Performance Analysis Of Orthogonal Frequency Division Multiplexing (OFDM) Over Fading Channel And Space Time Block Code

Performance Analysis Of Orthogonal Frequency Division Multiplexing (OFDM) Over Fading Channel And Space Time Block Code

K. Sujatha, Dr. S. Varadarajan

Assistant Professor in Kuppam Engineering College, Professor in S.V.University

Abstract

Analysis will be carried out for an OFDM wireless communication system using space time block code (STBC) at the transmitter and considering the effect and the wireless channel like delay spread and fading. The analysis will include the effect of imperfect timing recovery at the output of the receiver. The expression for Bit Error Rate with STBC and timing error will be developed. Performance results will be evaluated numerically. Performance degradation due to imperfect timing synchronization will be determined.

1. Introduction

   The target of next generation wireless communication is to achieve high data rates with low bandwidth. It should be power efficient. At present time Orthogonal Frequency Division Multiplexing is widely used for its bandwidth efficiency property. Because of its orthogonal characteristic more data can be transmitted at a certain amount of bandwidth compare to the other systems. Increasing the diversity gain is another way to achieve good performance. By using Space Time Block Code the antenna diversity gain can be increased. This paper shows the analysis of STBC-OFDM. At the end of this paper equations for Signal to Noise Ratio (SNR) and Bit Error Rate (BER) have been derived analytically using four transmitting antennas and one receiving antenna and 6 transmitting antennas and one receiving antenna.

2. Space Time Block Code Orthogonal Frequency Division Multiplexing

   Severe attenuation in a multipath wireless environment makes it extremely difficult for the receiver to determine the transmitted signal unless the receiver is provided with some form of diversity i.e. some less-attenuated replica of the transmitted signal is provided to the receiver. In some applications, the only

   practical means of achieving diversity is deployment of antenna array at the transmitter and/or receiver end. As the current trend of communication systems demands highly power-efficient and bandwidth-efficient schemes, techniques that provide such desirable properties are considered very valuable in next generation wireless systems. Making use of multiple antennas increases the capacity of the system with the associated higher data rates than single antenna systems. Space-Time coding is a power-efficient and bandwidth-efficient method of communication over fading channels by using multiple transmits antennas systems.

   1. System Model for STBC-OFDM

      We consider an OFDM system with transmit diversity, in which the total system bandwidth is divided into N equally spaced and orthogonal sub- carriers. We investigate the system with four transmission antennas and one receiving antenna. During the first time instant, the four symbols [ X0 X1 X2 X4] are transmitted from four antennas simultaneously, with X0, X1, X2 and X3 transmitted from all four antennas. In the second time slot [-X1* X0* -X3* X2], third time slot [-X2* -X3* X0* X1*] and fourth time slot [X3 X2 X1 X0] are transmitted.

      This encoding of the transmitted symbol sequence from the transmit antennas is given by then encoding

      matrix.

      For each transmit antenna, a block of N complex- valued data symbols {X(k)} for k=0 to N-1 are grouped and converted into a parallel set to form the input to the OFDM modulator, where k is the sub carrier index and N is the number of sub carriers. The modulator consists

      of an Inverse Fast Fourier transform (IFFT) block. The output of the IFFT at each transmitter is the complex baseband modulated OFDM symbol in discrete time domain and is given by

      1. Channel

         The channel is modelled by a tapped delay line with channel coefficients that are assumed to be slowly varying such that they are almost constant over the two transmission instants. The channel frequency response for the kth subcarrier is

         Where h (p) is the complex channel gain of the pth

         multipath component

      2. Phase Noise

         The phase noise (n) is modelled as a zero-mean continuous Brownian motion process with variance The phase noise increments take the form of a Wiener process, with independent Gaussian increments.

      3. Received Signal

         The time-domain received signals at the first and second transmission instances at the input to the FFT block are respectively given by

         Y0(n)=(h0(n)x0(n)+p(n)x1(n)+p(n)x2(n)+p(n) x3(n) +w(n)0)ej(n)

         Y1(n)=(-h0(n)x1*(n)+p(n)x0*(n)-p(n)x3*

         (n)+p(n) x2* (n)+w(n)1) ej(n)

         Y2(n)=(-h (n)x *(n)-h (n)x *(n)+h (n)x *(n)+h (n)

      4. DetectionwithImperfectChannel Estimation

      In the presence of imperfect channel estimation, we assume a channel estimation model such that the channels estimate H of the true channel H is given by

      =

      Where 0 , 1 , 2 and 3 are the errors in the channel estimate from the first ,second, third and fourth transmit antennas respectively, and are modeled as independent zero-mean complex Gaussian random variables with variances , , and

      2respectively.

      1. Variance

         As the noise signal has both positive and negative amplitude, it is squared, and then the mean has been taken, which is variance. We consider the variance of noise for calculation

         1. Variance of Noise

            The variance of the noise W, after some mathematical manipulations, is given by

         2. Variance of Channel Estimator Error

            0 2 1 3

            x * (n)+ (n)2) j(n)

            3 0 3

            The variance of is given by

            2 w e

            Y3(n)=(h0(n)x3(n)-p(n)x2(n)-p(n)x1(n)+p(n)x0 (n)+w(n)3) ej(n)

            Where represents linear convolution, subscripts indicate antenna index, and superscripts indicate transmission instant. The complex Gaussian random variable w (n) represents the Additive White Gaussian Noise (AWGN) term and (n) is the phase noise.

