Optimization of OFDM Systems Using Genetic Algorithm in FPGA

Optimization of OFDM Systems Using Genetic Algorithm in FPGA 1 S.Venkatachalam, 2 T.Manigandan 1 Kongu Engineering College, Perundurai-638052, Tamil Nadu, India 2 P.A. College of Engineering and Technology, Pollachi-462002, Tamil Nadu, India Abstract In this paper subcarrier and power allocation to each user at base-station maximize the user data rates, subject to constraints on total power and bit error rate. First, each sub-channel is assigned to the user with best channel-to-noise ratio for the channel, with random power distributed by water filling algorithm. The proposed genetic search helps fast convergence and can handle large allocations of subcarriers to users without performance degradation. The simulation results show that genetic algorithm approach will be used where complex computations are involved and near optimal solution are acceptable for optimum resource allocation. Keywords Adaptive modulation, frequency selective fading channel, multiaccess communication, multiuser channel, orthogonal frequency division multiplexing (OFDM), resource management. I. INTRODUCTION Many authors have recently considered the problem of subcarrier, bit and power allocation in multiuser orthogonal frequency division multiplexing (MU-OFDM) systems [7], [8], [10], [12]. In these studies it is assumed that the base station (BS) knows the channel state information (CSI) for all the users and, using the CSI, dynamically assigns a subset of subcarriers to each user and allocates the power and modulation scheme for each subcarrier. In general, a constrained optimization problem makes it formulated wherein the object is to minimize the total transmit power (resp. maximize the total data rate) for the entire OFDM block while satisfying some constraints for the average bit-error-rate (BER) and the data rate of each user (resp. the total transmit power). The optimal subcarrier, bit and power allocation is a challenging task and its complexity prohibitive in practical communication systems [6], [9]. To avoid this difficulty, a tractable approach is to divide this problem into two separate problems: first find the optimal allocation of subcarriers to users, and next find the optimal allocation of bit and transmit power for each user. The solutions for the bit and power allocation problem are given in [1]-[5].Several suboptimal solutions for subcarrier allocation have also been proposed in [7], [10], [12]. The main drawback of the algorithms proposed these references is their high computational complexity. While these algorithms may be applicable in wire line systems where the CSI remains static for extended periods of time, they are not suitable for the wireless environment where, even in the case of slowly fading channels, the CSI needs to be updated (and the solution recalculated) after several OFDM blocks. Recently several authors have considered the problem of imperfect channel state information and its effect on bit and power allocation. In this paper, however, our main focus is on reducing the computational complexity of the bit and power allocation algorithms. We therefore assume perfect knowledge of the channel state information. The problem of optimal subcarrier, bit and power allocation is divided into two separate problems. A simple but efficient algorithm is presented for subcarrier allocation. The optimal bit and power allocation problem is formulated as a mixed integer programming problem. II. BASIC OFDM SYSTEM The transmitter section of the OFDM system is shown in figure 1. The basic working principle of the OFDM is that a high bit rate input is split into parallel lower bit rates and transmitted across the channel. The use of parallel transmission effectively increases the symbol duration and reduces ISI considerably. OFDM uses orthogonal carrier frequencies to modulate input data. Orthogonally of the carrier frequencies ensures that multiple-access is made possible in OFDM and thus each subcarrier carries unique information corresponding to the input data. It also cancels Inter-Carrier Interference (ICI). OFDM is the wireless counterpart to Discrete Multitone Modulation. Figure 1: Basic OFDM Transmitter System A high bit rate data stream is divided into N parallel low bit data streams each at a rate of 1/N. Each data stream is modulated using different subcarriers (orthogonal carrier frequencies) in their respective sub channels. Pulse shaping methods (Rectangular Pulse Shaping in the case of OFDM) are employed to modulated signals in order to 854

