Wavelet Based Alternative Modulation Scheme Provides Better Reception with Fewer Errors and Good Security in Wireless Communication
Total Page：16
File Type：pdf, Size：1020Kb
ICSNC 2013 : The Eighth International Conference on Systems and Networks Communications ` Wavelet Based Alternative Modulation Scheme Provides Better Reception with Fewer Errors and Good Security in Wireless Communication Ramachadran Hariprakash Raju Balaji Sabapathy Ananthi Krishnaswami Padmanabhan Arulmigu Meenakshi Amman Instrumentation Dept, Instrumentation Dept Anna University College of Engineering, University of Madras University of Madras Chennai Tamilnadu, India Tamilnadu, India Tamilnadu, India Tamilnadu, India [email protected] [email protected] [email protected] [email protected] Abstract - In this paper, a different scheme of encoding digital data using wavelet functions instead of sinusoidal waves is explained. Data communications use various modes of encoding the data bits into a frequency signal. Phase shift keying of various forms such as Binary Phase Shift Keying, Quaternary Phase Shift Keying, etc., are in vogue in several current communication schemes, such as Global system for mobile communication. Errors in bits at the received end Fig. 2. The phase plot of QPSK symbols are having values in the through a wireless channel are common in such data complex plane marked. communication. These errors are mainly caused by improper phase changes in the detected audio signal. Since the method When symbols of various values are thus encoded as presented here with the use of wavelet functions provides analog sine modulation signals, we get a problem of several clues for identification of the data symbol instead of spectral leakage, since there are discontinuities from just by one criterion viz., the phase of the carrier as in the symbol to symbol waveforms. This introduces errors in Phase shift keying schemes, this method is found to be better the case of transmission with multiple carriers. For in performance. Simulation of the scheme was made with instance, a truncated sine wave for symbol 01 will have a Matlab and the results provide an improved bit error ratio. spectrum which spreads and is not confined to a single Also, by varying the wavelets as per the user’s choice, provides a higher level of security. point. The shape of the spectrum will be somewhat similar, as shown in Figure 3. Keywords - Data encoding; PSK Modem; Wavelet functions; Daubechie Wavelet; Bit Error Rate. I. INTRODUCTION Data communication has been employing several modes of encoding the data bits into an analog signal. Phase shift keying (PSK), in its various forms, such as Binary PSK, Quaternary Phase Shift Keying (QPSK), etc., use a baseband sine waveform with different phase positions to encode the data bits[1]. So far, alternatives to the sine wave signal for modulation have not been considered in any existing communication scheme, wired Fig. 3. The Fourier Transform (absolute value) of a data stream in a plain QPSK encoding modulating method is shown. or wireless. All of the current methods employ a combination of phase shifting and amplitude changes for An alternative modulation scheme using waveforms of encoding the data bits. For example, in Figure 1, the standard wavelet functions of the Daubechie (DB) type is QPSK modulation method uses four phases of the sine shown in Figure 1. These functions are mathematically wave, with 90o phase difference between symbols. In well defined and possess properties suitable for encoding phase notation, the four waves can be represented as and decoding. Four such wavelets, the DB4, DB6, DB8 0.7+0.7j, 0.7-0.7j,-0.7+0.7j, and -0.7-0.7j (Fig.2). and DB10 are shown as used for the same four symbols of data (00, 01, 10, and 11). Trying such alternative modulation is done with a view to provide fewer errors in reception and also with some security provisions. This is done by using wavelets assigned to the bit patterns that can be of user centric. Amongst the different wavelets known, such as Meyer [5], Coiflet [5], etc., the Daubechie wavelet [5], alone have several waveforms available for its different K- values and thus, it enables encoding more bit patterns per symbol. To understand the genesis and properties of Daubechie wavelets, one can refer Addison [2]. During the symbol Fig. 1. Comparison between existing sine wave QPSK modulation and time, the end points of the waveform reach zero level and proposed wavelet modulation. there is no discontinuity from symbol to symbol. This Copyright (c) IARIA, 2013. ISBN: 978-1-61208-305-6 50 ICSNC 2013 : The Eighth International Conference on Systems and Networks Communications ` helps in having a spectrum without any leakage. Well Section VI and the comparison with sine modulation is defined spectra result for such waveforms. So, in multiple detailed in Section VII. Section VIII deals with other carrier