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Analysis on Mean Square Error of LS method based Channel Estimation for MIMO OFDM Systems

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Abstract

Channel estimation is a mandate method for improving the performance of the orthogonal frequency division multiplexing (OFDM) system. The pilot-based least square (LS) scheme is for improving the accuracy while doing channel estimation and the symbol error rate (SER) to increase the performance of the wireless communication scenarios. Symbols are estimated with the initial channel information, and channel simulated estimation results can be obtained by linear interpolation. The minimum mean square error (MMSE) and linear minimum mean square error (LMMSE) algorithms are also compared with channel matrix. If the number of subcarriers increases, the dimension of the matrix becomes large. Therefore, we compute the Mean Square Error (MSE) of the LS channel estimated. Simulation shows provides a better performance of Bit Error Rate (BER).

Keywords: Channel Estimation, least square (LS), Mean Square Error (MSE), minimum mean square error (MMSE), linear minimum mean square error (LMMSE) ,Orthogonal Frequency Division Multiplexing, Bit Error Rate (BER) and Symbol Error Rate (SER).

I. INTRODUCTION

Nowadays the modulation methods exhibits maximum data rates over wireless channels broadband for applications such as internet wireless access, mobile communication future generation scheme, and wireless multimedia.

Orthogonal Frequency and Division Multiplexing is a digital modulation system to reduce the equalization in a selective frequency channels. The advantages is that it minimizes the fading selective frequency channels it against the robust and implementation. The Multiple inputs and Multiple Outputs communication is enabled through multiple receive and transmit antennas, the channel capacity could be increased. So that MIMO-OFDM schemes, its combination of MIMO and OFDM communication, it could produce high transmission performance. The advantage of the technology is to improve the performance of wireless communication systems [1][2]. When there is high noise variance, the channel accuracy of channel estimation is minimized. The second technique is minimum mean square error method to increase accuracy[3] The LMMSE method is to reduce the AWGN in the time domain, but it also has some drawbacks.[4] The inverse as when the number of subcarriers is more the reverse operation is more complex . The next method is linear MMSE (LMMSE) estimation. [5][6]

In MIMO-OFDM scheme [7], coherent signal detection needs impulse channel responses reliable estimate among receive and transmit antennas. These channels could

be calculated through training sequences. The training sequences transmitting are unsuitable for communication systems. A Second Order Statistics (SOS) based blind estimators introduced by single input and multiple output schemes. Between these methods, this subspace noise technique is believed to be a promising method due to good performance and simple structure. Through the fundamental structure, the sub-space techniques and subspace noise techniques for single inputs and single output (SISO) OFDM scheme has been attained a good performance.

Frequency hopping technology [8][9]. A subspace technique for SISO-OFDM scheme by using the redundancy its introduced through cyclic prefix (CP) insertion & described for channel identifiably condition. For MIMO-OFDM

Analysis on Mean Square Error of LS method based Channel Estimation for MIMO OFDM Systems

A.Raja 1, V.Thulasibai 2

1. Research Scholar, Sathyabama Institute of Science and Technology, Chennai & Assistant Professor (SG), Department of Electronics and Communication Engineering, Saveetha School

of Engineering, Saveetha Institute of Medical And Technical Sciences, Chennai, Tamil Nadu ,India.

2. Professor, Department of Electronics and Communication Engineering, KCG College of

Technology, Chennai, Tamil Nadu, India.

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scheme with CPs, these techniques could be gives an additional performance with respect into the existing methods.

ISI and inter-carrier interference (ICI) may affect the accuracy of channel estimation [10] The modulation scheme can be used as a key technology for 4th and 5th generation communication .The quadrature amplitude modulation method can improve the accuracy and the performance of channel estimation suitable the wireless system [11].

II. MIMO-OFDM SYSTEM MODEL

In our MIMO-OFDM techniques could be used to both VCs with and without system. Let nth frequency domain symbols in the jth transmit antenna,

(1) Here j is a transmit index antenna. If noted that CP is a P, and every modulator OFDM adds N-D zeros for VCs into the data block, its used to an N-point inverse Fast Fourier transform to that block, & in front of IFET vector, inserts the CP.

(2) The time signal sent to the channel, the elements in these vector sj(n) is pulse shaped through a transmit filter.