reduce the effects of ISI, reduce sensitivity to frequency and to minimize bandwidth requirements. Applying pulse shaping OFDM results in the subcarriers resembling sinc functions. This ensures that the sidebands of adjacent carriers overlap at zero crossings of the sinc function. This feature is shown in figure 2 and 3 for OFDM systems. The Inverse Fast Fourier Transform gives the Mathematical equivalent for pulse shaping. Thus, the IFFT of the modulated symbols is taken to obtain the required OFDM signal. Due to pulse shaping, the side lobes of the sinc functions are significant and there can be a lot of out-of-band interference. Also, pulse shaping requires that there is almost perfect frequency synchronization. The division of the signal to a large number of more of less independent channels will provide the flexibility needed for all foreseen future multimedia services (variable bit rate with different quality of services).potential drawbacks with OFDM as a multiple access concept are mainly based on that OFDM is a relatively young technique and there are open issues where still no optimum solution has been found. Topics which still are under active research are: Tools needed for the system to stay orthogonal. This is a problem essentially on the uplink. Studies have shown that there are methods for handling these types of problems. The high dynamics of the broadband signal implies a need of a wide range linear power amplifier (note that this is a general problem applicable to all broadband systems). OFDM is a spectrum efficient multiplexing technique that has proven functional in other concepts and standards as [1] [9] [10]. Figure 2: Single Carrier of OFDM In general it can be said that uncertainties concerning OFDM as a multiple access concept concerns the system uplink. The main issue is to keep the mobile synchronized to the base stations time and frequency grid. This means that the mobiles must transmit the information with some timing advance due to the different propagation delay of the radio channels. The mobiles need to be synchronized to preserve the system orthogonally and avoid inter channel interference (ICI). The downlink follows the same paths as the broadcast concepts and has already proven functional. Because all users are multiplexed in the base station they are always orthogonal to each other. Figure 3: Multiple carriers of OFDM III. OFDM AS MULTIPLE ACCESS CONCEPT The interest shown for the OFDM technique during the past years indicate interesting qualities as stated in [3][5]. According to results from different activities the most beneficial properties with the OFDM concept, from our point of view, are: Each transceiver will have access to all subcarriers within a cell layer (these enable very high bit-rates). There is more or less no need of frequency planning within a cell layer (it is performed with an Adaptive Channel Allocation algorithm). The technique will handle packet data services and mixtures of packet and circuit services. The subcarrier modulation is performed with a Fast Fourier Transform (FFT) which is a well-known algorithm and should be considered as a compact digital modulator (easy to implement). The division of the spectra to a large number of narrow banded, flat fading channels allows easy equalization even in environments with severe delay spread. IV. GENETIC ALGORITHM BASED ALLOCATION Genetic Algorithms (GAs) [6, 7, 12, and 15] provide learning method motivated by an analogy to biological evolution. Rather than search from general-to-specific hypotheses, or simple-to-complex, GAs generate successor hypotheses by repeatedly mutating (mutation is a genetic operator used to maintain genetic diversity from one generation of a population of chromosomes to the next) and recombining parts of the best currently known hypotheses. At each step, a collection of hypotheses called the current population is updated by replacing the fraction of population by offspring of the most-fit current hypotheses. The process forms a generate-andtest beam-search of hypotheses, in which variants of the best current hypotheses are most likely to be considered next. The genetic algorithms applications are inspired by many factors: A successful and robust method for adoption within biological systems. Possible to search spaces of hypotheses containing complex interacting parts, where the impact of each part on overall hypothesis fitness may be difficult to model. 855

Easily parallelized and can take the advantage of the decreasing costs of powerful computer hardware. The subcarrier allocation problem to multiple users has many different permutations; thereby making the solution space very large and a suboptimal allocation of subcarriers to users are acceptable. The GAs most suitable where the solution space is very large and a suboptimal solution may be sufficient in many scenarios. The problem addressed by GAs is to search the space of candidate hypotheses to identify the best hypotheses by a fitness function. The typical GA operates by iteratively updating a pool of hypotheses, called a population. During each iteration, the members of the population are evaluated according to the fitness function. A new population is then generated by probabilistically selecting the most-fit individuals from the current population which is