         3. Variance of Inter Carrier Interference

      Similarly, the variance of the ICI term is given by

3. Calculation of SNR and BER

   We present the bit error rate analysis for the case of 16QAM modulation using Gray code mapping for (b1 b2 b3 b4). It is important to note that although the presentation is only for 16QAM, the following analysis is valid for all square QAM constellations. The conditional BER for bit b1, condition on H0, H1, H2, H3 is given by

   and for bit b3 is given by

   From which the SNR is given by

   It follows a Chi-square distribution with probability density function (PDF) given by

   Due to the symmetry of square M-QAM constellations, the BER for the in-phase and quadrature bits are equal such that Pe (b1) = Pe(b2) and Pe(b3)=Pe(b4). Therefore the average BER is obtained by averaging the conditional BER of b1 and b3 over the PDF of the SNR . The average BER is therefore given by

   Similarly for 6:1 transmission system SNR is given by

   And BER is giver by

4. Results (STBC-OFDM):

   The parameters that uses in the calculation are shown in table-1

   Table 1: System and Channel Parameters (STBC- OFDM)

   Parameters	Values
   o p	0.1 0.2 0.02 0.4
   o 2	0.1 0.04 0.06
   Subcarriers (N)	64
   Channel Path Gains	-9.7 -0.9 -8.5-0.5

   Figure: 7 shows the SNR Vs BER graph for 2:1 transmission system. Figure: 8 shows the same graph for different value of noises. Then figure: 9 shows the graph of SNR Vs BER for 4:1 transmission system along with 2:1 and 1:1 system. It is seen that 4:1 graph

   is closer to the two axes than the others. It means that the BER is decreasing fast when the number of antennas increases. Figure: 10 shows the SNR Vs BER graph of 4:1 for different value of noises. Then figure: 11 shows the performance of 6:1 along with 4:1, 2:1, 1:1 transmission system. Figure: 12 shows the SNR Vs BER graph of 6:1 for different value of noise. From the figure: 11 receiver sensitivity graphs are plotted for different value of noises. It shows that transmission power decreases when number of antennas increase. The graph is shown in figure: 13. Another analysis can be drawn from the graph shown in figure: 13 is that for a fixed value of transmission power the noise term can be reduced by increasing the number of antennas.

5. Conclusion

   The equations for SNR and BER using 4:1 and 6:1 transmission system are derived. The effects of noise, carrier interference and channel estimator error on the system are analyzed. The SNR Vs BER curve shows that increasing the diversity gain improve the performance of the system. Receiver sensitivity graph shows the power efficiency characteristic of the system

6. References

1. Shankhanaad Mallick and Dr. Satya Prasad Majumder- Performance Analysis of an OFDM System in the Presence of Carrier Frequency Offset, Phase Noise and Timing Jitter over Rayleigh Fading Channels ICECE,2008.

2. Mehedi Hasan and Dr. Satya Prasad Majumder- Performance Limitation of SIMO OFDM Wireless Link Impaired by Carrier Frequency Offset Phase Noise and Fading

3. Mohamed Jalloh, Pankaj Das- Performance Analysis of STBC-OFDM Transmit Diversity with Phase Noise and Imperfect Channel Estimation

4. Siavash M. Alamouti- "A Simple Transmit Diversity Technique for Wireless Communications" IEEE Journal on Selected Areas in Communications, vo1.16, pp 1454, Oct 1998.

5. Vahid Tarokh, Hamid Jafarkhani, A. R. Calderbank- "Space-Time Block Codes from Orthogonal Designs" IEEE Transactions on Information Theory, vol.45, pp. 1456-1467, Jul 1999.

6. Vahid Tarokh, Ayman Naguib, Nambi Seshadri, and A. R. Calderbank- "Space-Time Codes for High Data Rates Wireless Communication: Performance Criteria in the Presence of Channel Estimation Errors. Mobility, and Multipath" IEEE Transactions on Communications, vo1.47, pp. 199207, Feb 1999

7. T.N. Zogakis and J.M. Cioffi- The effect of timing jitter on the performance of a discrete multitone system, IEEE Trans. Commun. Vol. 44, no. 7, pp. 799-808, July 1996.

8. T. Pollet and M. Moeneclacy- Synchronizability of OFDM signals, in Proc. Globecom95, pp. 2054-2058, Singapore, Nov. 1995.

9. P.H. Moose- A technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction IEEE, Trans. Commun, vol. 42, pp. 2908- 2914, Oct. 1994.

10. S. Wu and Y. Bar-Ness- OFDM Systems in the Presence of Phase Noise: Consequences and Solutions IEEE Trans. Commun. Vol. 52, No. 11, pp. 1988-1996, Nov. 2004.

Authors Profile

K. Sujatha, received the B.Tech degree in Electronics and Communication Engineering from Kuppam Engineering College in 2005 and M.Tech from Dr.M.G.R university in 2008.Currently

pursuing PhD from Jawaharlal Nehru Technological University, India. Research interests include wireless Communications and Wireless Networks

Dr. S. Varadarajan received the B.Tech degree in Electronics and Communication Engineering from Sri Venkateswara University in 1987 and M.Tech from NIT, Warangal He did his PhD in the area of Radar Signal Processing. He is fellow of Institute of Electronics and

Communication Engineers (IETE) and member of IEEE. Currently working as Professor in the department of ECE, Sri Venkateswara University, Tirupati, Andhra Pradesh India