(3) Here Q=N+P, & T is a sample duration in the time domain. If denoting k is the kth sample of OFDM symbol in a time domain, and K+nQ, the transmitted signal sj [t] is expressed as a

(4) The MIMO-OFDM system is modeled to increase the data rate in the wireless network. Figure 1a and 1b shows the transmitter and receiver model of the OFDM system.

a) Transmitter Model

b) Receiver Model

Figure 1: MIMO-OFDM system for generic wireless network.

MIMO-OFDM Transmitter unit:

The data input of the OFDM system is initially modulated with any one of the modulation technique like BPSK or QPSK based on the type of the fading channel. Then the modulated signal converted into parallel data using serial to parallel converter The data rate was reduced by N times were N is the total number of parallel stream. A

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small bandwidth is applied for each individual stream. Then a pilot signal is added to the parallel stream for specified period of block or for specified frequencies for all blocks. Then the parallel data stream is applied to the IFFT. The raw data is in complex form so IFFT is applied to convert the complex values to real values. A cyclic prefix is then added to the data stream to prevent inter symbol interface. Then this processed data is transferred through the number of transmitting antennas. The transmitted signal is represented as follows:

Where represents the input signal. To transfer the data through multiple antennas the space-time block coding is used. The space-time block code transmits the same data through all the transmitting antennas. It repeats the code for selected time and space. It produces higher improvements in error ratio when compared to the single antenna system. The space-time block coding utilizes trellis codes but simpler block code is also used in Alamoutis codes.

A complex orthogonal design is used by Alamouti code were the transmission data is arranged as a square matrix and the output value should satisfy complex orthogonality in order of space and time domain. The received signal is defined as:

The data rate of the received signal is achieved as -1. Thus the space-time block coding provides complete gain without the requirement of sacrificing the data rate. For example the code is developed for two transmitting antenna and single receiver antenna then the matrix of the code is given as follows

Based on the alamoutis method the sequence of transmitted data from different antennas is orthogonal to each other because the alamoutis matrix is S times of the Hermitian matrix were S is equivalent to the identity matrix like as follows

The subscript H refers to Hermitian matrix of identity matrix S and I is the identity matrix of size 2*2. In the receiver end, the signal received at time t and t+T is expressed in c* format. The equation is derived as follows, were the r1 and r2 refers to the received signal at time interval t and t+T.

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The Gaussian noise sample is represented as n1 and n2. The parameters of space-time block coding channel are assumed at the receiver end. From the parameters assumed the transmitted signals s1 and s2 can be regenerated from the received signal r1 and r2 using the following equation.

Using the results of Y1, Y2, X1, X2 and property of orthogonality of transmitted matrix the received signal s1 and s2 can be recovered from noise.

MIMO-OFDM Receiver unit:

Let consider that be the no of antennas used to receive the transmitted signals of , then the received signal is referred as . The received signal consists of original transmitted signal and noise induced in the communication channel. In initial state the cyclic prefix which is used as guard interval was removed from the received signal. And FFT analysis performed over the data signal, then by utilizing the pilot signals the impulse response of the channel is estimated. LS or MMSE technique was used to estimate CIR value. The figure 4.5b shows the blocks involve in retrieving information from the received signal.

The vectors are considered as (n)= and with length M.

is the vector of size L*1 initiated from the jth antenna of transmitter and to the ith antenna of the receiver. Maximum length of the channel is referred as L. The additive Gaussion noise vector is represented as n with size M*1.

III. LS AND MMSETECHNIQUE FOR MIMOOFDM SYSTEM:

To receive multi path signals in the MIMO-OFDM system the LS and MMSE techniques are utilized. In pilot-based LS algorithm [12][13] The pilot symbols are used to estimate the communication channel. Two approaches are used to add pilot symbols in the transmitting signal they are shown in figure 2.

(a) Block Type (b) Comp type

Figure 2: Techniques to add pilot symbols during transmission.

In the block type technique the pilot signals are added in all frequency bins with fixed periodic intervals in the OFDM block. Once the transmitting symbols were fixed the OFDM blocks was regularly transmitted through the communication channel. But in the comp type the pilot symbols are added to every OFDM symbols with frequency bins of specified period. In comp type the subcarriers are classified into groups and arranged as adjacent to each subcarrier. In all the groups the first subcarrier is utilized to transmit pilot signals. When K consecutive signals are taken for training then the equation with Hermitian matrix is rewritten as follows.

is referred as the vector of gaussion noise in subcarriers of the pilot symbols.

