# Design and Simulation of COFDM for High Speed Wireless Communication and Performance Analysis

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2 Following this introduction the remaining part of the paper is organized as follows. Section 2 provides brief overview of the COFDM system. This section explains the concept and introduces the OFDM system standard. In Section 3, the details of the modeling and simulation of the system using MATLAB is presented. Then, simulation results have been discussed in Section 4. Finally, Section 5 provides the conclusions. 2. OVERVIEW OF COFDM SYSTEM OFDM is derived from the fact that the high serial bit stream data is transmitted over large (parallel) number sub-carriers (obtained by dividing the available bandwidth), each of a different frequency and these carriers are orthogonal to each other. OFDM converts frequency selective fading channel into N flat fading channels, where N is the number of sub-carriers. Othogonality is maintained by keeping the carrier spacing multiple of 1/Ts by using Fourier transform methods, where Ts is the symbol duration. Since channel coding is applied prior to OFDM symbol generation which accounts for the term coded in COFDM. Orthogonality between sub-carriers is maintained if sinusoids have integer number of cycles in Ts given by (1) below Where f c is the sub-carrier frequency. Frequency Division Multiplexing (FDM) divides the channel bandwidth into sub channels and transmits multiple relatively low rate signals by carrying each signal on a separate carrier frequency. To ensure that the signal of one sub channel did not overlap with the signal from an adjacent one, some guard-band was necessary which is an obvious loss of spectrum and hence bandwidth. But since carriers are Orthogonal to each other in OFDM therefore it offers bandwidth efficiency as no guard band is required as shown in Figure 1 below. Figure 1. Bandwidth conservation (a) FDM (b) OFDM [1]. Figure 2 presents the power spectral density of OFDM signal for 97 subcarriers. It may be seen that the spectral shape is given by a sinc function. Also at the center frequency of each subcarrier, there is no crosstalk. Therefore, if we use FFT at the receiver and calculate correlation values with the center of frequency of each subcarrier, we recover the transmitted data with almost no crosstalk. (1) Figure 2. Power Sprectral Density of OFDM signal (a) On linear scale (b) Logarithnic scale [3]. The COFDM system consists of three main elements. These are Channel coding/interleaving, IFFT and Guard interval/cyclic prefix. These technical aspects make the system resistant to ISI and multipath fading. Fig. 3 presents the basic block diagram of OFDM transmitter and receiver. The basic principle of OFDM is to split a high-rate data stream into a number of lower rate streams to be transmitted simultaneously over a number of subcarriers. The relative amount of dispersion in time caused by multipath delay spread is decreased because the symbol duration increases for lower rate parallel subcarriers. The other problem to solve is the inter symbol interference, which is eliminated almost completely by introducing a guard time in every OFDM symbol. This means that in the guard time, the OFDM symbol is cyclically extended to avoid intercarrier interference [7]. The incoming data is first converted from serial to parallel and grouped into x bits each to be modulated by Quadrature Amplitude Modulation (QAM), Quaternary Phase Shift Keying (QPSK), or Binary Phase Shift Keying (BPSK). The required spectrum is then converted back to its time domain signal using an Inverse Fast Fourier Transform (IFFT), commonly used in most applications. The IFFT performs the transformation very efficiently, and provides a simple way of ensuring the carrier signals produced are orthogonal. The signals are then converted back to serial for transmission. A guard interval is inserted between symbols to avoid Inter symbol Interference (ISI) caused by multipath distortion. The discrete signals are converted back to analogue. Although it would seem that combining the inverse FFT outputs at the transmitter would create interference between subcarriers, the orthogonal spacing allows the receiver to perfectly separate out each subcarrier. The receiver performs the inverse process of the transmitter. The OFDM symbol in baseband is given by following (2): 23

3 Figure 3. Block diagram of OFDM transmitter and receiver. where N= no. of sub-carrier 2.1 Interpretation of IFFT & FFT The Fast Fourier Transform is a very efficient mathematical method for calculating DFT. It can be easily implemented in integrated circuits at fairly low cost. With the advances in VLSI and DSP technology the implementation cost of OFDM is drastically reduced since heart of OFDM is merely IFFT/FFT operation. But the complexity of performing an FFT is dependent on the size of the FFT. The direct evaluation of an N- point DFT using the following formula (3): (2) 2.2 Guard time and Cyclic prefix In order to overcome the problem of multipath fading environment and hence inter symbol interference ISI, it is common practice in OFDM technology to add guard interval between OFDM symbols. The guard interval is formed by a cyclic continuation of the signal so the information in the guard interval is actually present in the OFDM symbol. Guard interval makes the system robust against multipath delay spread. The guard interval is actually added by taking the copy of the last portion of the OFDM symbol and placing it at the start of the symbol as illustrated in Figure 4. Where k = 0, 1, 2.,N-1. DFT require N2 complex multiplications and N*(N-1) complex additions whereas use of FFT algorithm reduces the number of computations to the order of N/2*log2 (N) complex multiplications and N*log2 (N) additions. Moreover FFT algorithm works efficiently when N is a power of 2, therefore the number of sub-carriers is usually kept as power of 2. IFFT/FFT operation ensures that sub-carriers do not interfere each other. IFFT is used at the transmitter to obtain the time domain samples of the multicarrier signal. FFT is used to retrieve the data sent on individual sub-carriers. Therefore OFDM has a very simple implementation capability. (3) Figure 4. Guard time and Cyclic prefix. The last Tg portion of the symbol is appended and transmitted during the Guard time. Tu is the OFDM symbol time without guard interval. Tcp is the duration of the copied information in the guard interval using cyclic prefix. Therefore total OFDM symbol time Ts = Tu+Tcp. Guard time needs to be greater than maximum delay spread otherwise ISI results. The guard time also eliminates the need of a pulse shaping filter, and it reduces the sensitivity to time synchronization problems. Cyclic prefix helps in maintaining orthogonality between sub-carriers by 24