modulation methods as used in 802.11 and related attempts [12] bearing the name wavelets [13][14] and schemes, the method can be applied with definitely much finally, the paper ends with a conclusion section. better results. To point out the lacuna in an existing 802.11 multi II. ERRORS IN SYMBOLS – A COMPARISON carrier scheme, consider how the time signal is formed in The process of decoding a standard sine modulated that method, as clearly depicted in Figure 4. In this figure, (QPSK, 16 QAM) signal first requires the generation of for simplicity, five subcarriers are shown. Each subcarrier the reference sine wave from the first few data symbols, can have a particular phase angle of a few cycles of the which are the initialization symbols. A Costas loop is a sine wave used for modulation and this is represented as a technique [4] that is also used to generate this reference phase with a real part and an imaginary part, as shown in wave. If the reference signal is slightly out of phase, that the spectral representation as I and Q. gives errors throughout the data. Each carrier is at a frequency range which is twice, Then, a multiplication of the signal received with this thrice etc. of the first carrier. In order to generate the total reference is performed. The average of this product is time signal, which will include all the carrier frequencies, proportional to the cosine of the phase difference between from the low to the highest, in it, the present method just the reference and the received segment of the phase assumes that the symbol waveform can be represented as shifted sine wave in that time slot. For each time slot, the a phase of single value, such as 0.707+0.707j for one such phase is thus obtained. From this phase, the data symbol is QPSK symbol. From Figure 3, we note that is incorrect, decoded. With additional amplitude modulation as in because of the discontinuous nature of the segment of a QAM mode, the amplitude of the signal is also used to QPSK signal. In Global System for Mobile determine the symbol value. Communication (GSM), a Gaussian filter is applied to the In other words, the only information used for decoding symbol waveform called Gaussian minimum shift keying. is the phase of the signal. Phase of a sine wave is often Even still, there are discontinuities between symbols in subject to delays and changes en-route that is the reason the signal in time domain. for the errors in the received data. Let us now describe the decoding method when wavelet signals are used. A wavelet signal is a well defined mathematical signal, which has a compact support and a finite spectrum without spreading like the phase shifted sine wave segments. The pattern of each of the Daubechie signals is different and specific [5]. Thus, there are several criteria available for determining, in any one time slot, which wavelet is received. First of all, from the received data, which is converted into digital numbers from the analog to digital convertor in the receiver, we have to isolate the symbols. This is the process of synchronization. In this case, it is much easier than for sine phase modulated signals. The first few data symbols are known and are identical. The first peak and Fig. 4. The present method of forming a time signal for RF modulation in a Multi-carrier baseband scheme [3]. then the peak of the second symbol are fetched. The midpoint of data is a starting point for the second symbol. The mistake committed in the present scheme for We know the number of data points in a symbol from the getting the time signal from multiple QPSK (or even two peak positions. From then on, the data samples can be higher density schemes like 16QAM, 64QAM, etc.) lies in isolated easily. assuming that the spectrum of each carrier is a single The wavelet functions possess several peaks. The point phase. Only if the sine wave is continuous for all following criteria for decoding have been used by the time, the Fourier spectrum will be a single phase. So, authors. combining these single phases at f1, f2, f3… etc. through i). RMS value of the autocorrelation function: an inverse Fourier Transform (FT) to generate the total time slot signal is having spectral leakage errors. These This calculation resembles the calculation made in the spectral leakage errors can definitely contribute to inter- sine modulation existing methods. Correlation is symbol interference while decoding the signal at the multiplication, shifting and addition, and the estimation of the Root Mean Square (RMS) value. received end. The rest of the paper is arranged as follows. Section II ii). Peaks their ratios and spacing is another criterion: gives a comparison of errors for standard QPSK and Among the DB4 to DB20 wavelets, the peaks differ. wavelet modulation. Section III deals with the bit error The number of peaks increases for the higher degree estimates for the proposed method.