Fractal Communication System

Transcription

1 PACS : Df; Va V.N. Bolotov, S.E. Kolesnikov, Yu.V. Tkach, Ya.Yu Tkach, P.V. Khupchenko Institute for Electromagnetic Research, Mail Box 4580, Kharkov-22, Ukraine vbolotov@iemr.com.ua Contents Fractal Communication System 1. Introduction Fractal Signals Block Diagram and Components (Units, Modules) of Fractal Communication System Conclusions 178 Abstract A complex electromagnetic environment and an absolute necessity to protect transmitted data from unauthorized access call for development of novel technological solutions while establishing communication systems. One such approach would be a transition to fractal communication systems (FCS) that employ noise-immune signals with fractal spectra as information carriers. This work considers the fundamentals of FCS and presents results of its practical implementation in establishing computer communication links over air and coaxial cable. 1. Introduction At present, broadband communication systems have come into wide use. Those systems employ novel information carriers, i.e. ultra-wideband (UWB) waveforms. These waveforms ensure high-rate data transmission (up to 100 Мb/s) and provide the possibility to establish such UWB communication systems that are highly noise-immune and protect transmitted data from unauthorized access. Impulses with a wide spectrum, as accounted for by a very short width of the signal of less than 1 ns, are often chosen as information carriers. The principal disadvantage of these waveforms is such that their spectrum is determined, on the whole, by the width of the impulses which precludes their efficient adjustment. One of the alternative approaches being intensively elaborated at the present time bears on R&D on a noise-immune communication system that employs fractal signals of different kinds [1]. This fractal communication system (FCS) in its air- and cabletransmission varieties has been realized, for the first time ever, in Kharkov at Institute for Electromagnetic Research (IEMR). 2. Fractal Signals The advent of the state-of-the-art electronic technologies brought on the feasibility to form and transmit over cable or air such very short width signals that have an intricate amplitude-time relationship. In this way, it is now possible to form UWB waveforms of various types, including those with the fractal spectra, i.e. FUWB signals. According to the definition, the fractal signals are such signals the spectra of which, or their time-related implementations, have the self-similar structure, as assigned by the Cantor set. This research employs the fractal wavelet to construct the fractal communication system, the signal being a variety of the fractal signals. The fractal wavelet (FW) is a pulse of complex shape the spectrum of which represents the pre-cantor set [2]. The FW spectrum is self-similar, i.e. various parts of the spectrum look alike. The FW timerelated implementation is described by the following expression: s(t) = N cos((1 ξ)ξ n 2πf 0 t), (1) n=0 where 0 < ξ 1/2 and N. The selection of N and f 0 is associated with electronic 174

