Design of a Few Interleaver Techniques used with Gold Codes in Faded Wireless Channels

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1 Design of a Few Interleaver Techniques used with Gold Codes in Faded Wireless Channels Barnali Das Comm. Technology, barnalidasgimt@g mail.com Manash P. Sarma Comm. Engineering, manashpelsc@gmail. com Kandarpa K. Sarma Comm. Technology, kandarpaks@gmail.com Nikos Mastorakis Technical University- Sofia, Sofia, Bulgaria. mastor@tusofia.bg Abstract- Though wireless channels are indispensable components of a mobile communication system its stochastic behaviour is the primary reason of degradation of quality of service (QoS). As the authenticity and fidelity of transmitted data is always a matter of concern, there has been continuous efforts to achieve appreciable performance despite the stochastic behaviour observed in wireless channels. Several techniques have been proposed and implemented to achieve such a goal. Interleaving is one of the simplest and convenient techniques which is used efficiently in wireless applications. It has found its application for minimizing burst errors that creeps up in transmission. In this paper, performance evaluation of different interleaver techniques with Gold codes in terms of BER (Bit Error Rate), computational time, mutual information and correlation has been presented for the application in fading environment. Keywords- Interleaver, BER, AWGN, Rayleigh, Rician, Mutual Information, Correlation. I. INTRODUCTION One of the key concerns in mobile communication has been the necessity to meet increasing demands of spectrum space. Multiple access is a critical method through which spectrum space is efficiently utilized. But wireless channels are always filled with unpredictable behaviour for which quality of service(qos) suffers. Noise and errors due to fading make reception a critical phenomenon. One of the popular methods of using multi-access and mitigating fading effects has been the use of interleaver. Interleaving is the process of rearranging the ordering of data sequence before transmission. An interleaver [1] is a device that performs interleaving. A deinterleaver is always associated with every interleaver, that restores the original input data sequence. Channel coding is used to detect and correct a specific number of random errors. Forward Error Correcting (FEC) codes are used to minimize these errors by adding a number of redundant bits along with the transmitted data. But this type of error correcting codes cannot handle long burst of error. Moreover, these codes are computationally expensive to correct long error burst. Therefore, an interleaver is employed after channel coding so as to rearrange the ordering of coded data. The key purpose of the work presented here is to improve the performance of the communication system. We use this performance comparison to ascertain the improvement in quality of service (QoS) that can be achieved by combining Gold codes during transmission through a faded wireless channel. In Section II, we briefly explain the types of interleavers and the parameters considered for the proposed work, and a brief overview of related works of implementations of interleavers. The description of the proposed model is included in Section III. Results are shown in Section IV. Conclusion and future work are included in Section V. II. BACKGROUND AND RELATED WORK This section gives a brief idea about the interleavers used in this work. We have also discussed some of the previous works related to implementation of interleavers. A. Interleaving Interleaving is a process, which is performed before transmission to disperse the data bits so that even if a part of the information is corrupted while passing through the channel, it can be recovered by rearranging the data after reception. There are different types of interleavers, which effects the performance of a system. The interleavers used in this work are described in this section. 1) General Block Interleaver: A Block Interleaver (Fig. 1) accepts a sequence of bits at the input row-wise and the new sequence with the same number of bits is released at the output of the interleaver column-wise. 2) Matrix Interleaver: Matrix Interleaver (Fig. 2) is a type of block interleaver that performs interleaving by filling the input symbols row by row in a matrix and then output of the interleaver is read column by column. 3) Random Interleaver: Random Interleavers (Fig. 3) disorder the input data before transmission with different permutation pattern. Due to this disordering of data, the error burst gets

