Fast Fourier Transform of Frequency Hopping Spread Spectrum in Noisy Environment

OPTICAL COMMUNICATIONS (ELECTROSCIENCE '8), Trondheim, Norway, July -4, 8 Fast Fourier Transform of Frequency Hopping Spread Spectrum in Noisy Environment ABID YAHYA Collaborative MicroElectronic Design Excellence Center Universiti Sains Malaysia, Engineering Campus OTHMAN SIDEK Collaborative MicroElectronic Design Excellence Center Universiti Sains Malaysia, Engineering Campus MOHD FADZLI MOHD SALLEH School of Electric and Electronic, University Science Malaysia 43 Nebong Tebal, Pulau Penang, Malaysia Abstract: - Frequency hopping spread spectrum (FHSS) systems have traditionally been applied in low data rate applications where the received signal can be considered narrow band. In this paper we have discussed a synchronous coherently detected FHSS/BPSK system. Pseudonoise sequence generator has been implemented to select the frequencies for transmission or reception. We have investigated the spectral characteristics of both spread and nonspread BPSK waveforms. We have analyzed and simulated these systems with several variations by taking the Fast Fourier Transform (FFT) of FHSS with original binary sequence and with noisy signal. The simulated results have shown that a signal lingering at a predefined frequency for a short period of time limits the possibility of interference from another signal source generating radiated power at a specific hop frequency. Key-Words: - Frequency hopping spread spectrum, Correlation, Pseudonoise, Fourier transform Introduction Digital communication has become an essential part of the lifestyle in most parts of the world. The desire to access information and media around the globe, in the comfort of the home or the office, has lead to an exponential increase in the use of the Internet and other data services. The demand for such services has inspired telecom operators of large-scale wireless systems to seek new revenue by extending their service selection from the traditional voice service to provide data services on an anywhere-anytime basis. The performance of a communications system depends on system designer and environmental parameters. The relationship between these parameters and performance metrics of interest is usually complex and a small change in design parameter tends to impact all performance metrics of interest. In order to achieve the specific performance levels, emphasis has been given on the design parameters. The three-way divide between narrowband, direct sequence spread spectrum, and frequency hop spread spectrum is an example of a situation where such a choice must be made. Development of the first spread spectrum (SS) systems began at least six decades ago [-3]. During the world war II SS devices were already in action. The early systems were designed to provide low detectability or protection from jamming or interface. Most of the applications of SS techniques previously were in the fields of military applications such as radar and communication systems. Recently SS technique ISBN: 978-96-6766-79-4 3 ISSN 79-57

OPTICAL COMMUNICATIONS (ELECTROSCIENCE '8), Trondheim, Norway, July -4, 8 becomes very popular in many civilian applications. In the field of communications the SS technique is used in mobile networks communication and wireless local area network (WLAN). A SS system is one in which the transmitted signal is spread over a wide frequency band, much wider, in fact, than the minimum bandwidth required to transmit the information being sent. Frequency hopping spread spectrum (FHSS) Frequency hopping spread spectrum (FHSS) transmits short radio bursts on one frequency then randomly hops to another for the next short burst. The carrier signal changes frequency in a pattern known to both transmitter and receiver. The transmission source and destination must be synchronized, so they are on the same frequency simultaneously. Each user in FHSS follows a different and unique sequence of hops. The hop sequence is designed so as to minimize the likelihood that any given hop will land on the same frequency. At the same time as another user (design of spreading sequence). The code division is performed by varying the frequency hopping sequence from user to user. The code sequences do not guarantee that collisions will not occur [4-7]. The code sequence limits the amount of mutual interference to a definable level. Frequency hopping spread spectrum Implements frequency division multiplexing (FDM) and time division multiplexing (TDM) the pattern of channel usage is called hopping sequence. The time spend on a channel with a certain frequency is called dwell time. Frequency hopping spread spectrum has two types: Slow hopping: Transmitter uses one frequency for several bits periods i.e. frequency changes at a rate that is lower than the symbol rate. Fast hopping: Transmitter changes the frequency several times during the transmission of a single bit i.e. frequency changes at a rate that is higher than the symbol rate. Spread spectrum technology has been used to ensure security of the transmitted data for that purpose pseudonoise-sequence (PN) has been using on transmitter as well receiver end. The block diagram of FHSS with PN code generator is shown in the Fig.. A transmitted signal is modulated and spread out so that the signal is hidden within the noise level. At the receiver end, the signal is demodulated, received, and decoded to the same form that it was transmitted. Within a signal generation code, a data pulse waveform has been taken, which has been code modulated by multiplying the data stream with a pseudo-noise-sequence. The code modulation has spread the signal by the code pulse waveform. The PN code must be on both the transmitter and receiver sides so that the original data pulse can be recovered. A pseudo-random code generator drives a frequency synthesizer, which synthesizes the desired hopping frequency. A mixer provides the upconversion to the desired band and the power amplifier drives the antenna which sends the desired data stream through the air. Fig. Structure of the transmitter and receiver of FHSS system 3 Pseudonoise In practice, it is unrealistic to generate identical copies of white noise and as a result deterministic waveforms with cross correlation properties similar to white noise are used to implement this technique. Maximal-length (m-length) pseudo-random or pseudonoise binary sequences (PN sequences) are a popular choice since they appear to be random (having auto correlation approaching and impulse) over a finite range but are actually deterministic and periodic. Furthermore, they are relatively easy to generate using linear feed back shift registers and digital logic [8]. 3. Correlation Properties Correlation is a measure of similarity between any two variables. Although in this paper wave form correlation is done, these correlations can be separated into functions that are specific to the waveform pulse shape, and the discrete correlations between sequences. The waveform correlation properties solely determine from the discrete sequence correlations once pulse shape is ISBN: 978-96-6766-79-4 33 ISSN 79-57