2 Fractal Communication System equipment capabilities, being determined by the available digitization rates. The spectrum of this implementation (1) has the self-similar structure of the Cantor set and is determined by the parameters ξ and f 0. The spectrum frequencies of this fractal signal belong to the Cantor set points and are concentrated over the length [ f 0,f 0 ]. This observation is deduced from the fact that the Fourier-image of this signal is the generalized Cantor set function the carrier of which, as demonstrated in [2], is the Cantor set constructed in this case over the length [ f 0,f 0 ]. In this way, we introduce a parameter (maximum fractal spectrum frequency) f u = f 0 that determines the spectrum breadth. The minimum spectrum frequency of the fractal signal is not difficult to calculate, acting on the assumption that it is the corresponding righthand point of the first kind in the Cantor set, i.e. f l = f 0 (1 2ξ) [2]. The time-related implementation spectrum, as described by the expression (1), has the self-similar structure of the Cantor set, because the spectrum frequencies have semi-group symmetry. Thus, there is a hierarchy of spectra inserted into one another that have the similar analytic form. We were the first to produce those signals and study them experimentally [1]. The fact is widely known that in order to differentiate signals over the bandwidth occupied by them, one uses the fractional frequency band factor η: η = f u f l f u + f l, (2) where f u, f l the uppermost and lowermost frequencies in the spectrum of video-signal, i.e. the signal without center frequency. According to the definition in use, the signals that have η 0.01 refer to narrowband signals, those with 0.01 η 0.25, to broadband signals, and those with 0.25 η 1, to ultra-wideband waveforms. In case of the fractal wavelet, f u = f 0 and f l = f 0 (1 2ξ). Therefore, for the fractal wavelet the factor is independent of the position of the uppermost and lowermost limits of the spectrum, its value being determined by the expression: η = ξ 1 ξ. (3) (3) In this way, the parameter ξ, included in the analytic expression for the fractal wavelet (1), determines the degree of its fractional frequency band. Remember that 0 < ξ 1/2. For instance, for ξ = 1/3 the fractional frequency band factor is η = 0.5. Upon appropriate selection of the parameter ξ, the signals with the fractal spectra begin to belong to UWB waveforms and become FUWB signals. The spectra of the traditional UWB waveforms do not usually have clear-cut uppermost and lowermost limits. These limits are commonly determined at the Fig. 1. Theoretical spectrum of fractal wavelet. level of 10 db of the maximum amplitude value in the spectrum. The basic property that makes the fractal signals different from the traditional UWB waveforms is their possessing the precise uppermost and lowermost limits of the spectrum. In case of those signals, there is no need for setting up the level at which the uppermost and lowermost limits of the spectrum are fixed. Fig. 1 gives a typical spectrum of the fractal video-signal that has been calculated theoretically. The signals of this type are employed as modulating signals in the transmitter of our proprietary FCS. At an IEMR stand, which is designed to study FCS operability under the conditions of imposed external noise, we obtained experimental signals with the fractal spectra at different center frequencies ranging from 2 GHz to 8 GHz. Fig.2 presents a spectrum of fractal wavelet obtained experimentally with the width 200 ns at the center frequency 2 GHz. The spectrum breadth is 500 MHz. Measurements of the spectra of the fractal signals were taken at HP 8592A spectral analyzer. The transmitter-to-receiver signal transmission was made both over air and coaxial cable. The transmission of both video-fw signals and FW signals with center frequency was studied while transmitting the signal over the coaxial cable. The experiments employed B3199 high-frequency coaxial cable 50 m long. Upon passing of the video- FW signal through the cable, its shape and spectrum remained unchanged. There was a slight damping of the video-fw signal inside the cable at the level of 2 db over the length 50 m. The experiments on transmission of a FW-signal with the sinusoidal carrier frequency 2 GHz through the B3199 coaxial cable 50 m long involved a broadband transmitter and a receiver of the fractal signals which were operable throughout the bandwidth 1,700 MHz to 2,400 MHz. The experiments were carried out in the regimes of amplitude and phase signal modulation. In both regimes of amplitude and phase modulation, the shape and spectrum of the FW-signal with the sinusoidal carrier frequency underwent insignificant changes upon its passage through the B3199 cable Electromagnetic Phenomena, V.7, 1 (18),

3 V.N. Bolotov, S.E. Kolesnikov, Yu.V. Tkach, Ya.Yu Tkach, P.V. Khupchenko Fig. 2. Experimental spectrum of fractal wavelet at center frequency 2 GHz. 50 m long. The attenuation of the FW-signal over the length of 50 m was in this case as follows: for phase-modulated FW-signal by db, for amplitude modulation by 6 db. Thus, the experiments indicated that the FW-signal both with center frequency and without could be used in cable communications over considerable distances. The experiments conducted at IEMR indicated, as well, the feasibility of controlling the fractal signal spectrum limits. For this purpose, while creating the fractal signals, it is just enough to select the appropriate parameters ξ and f 0 in the analytical expression for their time-related implementation and carry the signal across the spectrum using the appropriate carrier frequency. By using the parameter ξ it is possible to vary the lacunarity of the fractal spectrum, i.e. to change the value of voids in it. For ξ = 1/2 the lacunarity disappears and we produce a solid spectrum of the fractal signal shaped as a step. Those kinds of spectra are characteristic of the linear frequency-modulated (LFM) signals. The lacunarity change in the fractal signal spectra was observed experimentally. In order to accomplish this, analog signals with a variable were produced. 3. Block Diagram and Components (Units, Modules) of Fractal Communication System The underlying operation principle of the FCS is the use of signals with the fractal spectra used as information carriers. The FUWB signals are noiseimmune [1], and they can be achievable for data transmission in a dense electromagnetic environment. Fig. 3. Sequential coding (11101) using fractal wavelets. As a matter of fact, our proprietary FCS is a means of digital communication in which the rectangular pulses are replaced by fractal signals, the availability of the fractal signal corresponding to transmitted character 1 and its absence to character 0. Fig. 3 gives an example of data coding using the fractal signals. Fig. 4 gives block diagram of data-transmission channel between two computers using fractal signals. The transmitting computer output signal (1, Fig. 4) comes to interface converter (2, Fig. 4) thereupon the data-containing signal is transferred to dedicated wavelet generator (WG) (3, Fig. 4) which, acting upon command issued by the incoming rectangular pulse, forms the analog signal of a preprogrammed shape. The digital part of the WG employs programmable logic integrated circuits (PLIC). Due to employment of reprogrammable memory the WG enables to obtain 20 and more kinds of signals, including orthogonal signals that are used in the communication systems. For the FCS to operate, WG memory incorporates 176 Electromagnetic Phenomena, V.7, 1 (18), 2007