2 randomized at the receiver. After randomization of the burst error, which has rearranged the whole block of the data, can now be easily detected and corrected. positive integer multiples of a fixed integer. Every new data to the input of the interleaver is feeded to the next shift register and the previous data in that register becomes part of the interleaver output. B. Mutual Information The measure of amount of information that a random variable X contains about another random variable Y, is known as mutual information [2], [3]. It reduces the uncertainty of one random variable due to the knowledge of the other. Mutual information can be defined as, Fig. 1: Block Interleaving where p(x,y) is the joint probability density function of the random variables X and Y, and p(x)and p(y) are the individual probability density function of X and Y respectively. C. Correlation Fig. 2. Matrix Interleaving Correlation is the degree of similarity between two or more quantities. Correlation is a mathematical operation that uses two signals to produce a third signal. This third signal is called the cross -correlation of the two input signals. If a signal is correlated with itself, the resulting signal is instead called the autocorrelation. D. Related Works Fig. 3. Random Interleaving Fig. 4. Convolutional Interleaving 4) Convolutional Interleaver: A Convolutional Interleaver (Fig. 4) is an interleaver which consists of a number of shift registers. The shift registers have a fixed delay each, which are This section presents some previous works related to interleavers. In [4], the performance of turbo codes with matrix interleaving is studied. Investigations of various issues related to the code performance are done. These include the design of the relative dimensions of the matrix interleaver, the effect of the interleaver length, the interaction between the interleaver and the number of decoding iterations, and the effect of interchanging the interleaver. A novel interleaving scheme for MC-CDMA system is proposed in [5]. In this type of interleaving, a circular shifting register is introduced into each subcarrier branch to decrease the correlation between subcarriers. In [6], interleavers are designed in a coded codedivision multiple-access (CDMA) scenario, where at the receiver multiuser detection is performed by employing an iterative turbo-like structure. The choice of interleavers affects both the maximum-likelihood (ML) performance and the impact of the suboptimality of the iterative receiver. In [7], the performance of turbo codes with different types of interleaver have been studied. The effect of the interleaver length, the interaction between the interleaver and the number of decoding iterations,and the effect of interchanging the interleaver between input and output are the various issues that have been investigated related to the code performance. In [8], a comparison between two interleavers viz. random and master

3 random interleaver has been presented based on the frequency of operation and hardware requirement. III. PROPOSED APPROACH The system model of the proposed architecture is illustrated in Figure 5. The proposed model is implemented in Matlab Simulink. Here, random number generator is taken as the source which generates random integers uniformly distributed in the range of [0, M-1] where M is the M-ary number. The vector of integer-valued or fixed-valued sequence is mapped to a vector of bits. Gold codes are used for spreading the sequence, which improves the QoS of the system. The number of bits per integer parameter value present in the integer to bit convertor block defines how many bits are mapped for each integer-valued input. The sequence of bits is then passed through an interleaver to rearrange the position of the data bits. The data is then passed through a BPSK modulator for modulation and transmitted through the channel. The channels used are AWGN, Rayleigh fading and Rician fading channels. The received data is then demodulated using a BPSK demodulator and then passed through a de-interleaver to recover the original data sequence. The data which is in terms of bit is mapped to a vector of integer with the help of bit to integer converter. The error rate is computed by comparing the received data with a delayed version of the transmitted data. The types of interleavers used are general block interleaver, matrix interleaver, random interleaver and convolutional interleaver. The system issimulated in Simulink for each interleaver, considering AWGN, Rayleigh and Rician channels, to obtain BER, computational time of the system, mutual information between channel input and output, and correlation between transmitted and received data. Fig. 6. BER of BPSK modulated signal through AWGN, Rayleigh and Rician channel using general block interleaver Fig. 7. BER of BPSK modulated signal through AWGN, Rayleigh and Rician channel using matrix interleaver Fig. 8. BER of BPSK modulated signal through AWGN, Rayleigh and Rician channel using random interleaver Fig. 5: Block diagram of the system model IV. RESULTS AND DISCUSSIONS Here, in this section the BER performance of different interleavers with Gold codes for wireless channels are shown in the figures 6, 7, 8 and 9. The computational time of the interleavers are tabulated in Table I. Mutual Information results are shown in figures 10, 11, 12 and 13 and correlation results are shown in the figures 14, 15, 16 and 17. Fig. 9. BER of BPSK modulated signal through AWGN, Rayleigh and Rician channel using convolutional interleaver