OPTICAL COMMUNICATIONS (ELECTROSCIENCE '8), Trondheim, Norway, July -4, 8 given. Crosscorrelation measures the extent of similarity between two sequences, and Autocorrelation measures the same for a sequence with itself, both correlations are a function of time delay, or shift. The autocorrelation values for side lobes are minimal to reduce multipath interference. The Crosscorrelation values between the sequences are low to minimize the multiple access interference. At the core of the sliding correlator technique (also known as the swept time delay cross correlation technique) are the cross correlation properties of linear systems. It is known from linear system theory that if white noise pt () is applied to the input of a linear system, and the output wt () is cross correlated with a delayed replica of the input, pt ( τ ), then the resulting cross correlation coefficient is proportional to the impulse response of the system ht) ( evaluated at the delay time [9]. Under the assumption that the channel is a linear time-invariant system this technique can be used to measure the channel impulse response. Assume white noise pt () with auto correlation function Rpp ( τ ) given by () is the input to a channel with impulse response ht (), then the output wt () of the channel is given by the convolution of ht () and pt () or wt () = h( ζ) pt ( ζ) () Eptpt [ ( ) ( τ )] = R pp ( τ ) () The cross correlation of the output wt () and a delayed version of the input pt ( τ ) is given by Rwp ( τ ) = E[ w( t) p( t τ )] (3) Using () in (3) the cross correlation can be expressed as R ( ) [ ( ) ( )] ( ) ( ) ( ) wp τ = E w t p t τ = E h ζ p t ζ p t τ (4) = h( ) Ept [ ( ζ ) pt ( τ )] d (5) Using a change of variables m= ( t ζ ) in (5) yields R ( τ) = h( ζ) E[ p( m) p( m ( τ ζ))] wp (6) Using the definition of the auto correlation of two signals, this can be written as Rwp ( τ) = h( ζ) Rpp ( τ ζ) (7) Equation (7) shows the convolution of the channel impulse response with the auto correlation of white noise. 4 Results and Discussion There are numbers of transformations that can be applied, among which the Fourier transform (FT) are probably by far the most popular. The Fourier transform lies in its ability to analyze a signal in the time domain for its frequency content. The transform works by first translating a function in the time domain into a function in the frequency domain. The signal can then be analyzed for its frequency content because the Fourier coefficients of the transformed function represent the contribution of each sine and cosine function at each frequency. Simulation has been carried out by using Matlab first of all data sequence has been generated by using rand function. Noise had been added to the original bit sequence as shown in Fig..When we plot time-domain signals as shown in Fig.3, we have obtained a timeamplitude representation of the signal. This representation is not always the best representation of the signal for most signal processing related applications. In many cases, the most distinguished information is hidden in the frequency content of the signal. The frequency spectrum of a signal is basically the frequency components (spectral components) of that signal. The frequency spectrum of a signal shows what frequencies exist in the signal. If the FT of a signal in time domain is taken, the frequency-amplitude representation of that signal is obtained. We have a plot modulated BPSK and FHSS as shown in Fig.4 and Fig.5 respectively, with one axis being the frequency and the other being the amplitude. These plots tell us how much of each frequency exists in our signal and from these results it clearly depicted that FHSS overcomes the other ordinary modulation. In direct spread spectrum the wide modulation is applied to a fixed frequency carrier signal for transmission. The spreading code directly spreads the information, and independent of the RF modulator. While in FH the information is left unchanged and directly modulates a carrier of varying frequency which has been plotted in Fig.6. This is showing the graphical display of tabulated frequency. The simulated results have shown that a signal lingering at a predefined frequency for a short period of time limits the possibility of interference from another signal source generating radiated power at a specific hop frequency. ISBN: 978-96-6766-79-4 34 ISSN 79-57