4 Fractal Communication System Fig. 4. Block diagram of the channel of data transmission by fractal signals between two computers: 1 Transmitting computer; 2 Interface converter; 3 Wavelet generator; 4 Fractal transmitter; 5 Transmitting broadband antenna; 6 Receiving fractal antenna; 7 Fractal high-pass filter; 8 Fractal receiver; 9 Band-pass low-pass filter; 10 Detector; 11 Comparator; 12 Rectangular pulse restoration schematic; 13 Interface converter; 14 Receiving computer. Fig. 5. Wavelet generator. an orthogonal system of the fractal signals. The WG is based on digital-to-analog converter (DAC) that enables to form signals with 4,096 levels of quantization. The maximum programmable signal amplitude is 2 volts. To comply with the dynamic range requirements and acting in consideration of the high sampling frequency of the signals formed, the WG is fashioned on a 4-layer printed circuit board. Fig. 5 shows the photographic image of this WG. The signal comes from the WG output to fractal transmitter (4, Fig. 4) in which the band-pass modulation and amplification of the signal takes place whereupon the resulting fractal signal is emitted into air at the center frequency 2 GHz from the transmitting broadband antenna (5, Fig. 4). The modulator and IEMR s proprietary fractal transmitter operate across the frequency band 1.8 to 2.15 GHz. A broadband antenna is used as transmitting antenna in this version of the device. For signal reception, such a wide-range fractal antenna (6, Fig. 4) is employed the outgoing signal of which passes through the high-pass fractal filter (7, Fig. 4) to the fractal receiver input (8, Fig. 4). The receiver performs amplification and extraction of the modulating signal from RF-signal received. In order to improve the performance of the FCS in a very complex electromagnetic environment, a fractal signal correlator can be used, however as regards commercial devices its employment is not advisable, because a device like that is very costly and using it will increase the total cost of the FCS on the whole. For the fight with interferences the system is outfitted with wide-range fractal filters (FF). The analog signal made noise-free with the aid of FF comes then to the rectangular pulse restoration circuit (10 12, Fig. 4) where it is converted into digital signal. The rectangular pulse restoration circuit is designed to form data bits in their durations and to bring out the beginning and end of packets in the information flow. A comparator is installed at the input of the rectangular pulse restoration circuit. At its output, such rectangular pulse is formed that corresponds to one data bit in the digital flow. A highspeed production line microchip is used as comparator that forms a positive pulse of the TTL level per each peak of video-signal with the width not less than 0.75 ns. From the comparator output the signal comes to interface converter (13, Fig. 4). Next, the digitized data comes to USB-port of the receiving PC (14, Fig. 4) where it is converted into such data that is compatible with the operation system logic. A dedicated proprietary soft-ware is used for this particular purpose. The interface converters of USB into RS-485 and RS-485 into USB are designed to match the data transmission rates of USB port (12 Mbit/s) Electromagnetic Phenomena, V.7, 1 (18),