A. LS Estimation Technique:

The MIMO-OFDM system concern simplifies the processing of receivers baseband by removing the MIMO equalizer. Zero forcing receivers which is referred as MIMO LS is used to simplify the process over received Y1, Y2,…. Yn signals. MIMO MMSE is used to detect the X1, X2, . . . Xmt signals. Using the LS and MMSE technique the channel matrix is known only at the receiver side of the system. The Xj(n) measured using LS technique is shown below:

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B. MMSE Estimation Technique:

The Xn (n) measures error MMSE estimation technique is shown below

The H is the Hermitan matrix and is set as one. MMSE technique is a complex process which consumes more execution time than LS technique. The channel estimation with different methods such as least square, Blink channel estimation, and linear minimum mean square error are explained below. The Figure 3 shows the Multiple Input and Multiple Output MIMO Orthogonal Frequency Division Multiplexing (OFDM) Least Square Error LSE CHAN EST LOOP channel estimation subcarrier 256, among Bit error rate (BER) and SNR [dB]. The BER ranges from 10-4 to 10-1 and the corresponding values SNR [dB] is 2 to 16. This graph having only one plots, it represents a TD Qabs LMMSE. Its initialize from 3 in SNR [dB] near 10-1 (BER) then gradually decreased up to 15 in SNR [dB] near 10-3 in BER values.

Figure 3: MIMO OFDM LSE CHANEST LOOP subcarrier 256

Figure 4 shows the mean square error of least square error channel estimation and SNR [dB] in the MIMO-OFDM, and channel estimation level ranges from 2 to 16 in SNR[dB] and MSE of LSE channel estimation ranges from 10-3 to 10-2. The MSE and LS simulation results initiated from 10-2 and it gradually decreases to 15. Here number of transmit antenna Nt is 2 as well as Number of receive antenna Nr is 3.The mean squared error of the least square channel calculated through the simulation results is compared with the theory. The red color line indicates the LS channel simulations and the blue color dot indicates the theory, this theory appears for each single point (3, 4, 5, etc...).

Figure 4: LSE CHANEST LOOP subcarrier 512

The line graph in figure 5 shows that Least Square and Mean Square Error in MIMO-OFDM. This simulation outputs between the SNR [dB] and Bit error rate (BER). The SNR [dB] ranges from 2 to 15 and BER values from 10-3 to 10-1. If demodulated Data is 1 in the BER, the codes are demodulates the transmitted through least square data and calculate the BER. The blue color line indicates the TD LMMSE (Linear Minimum Mean Square Error), these lines starting near 10-1 to gradually decrease to the 15.

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Figure 5: LS MSE IN MIMO-OFDM

Figure 6 show that Symbol Error Comparison between the SNR [dB] and symbol Error Rate for an OFDM system along with MMSE/LS estimator based receivers. The SNR [dB] ranges from 5 to 30, and the symbol error rate is 10-2 to 10-1. This graph showing two plots of different colors as well. The black color indicates the (MMSE) line, such as the blue color noted that Least Minimum Mean Square Error (LMMSE) line.

The LMMSE line starting from near 10-1 and gradually decreased up to 15. And then maintain constant for another 5 points, after that little increased at the end point. This blue line every 5 points directions move forward and backward also, but the black line starting from after the blue line only, this line only the forward move directions its decreased gradually at the end point 30.

Figure 6: SER Comparison

The 2 plots in Figure 7 shows that Mean Square Error (MSE) comparison between the SNR [dB] and MSE for an OFDM system with the Least Square and MMSE estimator based receivers. The SNR [dB] and MSE range from 5 to 25 and 10-3 to 10-1. The blue color line indicate the Least Minimum Mean Square Error (LMMSE), this line having 2 arrows both the forward and backward direction its smoothly decreased, such as the black line indicate (MMSE), but this line having only backward direction arrows.