forwarded to next generation population. Chromosome element -1 Subcarrie r 1 Chromosome element -2 --- Subcarrier 2 --- Figure 4: Coding of Genetic Algorithm Chromosom eelement n Subcarrier n GA is an artificial genetic system which is based on the processes of natural selection and natural genetic and has been effectively implemented in an optimization scheme. The genetic based optimization scheme is modeled by three major operators: Reproduction, Crossover and Mutation. Unknown variables are stored in a place, named Population and will be manipulated by the operators consecutively as shown in the basic GA Cycle diagram, figure5. The iterative improvement generally leads to near optimal solutions. The above discussion shows that GAs are suitable for the optimization of the subcarrier and bit allocation problem in a multiuser OFDM system. The processing steps in GA based algorithm are as follows: 1. Generate chromosome of N elements (minimum length of chromosome is assumed as 50, thus there are 50 subcarriers) and total number of chromosomes (population) as 30 for the experiment. Each element in the chromosome is a subcarrier allocated to a user (one user may be allocated more than one subcarrier). Thus the population is a 2-D array, where the rows represent chromosome number and column of a row represents subcarriers. 2. Evaluate- use the water-filling method to allocate each user s bits and subcarrier and calculate the overall transmission power. 3. Generate the new population using crossover and mutation probability. 4. Repeat step 2 and step 3 till the system converges. In this paper, the authors calculated each user s power requirement and the total transmission power required by all users. The subcarriers allocated as per the user s request arrives. The fitness is equal to the power required for all users or required by all subcarriers allocated to users. The lower the value of power P * k,n the higher the fitness. The genetic algorithms had built-in selection of stronger individuals to be the winners from the old generation to new generation. Each chromosome had the format shown in figure 4. The value of each element in the array (chromosome) is confined to a user signal and randomly generated. The array represents a solution to the optimization problem. Figure 5: Genetic algorithm cycle A. Initial population creation The features of initial population have important effects on the convergence speed and the final solution. Especially in our problem, the proper creation method for initial population is extremely important, because the search space is large and varies with different timeslots. Since we cannot compute out the feasible solution space before we search the optimal solution, we have to execute a refining algorithm when creating the initial population, so that the initial population includes far as more feasible and even "good" individuals as possible. The refining process is simple and only needs a linear searching time: for the sub-carrier channel, if the magnitude of the channel gain of the sub-carrier as seen by the assigned user is below a threshold, we set the assigned rate to be very small or even 0, otherwise we randomly assigned the transmission rate. So the purpose of the refining operation is to remove the solutions that obviously violate the energy constrains and select a feasible solution or even "good" chromosome in the refined population. 856

B. Fitness function The fitness should respond the individual performance: the "good individual" (its utility function is fairly large) has bigger fitness than the "bad one" (its utility function is fairly small). Therefore, the fitness function can be just defined as the system utility function (1). C. Selection, Crossover and Mutation operation In our genetic algorithm, an elitist model is adopted as the selection operator. By the model we first select the optimal individuals and directly copy them to the next generation, and then select the rest by the proportional model. The crossover scheme is selected as parents to produce an offspring. Because we have good population after refining the initial population, the crossover operations and mutation operation used in our algorithm is not special, and can be selected from the popular algorithm. V. OFDM SIGNALS OFDM is a communication method which can be viewed as a modulation scheme or a multiplexing technique. In OFDM, the carrier spacing is selected such that each subcarrier is orthogonal to the other subcarriers. Two signals are spectrally orthogonal if the following condition is true: ( ) convert them into parallel format since IFFT module requires parallel input to process data. The serial to parallel module does the conversion. These parallel symbols are transformed from frequency domain into time domain using IFFT module. These signals are converted into serial format and add a cyclic prefix to data frame before being transmitted. B. Simplified Receiver