BER Performance of OFDM System in Rayleigh Fading Channel Using Cyclic Prefix

In this research paper, we will focused on the bit error rate (BER) performance of Orthogonal-frequency division multiplexing (OFDM) of various modulation techniques. The Orthogonal Frequency Division Multiplexing (OFDM) is the popular modulation technique for the many wireless communication systems. In the wireless system, the signal transmitted into channel bounces off from the various surfaces resulting in the multiple delayed versions of the transmitted signal arriving to the receiver. The OFDM has trusted to be very effective in mitigating adverse multi-path effects of a broadband channel. The multiple signals are obtained due to the diffraction and reflection of electromagnetic waves around objects .The bit error rate (BER) performance of this type of systems are evaluated in the additive white Gaussian noise (AWGN) channel. The BER performance of the transmission modes are calculated by calculating the bit error rate (BER) versus signal to the noise ratio (SNR) under the Additive white Gaussian noise (AWGN), channel.


INTRODUCTION
It is very important to calculate the performance of the wireless systems by considering the transmission characteristics, parameters of the wireless channel and the device structure.The Bit Error Rate Ratio (BER) is considered to be one of the most extensively used performance measures for wireless communication systems and hence it has been extensively studied. In our research paper, we proposed a novel approach to calculate the average probability of error by using OFDM modulation techniques and by considering an approximation of the spatial filter. In present time, ULTRA WIDE BAND (UWB) communication technology is an emerging as a popular standard for high-data-rate applications over wireless communication networks. Due to the use of its highfrequency bandwidth ,the UWB can achieve very high data rates over the wireless connections of multiple system devices at a low transmission power close to the noise floor.Since the power level required for the UWB transmissions is low, so UWB devices will not generate significantly harmful interference to the other communication standards. A major difference between conventional radio transmissions and the UWB is thatthe conventional systems sends information by changing the power level, frequency, and/or phase of a sinusoidal wave whereas in the UWB transmissions information is transmitted by generating radio energy at the specific time intervals and covering a large bandwidth, thus enabling pulse-position or time modulation.In the wireless channels, several models have been introduced and investigated to calculate SNR. Every models are a function of the distance between the transceiver, the path loss exponent and the channel gain. The Several probability distributed functions are also available to model a time-variant parameter i.e. channel gain. It is highly believed that the OFDM results in an improved multimedia download services requiring high data rates communications, but this condition is significantly controlled by inter-symbol interference (ISI) due to the existence of the multiple paths. The Multicarrier modulation techniques, including OFDM modulation are considered as the most depending technique to overcome this problem .The OFDM technique is a multi-carrier wireless transmission technique which is being considered as an excellent method for the high speed bi-directional wireless communication of data.

II.
OFDM TECHNIQUE The Orthogonal frequency division multiplexing (OFDM) is a wireless communications technique that breaks a communications channel into a number of equally spaced frequency bands. A sub-carrier having a portion of the user information is sended in each band. Each sub-carrier is the orthogonal (i.e. independent of each other) with other subcarrier; distinguishing OFDM from the commonly used The data are transmit over parallel sub-channels with each sub-channel modulated by the modulation scheme such as BPSK, QPSK, QAM etc. The benefitof theOFDM is its ability to cope with severe channel conditions compared to a single carrier modulation scheme but still maintain the data rates of a conventional scheme with the same bandwidth. The Orthogonal Frequency Division Multiplexing has become one of the main physical layer techniques used in the modern communication systems.

III.
CHANNEL MODEL 1. AWGN Channel :When the impairedcommunication channel are linear addition of wide band or the white noise consisting constant spectral density over infinite period and the amplitude is Gaussian distribution then such a channel model is known as AWGN channel [1].

Fig.3:Gaussian distribution of white noise
The High data rate communication over the additive white Gaussian noise channel (AWGN) is limited by the white noise .The received signal in the interval range 0≤ t≤ T may be given asr(t)=sm(t) + n(t) Where n(t) represents the sample function of additive white Gaussian noise (AWGN) process with power-spectral density. 2. Rayleigh channel model:TheRayleigh fading environment is described by the many multipath components, each having relatively similar signal magnitude, and uniformly distributed phase, that means there is no line of sight (LOS) path between transmitter and receiver.The channel in which the signal takes various path to reach the receiver after getting reflect from various objects in the environment. The signal receiving at receiver is sum of the reflected signal and the main signal. The signal in the environmentget diffracted or reflected from the objects like tree, building,moving vehicle etc and imposes problem when the envelope of the ndividual signal is added up [2].

International Journal of Advanced Engineering Research and Science (IJAERS)
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IV. MODULATION SCHEMES (i). Binary Phase Shift Keying (BPSK)
The PSK uses a finite number of phases; each areassigned with a unique pattern of binary digits. Generally, each phase encodes an equal number of the bits. Each pattern of the bits generates the symbol that is denoted by the particular phase. The BPSK is the simplest type of phase shift keying (PSK). It consists of two phases which are separated by 180° and so they can also be named as 2-PSK. It does not matter exactly that where the constellation points are positioned, and in the below figure they are represented on the real axis, at 0° and 180°. The QPSK have four points on the constellation diagram, and areequispaced around a circle. With four phases, QPSK can encode the two bits per symbol, shown in the figure with gray coding to reduce the bit error rate (BER)some times it misperceived as twice the BER of the BPSK. The mathematical studies shows that QPSK can used either to double the data rate when compared with a BPSK system while maintaining the same bandwidth of the signal, or to maintain the BPSK data ratebut halving the needed bandwidth.

(iii). Quadrature amplitude modulation (QAM)
TheQAM is the modulation scheme which encode the information into a carrier wave by varying the amplitude of both the carrier wave and a -quadrature carrier that is 90ᵒ out of phase with the main carrier wave in accordance with the two input signals. It means that, the amplitude and the phase of the carrier wave are simultaneously varied in accordance to the information we want to transmit.The symbol rate is one fourth of the bit rate. So this modulation format produces a more spectrally efficient transmission. It is more efficient than BPSK, QPSK.

Simulation Results and Graphs
MATLAB software has been used to simulate the OFDM scheme with different modulation schemes and the performance is plotted in the form of Bit Error Rate (BER) vs Signal to Noise Ratio(SNR) plots, as shown in the below figures. The probability of error has also been computed and plotted against the SNR. Figure 12 shows the power spectral density plot against the sampling frequency, which shows the orthogonality of the OFDM signals.