white complex Gaussian channel noise. From a multi-amplitude signal constellation, the transmitted symbols (s(x)) are

   N N0 ,

   N1 ,

   Nn1

   DFTn (N )

   T

   T

   (6)

   considered. Supposing that the D/A and A/D converters comprise ideal low-pass filters along with bandwidth 1/Ts. Here, Ts symbolizes the sampling interval and TC denotes the time length of a cyclic extension, which is used to eradicate inter-block interference and to maintain the orthogonality of tones.

   The channel impulse response g(x) can also be described as the function of a time limited pulse train. It takes the form as

   Where N is an i.i.d complex zero-mean Gaussian noise

   vector, The above descriptions can be written in the form of matrix as follows,

   s' XQg N

   (7)

   Here, X is the matrix that contains the elements of x on its diagonal.

   follows, [3]

   g(x) kx

   k

   k Ts

   (1)

3. P PROPOSED PROBLEM

   In this paper, the channel is assessed using Minimum Mean-

   The amplitudes ( k ) are complex valued and take value between 0 kTs TC .

   Square Error (MMSE) and Least-Squares (LS) channel estimators. Consider the channel vector g is Gaussian and uncorrelated with the channel noise N, then the MMSE estimate of channel g can be given as follows, [8]

   Using n-point discrete-time Fourier transform (DFTn), the system is modeled as follows,

   ^

   g MMSE = R

   gs'

   1 '

   R S

   R S

   s's'

   (8)

   S ' DFT IDFT (S ) g

   • N

   The terms in equation (8) can be derived as,

   Where,

   S S0 ,

   n

   S1 ,

   n n

   T

   T

   gg

   gg

   Sn1 ,

   (2)

   Rgs'

   Egs '( H ) R

   QH X H

   (9)

   0

   0

   1

   1

   S ' S ' ,

   S ' ,

   S

   S

   '

   n1

   T and

   N N0 ,

   N1 ,

   Nn1

   T are the vectors of i.i.d

   R ' '

   Es' s'( H ) XQR

   QH X H 2 I

   s s

   s s

   N

   N

   n1

   n1

   gg

   gg

   n

   n

   complex Gaussian varables. Another vector (10)

   g g0 ,

   g1 ,

   g T is well thought out by the

   Where,

   R and

   R are the cross covariance matrix

   g / n

   gs '

   s's'

   cyclic equivalent of sinc-functions. symbolizes the

   response of observed channel impulse after sampling the frequency response of g(x) and it is given as,

   between g and s and the auto-covariance matrix of s respectively. And then, Rgg denotes the noise variance (i.e)

   1 j x(n1)

   m sin k

   EN (x) 2 . We presume that both auto covariance matrix

   g(x) k e n R

   n

   n

   n k sin

   k

   x

   (3)

   ( gg ) and noise variance are known values.

   The estimation of MMSE in frequency domain is computed

   A set of n independent Gaussian channels of the system can be described as,

   as follows,

   ' h ^ ^

   H H '

   s (x) h(x)s(x) N(x)

   where, x= 0, 1n-1 (4)

   MMSE

   = Q g

   MMSE

   QO

   MMSEQ X s

   (11)

   In the above equation, h(x) represents the complex channel attenuation produced by the vector

   Where, the value of OMMSE can be given as,

   OMMSE=

   Rgg

   QH X H XQ1 2 R

   1 QH X H XQ1

   (12)

   V. CONCLUSION

   In this paper, a channel estimation scheme is based on pilot aided block type training symbols using LS and MMSE

   N

   N

   gg

   gg

   For the cyclic impulse g, the LS estimator minimizes

   s' XQg H s' XQg and produces,

   ^

   algorithm. The Channel estimation is one of the fundamental issues of OFDM system design. The MMSE is compared with LS and the MMSE performs better than the LS. The channel is assessed using Minimum Mean-Square Error (MMSE) and Least-Square(LS) channel estimators.

   hLS

   QOLS

   QH X H s'

   (13)

   REFERENCES

   1. Yen-Hui Yeh, Sau-Gee Chen, DCT-Based Channel Estimation for OFDM Systems, IEEE Communications Society,2004.

      The value of OLS can be derived as,

   2. Feifei Gao, Tao Cui, A. Nallanathan and C. Tellambura, Maximum Likelihood Based Estimation of Frequency and Phase Offset in DCT

      OLS

      ^

      Q H X

      H XQ1

      (14)

      OFDM Systems under Non-Circular Transmissions: Algorithms, Analysis and Comparisons, IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 9, SEPTEMBER 2008

   3. Jiang, Bin, Wenjin Wang, Haiming Wang and Xiqi Gao, "Two dimensional DCT-based channel estimation for OFDM systems with virtual subcarriers in mobile wireless channels." Communications,

      The equation for hLS

      is further reduced as,

      2008. ICC'08. IEEE International Conference on. IEEE, 2008.

   4. Xiang, Wei, Julian Russell, and Yafeng Wang. "ICI reduction through shaped OFDM in coded MIMO-OFDM systems."

      ^

      hLS

      = X 1s'

      (15)

      International Journal on Advances in Telecommunications 3.3 and 4 (2011): 194-205.

   5. Moussa Diallo, Rodrigue Rabineau, Laurent Cariou and Maryline H´elard, On improved DCT based Channel Estimation with very low complexity for MIMO-OFDM systems, IEEE, 2009

      The estimation value obtained from LS estimator is also

      equivalent to zero-forcing estimator.

4. SIMULATION RESULTS

In the proposed part, we first implement the channel estimation of the OFDM by using the LS and MMSE using DCT [3]

1. S Sujatha, P Dananjayan, "Modified SLM combined with interleaving and pulse shaping method based on PAPR reduction using DCT OFDM system", International Conference on Advanced Communication Control and Computing Technologies, pp. 101-105, 2016.

2. S Sujatha, P Dananjayan, PAPR Reduction in MIMO OFDM System using Modified SLM based Constant Modulus Algorithm with IDCT Matrix, vol. 14, no. 5, pp. 588, 2016.

0

10

LS MMSE

-1

10

-2

10

Bit Error Rate

Bit Error Rate

-3

10

-4

10

-5

10

0 5 10 15 20 25 30

SNR in dB

Figure 2. BER Vs SNR for Channel estimation of OFDM using LS and MMSE.