Amended ( Wavelet ) Multiband OFDM Cognitive Radio System

This study focuses on improving the functioning of multiband Orthogonal Frequency Division Multiplexing (OFDM) system by utilizing wavelet transform as a substitute to Fast Fourier Transform (FFT). The performance is further refined by apt inclusion of modulation technique. Error control codes are utilized which aims at the removal of error from the transmitted bits. In addition to attain diversity Alamouti code is concatenated with error control codes. OFDM is the best fit for cognitive radio and sensing the free holes is the key task of any cognitive system. This study additionally also analyses the performance of energy detection based spectrum sensing in the presence of various noise models.


INTRODUCTION
The wide spectral width of ultra wide band spectrum extending from 3.1 to 10.6 GHz makes it difficult to handle.To overcome these challenges multiband OFDM came into existence by virtue of its high data rates, less power consumption and need of less silicon space (Balakrishnan et al., 2003).The multiband OFDM divides the spectrum into numerous sub-bands (Praveenkumar et al., 2012), among which the 128 available sub-carriers with sub-carrier spacing of 4.125 MHz, 100 is used for data transmission, 12 as the pilot carriers, 10 as guard tones and 6 as null tones.In ultra wide band the entire spectrum is divided into 5 major groups, consisting of 3 sub-bands with an exception of the last group with 2 sub-bands making a total of 14 (Avila et al., 2012).
The block diagram depicting the MB-OFDM is shown in Fig. 1.A random sequence of input data generated by a scrambler followed by encoding the channel using an encoder.The error control codes are used to correct multipath fading of the communication channel, concatenation of such codes is implemented to increase the coding gain and efficiency of the system in noisy environment.The encoded bits are then fed into a 3-stage interleaver which provides stability against burst error and are mapped into constellation samples.An OFDM modulator converts the mapped output from the IFFT block into OFDM symbols.The demodulation and decoding of retrieving the original sequence is administered by the receiver (Thenmozhi et al., 2012;Batra et al., 2006).
For reliable communication, error control codes are added along with the message Reed Solomon codes, which are non-binary and depends on Galois field.The relation 2x = Y -l signifies its error correcting capability, here Y represents the length of the code and 1 represents the message.The maximum length of the code is given by 2 c -1 where c is the number of bits (Viraktamath and Attimarad, 2010).The performance of the convolutional codes depends on the constraint length which is nothing but the number of stages of shift register.With the increase in constraint length the accuracy increases.
The turbo codes are implemented by serial or parallel connections with convolutional codes and its recital is influenced by the decoding algorithm, interleaver size and constraint length (Hoosier et al., 2000).
The binary phase shift keying is preferred due to its simplicity and durability and has 180° phase change between binary one and binary zero.The transmitted signal is given by Sanjeev and Swati (2010): where, The probability of error is given by: where, M 0 = Power spectral density of noise Quadrature Amplitude Modulation (QAM) has both amplitude change and phase change.QAM supports M-ary signaling and the type of QAM to be where, E = Amplitude of the signal d o (t) = Odd number sequence d e (t) = Even number sequence Quadrature phase shift keying introduces a phase change of 45° between the bits in the symbol and 90° phase shift between symbols.It supports two bits at a time .The probability of error is given by:

METHODOLOGY
Wavelet transform: The IDWT and DWT blocks replace the IFFT and FFT blocks respectively in the transmitter and receiver of Fig. 1.The time and frequency domain both support the wavelet transformation, which plays key role in wide range of applications in many fields like image processing, signal processing etc.The primary operation of wavelet transform is filtering.In the wavelet tree the incoming signal is portioned into low and high frequency components.High frequency components provide precise outcome while low frequency components provide approximate output (Gupta et al., 2008;Das et al., 2011).
Haar wavelet gains popularity because of ease and simplicity (Mahmoud et al., 2007).Wavelet coefficients are generated by reversal of order of scaling coefficients and sign change of the second term.From the inner product of data and coefficients the scaling and wavelet functions could be obtained.Symlet wavelet (Chavan et al., 2011) transform, a modified version of Daubechie is more symmetric having even index number and minimal phase.Yet the most efficient and symmetric wavelet than the above wavelets is the Coiflet wavelet.
Cognitive radio: Cognitive radio is an artificial intelligence (Haykin, 2005) based device that changes its parameters according to the environment.Spectrum sensing is the basic step in cognitive radio from which it comes to know about the free spectrum.The main focus is on the performance of energy detection based spectrum sensing under various noise models like AWGN, Rayleigh fading, Rician fading and lognormal fading.
The block diagram of the energy detector method is as shown in Fig. 2. In energy detection method the Power Spectral Density (PSD) of the incoming signal is found out and it is compared with the threshold.Based on the following hypothesis the decisions are made:  Additive White Gaussian Noise (AWGN) can be conceived as a channel model that has a constant power spectral density.Thus, it is obtained through several natural sources and is called so due to the addition of white noise.It is suitable for satellites and has applications in deep space communication links though not been much used for terrestrial links.The received signal is the signal additively combined with noise.The PSD is given as: where, σ is the variance of noise.
Rician noise model assumes that there is at least one Line of Sight (LOS) path between transmitter and receiver.The noise model is based on the parameter known as Rican factor K. It is defines as the power in the LOS path to the power in the other paths.Hence as the value of K increases the signal strength increases which in turn reduces the error.Rayleigh noise model assumes that is no line of sight communication between the transmitter and the receiver.The signal gets attenuated following the Rayleigh distribution (Rasheed et al., 2010).
In this study Haar and Symlet wavelet transforms are exchanged in the place of FFT.To battle with the channel noise Reed Solomon code, Turbo code and convolutional code are utilized.To achieve diversity Alamouti code is concatenated with the error control codes and the act of the multiband OFDM system is analyzed in the presence of BPSK, QPSK and QAM.Further with the multiband OFDM acting as cognitive radio its performance is analyzed in the occurrence of various noises.

RESULTS AND DISCUSSION
The outputs are obtained by means of MATLAB tool.The performance metric is Bit Error Rate (BER) versus Eb/N 0 curve plotted for the multiband OFDM system Figure 3a and b displays the result of Alamouti code combined with Reed Solomon code.Here the traditional Fast Fourier Transform is modified with wavelet families namely Symlet and Haar respectively.Since these wavelet families satisfy orthogonality property they become best choice for the replacement of FFT with BPSK as the modulation scheme.It is highly desired because it is fewerfaultscheme when compared with other schemes.In both the cases due to better coding gain and diversity for a given BER of 10 -4 the concatenated code domineers the individual ones.Figure 5a and b shows the output of the turbo concatenated with Alamouti code with FFT being replaced with wavelet family Haar and Symlet respectively.The concatenated code offers better results when compared with individual code for a given BER of 10 -5 .The results are plotted for QAM modulation techniqe.When compared with other concatenated schemes this method provides better output in terms of BER.
Figure 6 gives the comparison between for various values of Rician factor which is denoted by K.As the K value increases the line of sight communication dominates and the probability of encountering deep fade decreases and it approaches the AWGN performance.
Figure 7 gives the comparison between probability of false alarm (p f ) and probability of missed detection  QAM modulation technique.Simulation results prove that with proper choice of modulation technique, FEC and wavelet family the presentation of the multiband OFDM can be significantly improved.In addition when treated as cognitive radio is analyzed in the presence of various noise models.

Fig. 1 :
Fig. 1: Block diagram of multiband OFDM system used is chosen based on the application (Bernard and Pabitra, 2001): H o = Noise -Primary user absent H 1 = Signal + noise -primary user present

Fig. 7 :
Fig. 7: Comparison between various noise models CONCLUSION The performance of DWT based MB-OFDM is monitored for Symlet and Haar wavelet families.Convolutional code, Turbo code and Reed Solomon codes are used as channel coding to counteract the channel noise and further to improve the diversity they are combined with Alamouti code.The performance is also analyzed in the presence of BPSK, QPSK and