Chaotic Radio for Audio Communications Phanumas Khumsat and Gklanarong Noulkeaw Department of Electrical Engineering, Faculty of Engineering, Prince of Songkla University Hat-Yai, Thailand 90112 e-mail:
[email protected] Abstract— Chaotic wireless communication system suitable for audio transmission has been designed and implemented. The chaotic module was based on Chua’s circuit and it has been realized from inductor, capacitor, resistor, and non-linear negative resistor. The negative non-linear resistor was constructed from resistors and operational amplifier. Chaotic masking technique has been selected as a mean of chaotic data modulation whereas synchronization relies on Pecora-Carroll technique. The chaotically-modulated signal has been further frequency modulated to frequency centered at 9 MHz making the system immune to non-linearity of the communication channel. Such frequency modulation process was achieved by voltagecontrolled oscillator inside 74HC4046 IC. On the receiving end, the FM demodulation was performed by employing phase-locked loop technique. Measured results of the presented radio system are also given.
I. INTRODUCTION Non-linear system dynamic has been extensively studied in various fields [1] ranging from meteorology, biology, engineering, etc. In field of communication electronics, chaotic modulation is emerging as a strong alternative to meet future demands on higher data rate and better security [2-6]. This work presents possibility in exploiting chaotic technique in a wireless radio system for audio transmission. II.
SYSTEM OVERVIEW
Fig.1 illustrates conceptual block diagrams for a chaotic radio system presented in this work. At transmitter, information signal S is chaotically encrypted by a chaotic module before being passed to an RF modulator, a power amplifier and eventually radiated into free space. At a receiving end, the signal is picked up by an antenna and bandpass filtered before being demodulated by an RF demodulator and eventually the information signal is recovered by a chaotic module which is reciprocal to the one inside the transmitter. At the transmitter, an audio signal (information) S is combined with a chaotic signal (simply known as a masking technique [7]) generating from a chaotic module which is based on Chua’s circuit [3] shown as a driving system in Fig.2a. In order to be able to fully recover an information
(a) Transmitter
(b) Receiver Fig.1 Chaotic radio system. signal at the receiver, Pecora-Carroll synchronisation technique [8] is selected due to its simplicity and suitability for data signal extraction from a chaotically-masked signal. Such synchronization technique incorporate a chaotic response system basically constructed from the same Chua circuit as shown in Fig.2b. A driving system at the transmitter is described by differential equations [5] 1 d V1 G = (V2 − V1 ) − I R (V1 ) dt C1 C1
(1a)
d V2 1 G ((V 1 + S ) − V2 ) + I3 = dt C2 C2
(1b)
d I3 1 = − V2 dt L
(1c)
The module renders a chaotically masked signal V1 + S for further signal processing down the transmission chain. Similarly, for a response system at the receiver [5] ∧
∧ 1 d V1 G ∧ ∧ = (V2 − V1 ) − I R (V1 ) dt C1 C1
∧
∧ d V2 G 1 ∧ = ((V1 + S ) − V2 ) + I3 dt C2 C2
(2a) (2b)
∧
d I3 1 ∧ = − V2 dt L
(2c)
Where G = 1/R, IR(⋅) being a current flowing through the nonlinear negative resistor (NR) whose I-V characteristic is described by (GbVR + (Gb − Ga ) E if VR < − E I R (VR ) = GaVR if − E ≤ VR ≤ E (G V + (G − G ) E if V > E a b R b R
(3)
and it is realised by the circuit in Fig.3, with the parameter values Ga = -757.58 µS, Gb = -409.91 µS, and E = 1V. If all the passive components are perfectly matched between driving and response systems, the same state variable ∧ ∧ signals are attained and we would have V1 = V1 and V2 = V2 , therefore a perfect data recovery can be achieved, i.e. ∧
∧
S = (V1 + S ) − V1
= V1 + S − V1 = S
(a) V1 (top) and V2 (bottom)
(4)
(a) Chaotic driving system based on Chua’s circuit (b) V1 and V2 in X-Y mode displaying Chua attractor
(b) Chaotic response system Fig.2 Chaotic modules employed inside transmitter (a) and receiver (b)
(c) Spectrum shape of V1 + S (1.25kHz/div) Fig.4 V1, V2 signals from the transmitter’s chaotic module. A chaotically masked signal V1 + S is further frequency modulated before injecting into a power amplifier as explained in the following sections. Fig.3 Nonlinear negative resistor [4] Measured V1 and V2 signals from transmitter chaotic module are depicted in Fig.4. An X-Y mode plot of V1 and V2 in Fig.4b illustrates the corresponding Chua attractor while the V1 + S spectrum is shown in Fig.4c.
III.