4 From the results obtained, we observed that the BER performance using Gold code gives better performance than without using it. At db we see that there is a significant gain in terms of db due to the use of Gold codes with interleaver design. Among all the interleavers we found the block interleaver to be better than other interleavers. BER obtained through AWGN and Rician is better than that obtained using Rayleigh channel. The BER in case of Rayleigh channel is slightly higher than other channels since it is a nonline-of-sight (NLOS) method, which consists of many obstacles in its path. The computational time has been calculated for the entire process i.e. from generation of the data till its reception. From Table I showing the computational time, we find that block interleaver is better in case of AWGN channel. In case of Rayleigh and Rician, matrix and random interleavers are respectively found to be better. Computational time of convolutional interleaver is poor since it consist of a set of shift registers with a fixed delay. Fig. 11. Mutual Information of AWGN, Rayleigh and Rician channel using matrix interleaver TABLE I: COMPUTATIONAL TIME OF DIFFERENT INTERLEAVERS THROUGH WIRELESS CHANNELS Interleavers AWGN Rayleigh Rician General Block s s s Matrix s s s Random s s s Convolutional s s s Fig. 12. Mutual Information of AWGN, Rayleigh and Rician channel using random interleaver From the Figures 10 to 13, we see that the mutual information between input and output of AWGN and Rician fading channel is better compared to that of Rayleigh fading channel for each interleavers. In case of Rayleigh fading channel due to its NLOS behaviour, a sizeable section of the information is corrupted due to reflections from the obstacles. As a result, the output contains less information about the channel input. Fig. 13. Mutual Information of AWGN, Rayleigh and Rician channel using convolutional interleaver The correlation property holds good for the system using block, matrix and random interleaver. The correlation properties of the interleavers are shown in figure 14, and 17. For convolutional interleaver, the correlation property is not so fruitful compared to the other interleavers. Fig. 10. Mutual Information of AWGN, Rayleigh and Rician channel using general block interleaver Fig. 14. Correlation property of AWGN, Rayleigh and Rician channel using block interleaver

5 platform to investigate efficiency in fading environment in real time. VI. ACKNOWLEDGEMENT The authors are thankful to the Ministry of Communication and Information Technology, Government of India for facilitating the research. REFERENCES Fig. 15. Correlation property of AWGN, Rayleigh and Rician channel using matrix interleaver Fig. 16. Correlation property of AWGN, Rayleigh and Rician channel using random interleaver Fig. 17. Correlation property of AWGN, Rayleigh and Rician channel using convolutional interleaver V. CONCLUSION AND FUTURE SCOPE Here, in this paper, a comparative work has been performed for different interleavers with Gold codes in terms of BER, computational time, mutual information and correlation. From previous works, we see that interleaving is performed mainly with turbo code which is a convolutional error correcting code. Here, we have used random data as the source and then converted into bits before interleaving, which gives better performance in case of AWGN and Rician fading channel. Though the computational time and design complexity is more in case of interleaver based system, but there are definite trade-offs with improved performances. The mutual information between channel input and output shows that the system performance is better using an interleaver. The correlation property also holds good for the system. The model that has been designed can be implemented in hardware [1] K. Andrews, C. Heegard and D. Kozen, A Theory of Interleavers, School of Electrical Engineering, Department of Computer Science, Cornell University, Ithaca, New York. [2] D. Guo, S. Shamai, S. Verd, Mutual Information and Minimum Mean-Square Error in Gaussian Channels, IEEE Transactions on Information Theory, vol. 51, no. 4, pp , April, [3] R. R. Perera, T. S. Pollock, T. D. Abhayapala, Bounds on Mutual Information of Rayleigh Fading Channels with Gaussian Input, Department of Information Engineering Research School of Information Sciences and Engineering, The Australian National University, ACT 0200, Australia. [4] M. A. Kousa, Performance of turbo codes with matrix interleavers, The Arabian Journal for Science and Engineering, vol. 28, no. 2B, pp , October [5] S. Feng and C. Shixin, Interleaving Scheme for Multicarrier CDMA System, Journal of Electronics(China), vol. 21, no. 1, pp , January [6] A. Chheda and D. W. Paranchych, Interleaving Methodology and Apparatus for CDMA, Nortel Networks Limited, St. Laurent(CA), March 9, [7] Y. J. Harbi, Effect of the Interleaver types on the Performance of the Parallel Concatenation Convolutional Codes, International Journal of Electrical and Computer Sciences IJECS-IJENS, vol. 12, no. 03, pp , June [8] A. Rai, N. Yadav., P. Chauhan, Performance Comparison of Interleavers, International Journal of Electronics Engineering, pp , 2010.