OPTICAL COMMUNICATIONS (ELECTROSCIENCE '8), Trondheim, Norway, July -4, 8 Original Bit Sequence 4 3 FHSS of Orginal signal - 5 5 5 5 5 Noisy signal 4 3 FHSS of Noisey signal - 5 5 5 5 5 Fig. Binary data stream with and without noise BPSK Modulation of orignal Signal - 5 5 5 BPSK Modulation of Noisy Signal - 5 5 5 Fig.5 Structure of the transmitter and receiver of FFH system 5 45 4 35 3 5 5 5 - -.5.5.5.5 3 Fig.6 Histogram of FHSS system Fig.3 BPSK modulation of original and noisy signal.5.5 FFT of BPSK Modulated Orignal Signal 5 5.5.5 FFT of BPSK Modulated Noisy Signal 5 5 Fig.4 BPSK modulation of original and noisy signal 5 Conclusion The performance of a communications system depends on system designer and environmental parameters. The relationship between these parameters and performance metrics of interest is usually complex and a small change in design parameter tends to impact all performance metrics of interest. In order to achieve the specific performance levels, emphasis has been given on the design parameters. There are numbers of transformations that can be applied, among which the Fourier transform (FT) are probably by far the most popular. We have investigated the spectral characteristics of both spread and non-spread BPSK waveforms. We have analyzed and simulated these systems with several variations by taking the Fast Fourier Transform (FFT) of FHSS with original binary sequence and with noisy signal. The simulated results have shown that a signal lingering at a predefined frequency for a short period of time limits the possibility ISBN: 978-96-6766-79-4 35 ISSN 79-57

OPTICAL COMMUNICATIONS (ELECTROSCIENCE '8), Trondheim, Norway, July -4, 8 of interference from another signal source generating radiated power at a specific hop frequency. References: [] R. A. Scholz, The origins of spread-spectrum communications," IEEE Trans. On Comm., vol. COM- 3, pp. 8{854, May 98. [] R. C. Dixon, Spread spectrum techniques," IEEE Press, New York, Tech. Rep., 976. [3] R. A. Dillard and G. M. Dillard, Detectability of Spread-Spectrum Signals. Boston. London: Artch House, 989. [4] S. Haykin, Communication systems, 4th ed. New York: Wiley,. [5] W. E. Kock, Radar, Sonar, and Holography. New York: Academic Press, 973. [6] M. I. Skolnik, Introduction to radar systems, 3rd ed. New York: McGraw-Hill,. [7] A. W. Rihaczek, Principles of High-Resolution Radar. Boston. London: Artch House, 996. [8]. Anderson, C., Design and Implementation of an Ultrabroadband Millimeter-Wavelentgh Vector Sliding Correlator Channel Sounder and In-Building Multipath Measurements at.5 & 6 GHz, Masters Thesis, Virginia Polytechnic Institute and State University, http://scholar.lib.vt.edu/theses/index.html, May. [9] J. D. Parsons, D. A. Demery, A. M. D. Turkamani, Sounding Techniques for Wideband Mobile Radio Channels: A Review, IEE Proceedings, vol. 38, no. 5, pp. 437-446, October 99. ISBN: 978-96-6766-79-4 36 ISSN 79-57