PRACTICAL CIRCUIT IMPLEMENTATION
Practical realisation of the aforementioned system is illustrated in Fig.5 (transmitter) and Fig.6 (receiver). All passive component values are with 1% accuracy. Signal summation between V1 and S is done with a summing amplifier. The output signal V1 + S is further attenuated by a factor of 1/3.3 so that the signal swing is within an input range
of a frequency modulator. Frequency modulation (FM) is selected to make the system immune to non-linearity of the communication channel and it is achieved by means of a voltage-controlled oscillator (VCO) inside 74HC4046 IC [9] with a centre frequency at 10MHz by selecting appropriate resistors (R1 = 2.2kΩ and R2 = 10kΩ) and capacitor (300pF). The VCO constant k0 has been measured to be 3.08MHz/V for input range between 1.0 – 4.0V under 5 V supply. The outcoming FM signal drives a power amplifier (MSA31111) whose output connected to antenna via an appropriate 50-Ω matching network. At receiver, an incoming signal is amplified by a low noise amplifier (BGA2011) and filtered by a passive bandpass filter before entering an FM demodulator. An FM modulation is carried by exploiting phase-lock loop technique also employing 74HC4046 whose VCO is designed to be identical to that in the modulator. An exclusive-OR has been utilized as a phase comparator with a lag filter (50kΩ, 3.3kΩ and 300pF) acting as a loop filter which renders a loop damping ratio of 1 / 2 . It achieves a capture range and locked range of 7.310MHz and 4.5-15MHz. The rest of the receiver circuit deals
with signal decryption based on the original architecture of Fig.2b. IV.
EXPERIMENTAL RESULTS
The system prototype has been constructed and tested using discrete components on printed circuit boards. Audio signal is supplied from an MP3 player. Measured signals are captured in Fig.7 – Fig.8. Degree of synchronization is inspected by comparing the respective signals from the ∧
transmitter and the receiver. Fig.7 depicts V1, V 1 comparison on an oscilloscope in normal and X-Y modes which indicates a fairly good level of synchronization. Similarly, transmitted ∧
and recovered audio signals (S and S ) are compared in Fig.8, although the signal is clearly audible, the level of mismatch is still quite significant compared to the synchronization of V1, ∧
in Fig.7. Such mismatch may not only come from a chaotic synchronization problem, but from imperfections of the design in other parts of the systems. V1
Fig.5 Transmitter
Fig.6 Receiver
∧
∧
(a) V1 (top) vs V 1 (top) in time domain
∧
(a) S (top) vs S (bottom) in time domain
∧
(b) V1 vs V 1 in X-Y mode
(b) S vs S in X-Y mode
Fig.7 State voltage signal comparison between the transmitter and receiver
Fig.8 Audio signal comparison
V.
CONCLUSION
Chaotic radio for audio communication has been successfully demonstrated. Chaotic masking technique was selected for analog signal encryption where synchronization is based on the principle proposed by Pecora and Carroll. Chaotically masked signal was frequency modulated using a voltage-controlled oscillator with a centre frequency of 10MHz. FM demodulation has been achieved by means of phase-lock loop technique. REFERENCES [1] M. Longair, Theoretical Concepts in Physics, 2nd edition, The Cambridge University Press, 2003. [2] G. Kolumbán, M. P. Kennedy, L. O. Chua, “The Role of Synchronization in Digital Communications Using Chaos-Part I: Fundamentals of Digital Communications,” IEEE Transactions on Circuits and Systems-I, vol. 44, no. 10, pp. 927-936, 1993. [3] M. P. Kennedy, “Three Steps to Chaos-Part I: Evolution,” IEEE Transactions on Circuits and Systems-I, vol. 40, no 10, pp. 640-656, 1993.
[4] M. P. Kennedy, “Three Steps to Chaos-Part II: A Chua’s Circuit Primer,” IEEE Transactions on Circuits and Systems-I, vol. 40, no 10, pp. 657-674, 1993. [5] G. Kolumbán, M. P. Kennedy, L. O. Chua, “The Role of Synchronization in Digital Communications Using Chaos-Part II: Chaotic Modulation and Chaotic Synchronization,” IEEE Transactions on Circuits and Systems-I, vol. 45, no 11, pp. 1129-1140, 1998. [6] D. Kanakidis, A. Argyris and D. Syvridis, “Performance Characterization of High-Bit-Rate Optical Chaotic Communication Systems in a Back-to-Back Configuration” Journal of Lightwave Technology, vol 21, no. 3, pp.750-758, 2003. [7] K. M. Cuomo, A. V. Oppenheim and S. H. Strogatz, “Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications,” IEEE Transactions on Circuits and Systems-II, Vol. 40, No. 10, October 1993. [8] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters , vol. 64, no 8, pp. 821-824, 1990. [9] Philips, 74HC4046 datasheet.