Figure 8: MSE Comparison

LS

MMSE

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The Figure 9 shows that OFDM estimation between EsNodB and channel MSE. This graph has 5 plots, for the estimation of channel mean square error corresponding to the values of EsNodB. Each plot has different colored representation. The channel MSE ranges from 10-6 to 100 and for the values of EsNodB ranging from 0 to 40. The five plots for channel MSE corresponding to the EsNodB values are, the Least square initialize for channel MSE from 100 and then gradually decreased up to 103 as well as the dots represents the LS theory presents in this plots.

TD Qabs LMMSE starting near 100 and then exceeding at the point of 5 to 15, after that step by step decreased up to 10-5. Then another plots TDD LMMSE, theory LMMSE and MMSE plots bringing together at the point of 30 up to 40 gradually decreased near 10-5. Theory LMMSE is starting from 10-2 and MMSE starting from 10-1 exceeding at the point 15 to 40.

Figure 9: OFDM Estimation

Conclusion

Channel estimation plays an important role in minimizing noise and interference in MIMO networks. The channel estimate with different methods such as Least square, minimum mean square error, Linear minimum mean square error simulated and discussed. The computational complexity reduced with addition of FFT IFFT blocks and achieved better bit error rate.

References

[1] Wang, S.; Manton, J.H. Blind channel estimation for non-CP OFDM systems using multiple receive antennas. IEEE Signal Process. Lett. 2009, 16, 299–302.

[2] Inserra, D.; Tonello, A.M. Training symbol exploitation in CP-OFDM for DoA estimation in multipath channels. In Proceedings of the 21st European Signal Processing Conference, Marrakech, Morocco, 9–13 September 2013.

[3] Sutar, M.B.; Patil, V.S. LS and MMSE estimation with different fading channels for OFDM system. In Proceedings of the International Conference on Electronics, Communication and Aerospace Technology, Coimbatore, India, 20–22 April 2017.

[4] Tang, R.G.; Zhou, X.; Wang, C.Y. A novel low rank LMMSE channel estimation method in OFDM systems.

In Proceedings of the 17th IEEE International Conference on Communication Technology, Chengdu, China, 27–30 October 2017.

[5] Tong, Z.R.; Guo, M.J.; Yang, X.F.; Zhang, W.H. Performance comparison of LS and LMMSE channel estimation algorithm for CO-OFDM system. In Proceedings of the 3rd International Conference on Mechanical and Electronics Engineering, Hefei, China, 23–25 September 2011.

[6] Ohno, S.; Munesada, S.; Manasseh, E. Low-complexity approximate LMMSE channel estimation for OFDM systems. In Proceedings of the Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, Hollywood, CA, USA, 3–6 December 2012.

[7] Han, X.; Yin, J.W.; Yu, G. Multiple-input multiple-output under-ice acoustic communication in shallow water. In Proceedings of the 11th ACM International Conference on Underwater Networks and Systems, Shanghai, China, 24–26 October 2016.

[8] Lv, S.; Shen, X.H. Research on shallow water acoustic communication based on frequency hopping. In Proceedings of the IEEE International Conference on Signal Processing, Communications and Computing, Hong Kong, China, 12–15 August 2012.

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[9] Yang, T.C. Properties of underwater acoustic communication channels in shallow water. J. Acoust. Soc. Am.

2012, 131, 129–145.

[10] Ding, W.B.; Yang, F.; Song, J. Out-of-band power suppression for TDS-OFDM systems. In Proceedings of the IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, London, UK, 5–7 June 2013.

[11] Hu, S.; Wu, G.; Yang, G.; Li, S.Q.; Gao, B. Effectiveness of preamble based channel estimation for OFDM/OQAM s/m. In Proceedings of the International Conference on Networks Security, Wireless Communications and Trusted Computing, Wuhan, China, 25–26 April 2009.

[12] Al-Ogaili, F.; Elayan, H.; Alhalabi, L.; Al-Shabili, A.; Taha, B.; Weruaga, L.; Jimaa, S. Leveraging the `LS criterion for OFDM sparse wireless channel estimation. In Proceedings of the 11th IEEE InternationalConference on Wireless and Mobile Computing, Networking and Communications, Abu Dhabi, UAE,19–21 October 2015.

[13] Khan, A.M.; Jeoti, V.; Zakariya, M.A. Improved pilot-based LS and MMSE channel estimation using DFT for DVB-T OFDM systems. In Proceedings of the IEEE Symposium on Wireless Technology &

Applications, Kuching, Malaysia, 22–25 September 2013.

References

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