Block Diagram Figure 7: Simplified receiver block diagram Figure 7 show the basic block diagram for receiver module. There are five modules in the receiver block and as mentioned before, cyclic prefix removal will not be included into the design. The received data is in serial format, thus, since FFT input is in parallel, a module which converts from serial to parallel is required. Output from FFT is converted back to serial format through parallel to serial converter. The conversion is required since the serial data need to be transmitted. Finally the serial output is demodulated using demapping module to get the transmitted data. Where T is the period, Â1 and Â2 are input signals, and P denotes complex conjugate. A. Simplified Transmitter Block Diagram VI. SIMULATION RESULTS Figure 6: Simplified transmitter block diagram Figure 6 show the simplified block diagram of OFDM transmitter. It can be seen that the block is divided into several parts with each block function different and this is to ensure that the system works effectively. Since the main component is processing block, so, the work is started from this part. All block set function is implemented in the FPGA development board. Cyclic prefix is a module, which is used to concatenate partial end of information bit and put at the beginning of the information frame. But in this project cyclic prefix is not included in this design because it is not within the scope of the investigation. The generation of OFDM signal started from amplitude modulation mapping bank. The serial input data is mapped to appropriate symbol to represent the data bits. These symbols are in serial format and are needed to Figure 8: BER of AWGN channel The BER curve for AWGN channel is shown in figure 8 the target bit error rate is set to 10-5 857

increased complexity and higher transmitter and receiver demands. However, for certain systems, modern digital signal processing techniques now make it possible to use this modulation system to improve the reliability of the communications link. From the above simulated waveforms, the transitions can be observed which will be useful for understanding the performance of the system in real world implementation. The power estimation is done to approximately determine the amount of power required for implementation. Future scope is to generate number of bits assigned to each carrier which can be varied with a bound on average BER. REFERENCES [1] G. Young, K.T. Foster and J.W. Cook, 1995, "Broadband Multimedia Delivery over Copper", BT Techno J., Vol 13, No. 4, October 1995. Figure 9: BER of Rayleigh fading channel The BER curve for Rayleigh fading channel is shown in figure 9 the target bit error rate is set to 10-4. [2] William Stallings, 2002, Communications and Networks, Prentice Hall, ISBN: 0-13-040864-6, 2002. [3] L. C Cimini, 1985, Analysis and Simulation of a Digital Mobile Channel Using Orthogonal Frequency Division Multiplexing, IEEE Transactions on Communication. N.7 July 1985. [4] S. B. Weinstein and P. M.Ebert, Data Transmission by frequency division multiplexing using the Discrete Fourier Transform, IEEE. [5] M. Alard and R. Lasalle, 1987, Principles of Modulation and Channel Coding for Digital Broadcasting for Mobile Receivers, EBU Review - Technical, August 1987. [6] A. Coley, 2003, An Introduction to Genetic Algorithms for Scientists and Engineers, World Scientific, ISBN: 981-02-3602-6, 2003. Figure 10: Simulation result for transmitter [7] H. S. Kim, J. S. Kwak, J. M. Choi and J. H. Lee, 2004, Efficient Subcarrier and Bit Allocation Algorithm for OFDMA System with Adaptive Modulation, IEEE Vehicular Technology Conference, V59, n3, pp.1816-1820, 2004. [8] J. J. Beek, O. Edfors, P. O. Borjesson, M. Wahlqvist and C. Ostberg, 1996, A conceptual Study of OFDM-based Multiple Access Schemes, Technical Report# 10/0363-5/FCPA 109 0001, August 21 1996. [9] European Broadcasting Union, "Digital sound broadcasting to mobile, portable and fixed receivers". [10] Y. Wong, C. Y. Tsui, R. S. Cheng and K. B. Letaief, 1999, A Real-time Sub-carrier Allocation Scheme for Multiple Access Downlink OFDM Transmission, IEEE VTC 99. Figure 11: Simulation result for receiver VII. CONCLUSION OFDM techniques are quickly becoming popular for advanced communications networks. Advances in VLSI technology have made it possible to efficiently implement a FFT block in hardware. OFDM should not be considered for every communication system because of its [11] H. F. Harmuth, 1960, On the transmission of information by the orthogonal time function, AIEEE Trans.Vol.79, pp.248-255, July 1960. [12] Y. F. Chen, J. W. Chen and C. P. Li, 1994, A Real-time Joint Subcarrier, Bit and Power Allocation Scheme for Multiuser OFDM-based Systems, IEEE VTC 04. [13] J. Rinne and M. Renfors, 1994, The Behavior of OFDM signals in an amplitude limiting channel, in Proc.of.ICC 95.pp.381-385, 1994. 858

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