4 converting linear convolution into circular convolution in multipath environment and also avoids ICI (Inter channel interference). 2.3 Convolutional coding and Interleaving An OFDM system employs conventional forward error correction codes and interleaving for protection against burst errors caused by deep fades in the channel. Often it is concatenated with a block code for improving the performance. A Viterbi decoder for decoding a convolution code is easy to implement. Though coding improves the performance of the system, it decreases the spectral efficiency. Codes of different rates are used in conjunction with different modulation schemes to support different QOS. While error correction codes provide coding gain in the system, interleaving provides diversity gain. For OFDM, when a deep fade occurs in the channel the bits within the deep fade are erased. Interleaving the bits across different frequency bins distributes the energy within a symbol among different sub-carriers. Since distinct sub-carriers undergo different fading conditions, the probability that all the bits corresponding to a symbol are lost, decreases significantly. An uncoded OFDM system cannot exploit frequency diversity. Since in frequency selective fading channels, the sub-carriers separated by coherence bandwidth are independent of each other, the frequency diversity can be realized by spreading coded bits over different sub-carriers in such a way that adjacent bits are separated by coherence bandwidth. Coding and interleaving, diversity, equalization techniques decrease the irreducible error floors caused due to delay spread. An interleaver permutes symbols according to a mapping. A corresponding deinterleaver uses the inverse mapping to restore the original sequence of symbols. Interleaving and deinterleaving can be useful for reducing errors caused by burst errors in a communication system. A convolutional interleaver consists of a set of shift registers, each with a fixed delay. Figure 5 shows a convolutional encoder with constraint length L = OFDM physical layer parameters (IEEE a Standard) The OFDM physical layer parameters as per IEEE a standard are as shown in Table I and Table II. TABLE 1. PHYSICAL LAYER PARAMETERS Figure 5. Convolutional encoder (L=7) [7]. TABLE 2. PHYSICAL LAYER PARAMETERS 3. THE SIMULATION MODEL Figure 6 presents the complete block diagram of the COFDM system which was modeled and simulated by us in MATLAB environment. The main objective of this simulation study is to evaluate the BER performance of the COFDM system using convolutional coding with interleaving. The simulation parameters are obtained from Table I and Table II. A frame based processing is used in this simulation model. The system model was exposed to AWGN channel, Rayleigh fading channel and Rician channel for performance analysis. The important blocks of the simulation model is discussed in detail as follows: 3.1 Energy dispersal scrambler In order to ensure appropriate energy dispersal in the transmitted signal, the individual inputs of the energy dispersal scramblers shall be scrambled by a modulo-2 addition with a pseudorandom binary sequence (PRBS), prior to convolutional encoding. 25

6 Bit Error Rate Bit Error Rate Bit Error Rate----> Bit Error Rate IJCA Special Issue on 2nd National Conference- Computing, Communication and Sensor Network Figure 7 presents the BER performance for QPSK in AWGN and Rayleigh fading channel. As can be seen from Figure 7 that both theoretical and experimental BER are in good agreement with each other. It is concluded that use of channel coding could improve the BER performance. Bit error probability curve for QPSK == 4PSK modulation AWGN-theory AWGN-simulation RAYLEIGH- theory RAYLEIGH- simulation performance. It also seen that QAM lower SNR values as compared to PSK. Bit error probability curve for all modulations using AWGN channel BPSK QPSK 16-QAM 8-PSK 16-PSK 32 QAM 32-PSK Figure SNR in db-----> BER performance for QPSK modulation in AWGN & Rayleigh fading channel. Figure 8 shows that to achieve a BER of, the coded BPSK with Viterbi 3-bit soft decision decoding gives a coding gain of 2.5 db and 6 db compared with Viterbi hard decision decoding & uncoded BPSK modulation, respectively. Convolutional code with constraint length L=3, code rate 1/2 and generator polynomial in octal (7, 5) was used as parameters for this simulation. BER curve for BPSK modulation in AWGN channel with CC rate - 1/2, gen.poly - [7,5] simulation-uncoded Viterbi-HARD DECISION Viterbi-SOFT DECISION Figure 9. BER performance for BPSK, QPSK,16- QAM, 64-QAM, 8-PSK,16-PSK,32-PSK modulation in AWGN channel. Fig. 10 presents the effect of Rayleigh fading channel channel to the performance of COFDM system for different digital modulation techniques. For this the system was exposed to fading channel with Doppler frequency 40 Hz (i.e., v= 48 km/hr). It may be evaluated form the result that BPSK requires the least SNR for the same BER performance of and as we move towards higher modulation techniques higher transmitter signal power is required to achieve the same performance. Bit error probability curve for all modulations using rayleigh channel BPSK QPSK QAM 8-PSK 16-PSK 32-PSK 6 db Figure 8. BER performance for BPSK modulation in AWGN channel using Hard-Soft Viterbi decoding. Figure 9 presents the effect of AWGN channel to the performance of COFDM system for different digital modulation techniques. It may be evaluated form the result that BPSK requires the least SNR for the same BER performance of and as we move towards higher modulation techniques higher transmitter signal power is required to achieve the same Figure 10. BER performance for BPSK, QPSK, 8- PSK,16-PSK,32-PSK modulation in Rayleigh fading channel. 27

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