5 V.N. Bolotov, S.E. Kolesnikov, Yu.V. Tkach, Ya.Yu Tkach, P.V. Khupchenko Fig. 6. Characteristic directivity pattern of fractal antennas. Parameters Table 1. Fractal communication system Data transmission rate, Mbit/s Broadband operability, MHz Type of modulation AM, PhM Signal output, dbm 1 15 Sensitivity, dbm -130 Operating frequency range, GHz Transmission distance, m 100 and devices incorporated in the channel of data transmission as carried by fractal signals ( Mbit/s) and to form trigger signals that come to the WG. IEMR has a proprietary technology for manufacturing the fractal antennas and filters employed in the above FCS. The fractal antennas in use [3] have a circular directivity pattern which can be attributed to their applications in this particular communication system (Fig. 6). The IEMR s stands were the first to display the air- and cable-operated FCS. The data exchange took place between computers at the center frequency 2 GHz using wide-range signals with the fractal spectra (Fig.2) over air to distances up to 100 m and over a 50 m-long cable of the type B3199. The computer link using the video-fractal signals was established only over cable. The FCS testing was conducted under the conditions of imposed external noise. The FCS proved to transmit undistorted information, with the signal-to-noise ratio (SNR) at the receiver input being -10 db. The SNR measurements were taken across the fractal signal frequency band. The principal technical performances of the FCS were evaluated at the experimental stand, as shown in Table 1. The equipment used enabled to implement various types of the UWB waveforms. For this purpose, we employed the reference generator Arbitrary Waveform Generator AWG 2041, which could generate analog signal over appropriate digital signal introduced into its memory beforehand. The digitization frequency of this generator was 1 GHz. As a result of our experiments, we demonstrated that other types of UWB waveforms do not affect the data transmission made with this FCS. In this way, the FCS can provide an effective code division for users and utmost security against unauthorized access to data transmission. For the FCS benefit, IEMR has developed a smallsize analog Waveform Generator that is programmable for specific assignment and named Wavelet Generator. This generator can generate systematic orthogonal analog signals based on the base wavelet [4]. The signal orthogonality property is known as being widely used in communication systems. In this way, WGs can be effectively used in R&D and manufacture of the modern communication systems. Not only can signals with the fractal spectra be used in the communication systems, but they also can be of much use to creation of novel UWB radars. The basic merit of these FUWB radars is such that they can be operable in various wavelength ranges, being self-similar at one and the same time. This property enables to spot object at different scales leading to considerably improved resolution of FUWB radars and opening up new vistas for creation of novel image recognition systems. The signals with the fractal spectra employed in radiolocation have another big advantage. The signals of this type are noiseimmune and they can be used to decrease the effect of countermeasures on radiolocation probing. 4. Conclusions IEMR is the first research institution to have developed, manufactured and tested a noise-immune system of two-channel fractal communication which is designed to operate in a dense electromagnetic environment and secure against unauthorized access to information transmission. Our proprietary system can transmit data both over cable lines using the video-fractal signals and over air using the center frequency modulation by signals with fractal spectra of various kinds. Creation and operability of the system was ensured by our proprietary R&D on critically important builtin units, such as: a programmable modulating signal generator enabling to form fractal signals of more than 20 kinds; a fractal signal transmitter incorporating dedicated antennas. Of additional importance for this system are dedicated filters designed to extract the fractal signals from surrounding noise and other ECM signals. It is very important, as well, that these filters enhance the immunity of this system relative to the impact of high- 178 Electromagnetic Phenomena, V.7, 1 (18), 2007

6 Fractal Communication System power, short-width pulsed signals. The units and parts included in the above fractal communication system have been developed and manufactured so that the majority of them can be usable as components in future systems of UWB radiolocation, dedicated communication systems, etc. The component base characteristics that we keep improving constantly enable, respectively, to better the performances of next generations of the fractal communication system which opens up inexhaustible possibilities for its future applications. Manuscript received October 22, 2006 References [1] Bolotov V.N., Tkach Yu.V. Generation of Fractal Spectrum Signals // Technical Physics V. 51,. 4. P [2] Bolotov V.N. The Cantor Distribution and Fractal Transition Scattering // Technical Physics V. 47, 2. P [3] Bolotov V.N., Kirichok A.V., Tkach Yu.V. Experimental Research of Fractal Antennas // Electromagnetic Phenomena V. 1,. 4. P (in Russian). ( [4] S. Mallat. A Wavelet Tour of Signal Processing. Academic Press p. Electromagnetic Phenomena, V.7, 1 (18),