FREQUENCY HOPPING TRANSCEIVER SYSTEM WITH APPLICATION TO RADAR Sami A. Mostafa Electronics Technology Dept., Bishah College of Technology, Bishah, Kingdom of Saudi Arabia. Tel. 00966501641833, e-mail
[email protected]
Abstract The well-known types of the conventional communication systems are designed to transmit and receive on a single fixed frequency channel. These systems are vulnerable to jamming, interference, and multipath problems. It was found that, the repeated switching of frequencies during RF transmission according to specified techniques will minimize sensitivity of the system to jamming and interference and may solve some of the multipath problems. One of these techniques is the frequency hopping. Frequency hopping transceiver is capable of hopping its operating frequency over a given bandwidth many times in a specified time period. This renders the hopping system virtually impossible to intercept or jam. The transmitter and receiver must keep hopping in synchronism with each other in order to maintain correct data transfer. The frequency hopping sequence is designed to follow certain algorithm. In the present work, at first, a theoretical background is introduced to summarize the subject of frequency hopping (FH) technique. Fast frequency hopping (FFH) as well as slow frequency hopping (SFH) will be discussed. Fast frequency hopping will be considered rather than SFH because its performance is significantly better than SFH[1]. In fact, the main reason is that fast hopping introduces frequency diversity. The block diagram of the FFH communication system will be simulated and evaluated using matlab environment. The frequency hopping procedure will be carried out pseudo randomly according to the Gamma random distribution which is proved to have the best correlation properties. An FFH radar system will be simulated and evaluated. The auto- and cross-
correlation functions of the FFH radar transceiver, as a measure of the system performance will be calculated, and evaluated. 1. Introduction In a single frequency transceiver system, it is often desirable to concentrate the frequency spectrum in as narrow a region of the frequency as possible in order to conserve available bandwidth and to reduce power. On the other hand the basic spread spectrum technique is designed to encode the transmitted signal by spreading its power across as much of the frequency spectrum as possible. The same code is used in the receiver (operating in synchronism with the transmitter) to despread the received signal so that the original transmitted signal may be recovered. There are many types of spread spectrum communication systems. Direct Sequence Spread Spectrum (DSSS) and Frequency Hopped Spread Spectrum (FHSS) are the most widely used [2]. In most cases FHSS signals are preferred over DS spread spectrum signals because of the stringent synchronization requirements inherent in DSSS signals. 2. FH Spread Spectrum System In a FH spread spectrum communication system the available channel bandwidth is subdivided into a large number of continuous frequency slots. In any transmitting interval, the signal occupies one or more of the available frequency slots. The selection of the frequency slot(s) is made pseudo randomly according to the output from a pseudo random (PN) generator, which obeys certain random distribution (in this work
Uniform, Gauss, Poisson, Chi-square, Rayleigh, and Gamma random distributions are introduced and compared). Considering the rate at which the hopping process occurs, we have: 2.1. Slow-frequency hopping (SFH) The bit rate is an integer multiple of the hop rate i.e., several bits may be transmitted over each frequency hop interval. See Figure 1 [7].
Figure 2: SFH transceiver system.
2.2. Fast Frequency Hopping (FFH) The hop rate is an integer multiple of the bit rate i.e., the hop frequency may change several times during the transmission of one bit. See Figure 3
Figure 1: Demonstration of SFH technique
Thus: Br =n Sr n=1,….,N (1) where: Sr … frequency hopping rate (slots per second), Br … transmission rate (bit per second), N… is the maximum number of Bandwidth frequency slots Smax and n.. is an arbitrary integer number varying randomly from 1 to N, i.e the PN generator seed value. Figure 2 illustrates a simplified block diagram of a SFH transceiver system, where f is the triggering frequency (seeding) of the PN generator and n.f is the triggering frequency of the sampling circuit of the encoder (bit generator). As shown in Figure 2, the frequency synthesizer generates the carrier frequency depending on the output of the PN sequence generator. The mixer, in the receiver side, will exhibit an output only if the input bit carrier frequency is the same as the frequency synthizer output, i.e it removes the carrier frequency that was introduced by the transmitter. This operation requires the PN sequence generator to be properly synchronized in time with the receiver signal.
Figure 3: Demonstration of FFH technique.
Thus: Sr = n Br n=1,….,N (2) Figure 4 illustrates the FFH radar system. The triggering frequency of the sampling circuit of the encoder (bit generator) satisfies the FFH condition stated in Eq.2.
Figure 4: FFH transceiver system.
3. Simulation of FFH Radar System Figure 5 shows the block diagram of the FFH radar system. The synchronization process here is carried out accurately. For the FFH
radar system, the hop rate is an integer multiple of the pulse repetition rate i.e., the pulse carrier frequency will change or hop several times during the transmission of one pulse.
Figure 5: FFH radar system.
Figures 6, and 7 describe the main program which is used to simulate the FFH radar system. At first, Figure 6 illustrates the radar pulse train generator. The PN generator, which obeying the Gamma random number generator. Some types of random distributions (Uniform, Gauss, Poisson, Chi-square, Rayleigh, and Gamma) are compared to select the PN generator type which is used to feed the main program. The autocorrelation function is used as a measure to choose which of the distributions is most suitable to the radar system [3]. Figures 7 (a,b,c,d,e, and f) illustrate the auto-correlation function (ACF) of the random distributions. It is shown from the figures that Gamma random distribution, Figure 7(e), exhibits the most suitable ACF concerning the radar system. The second part is the modulator of the radar transmitter. The inputs are the pulse train coming from the pulse generator with pulse duration ε and pulse repetition period T, and the hopping carrier frequency coming from the frequency synthesizer. Let us choose a searching radar that may have the following pulse generator timing diagram: (see Figure 8) pulse duration (ebs (ε)) = 10 µsec. , pulse repetition period (T) = 1 msec. Since R = c.τ /2, where c is the speed of light, and τ is the maximum available time delay of the radar signal (1 msec. in our case), thus, the radar maximum range is R = 150 Kms.
Figure 6: Radar pulse train generator. A C F - u n ifo r m ( a )
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Figure 7: Auto-correlation functions of the random distributions: (a)Uniform. (b)Poisson. (c)Gauss.(d)Chi-square. (e) Gamma. (f) Rayleigh.
Figure 8: Timing diagram of a 150 Kms searching radar.
The frequency synthesizer is hopping many times during the transmission of a single pulse, that is, if the band of frequencies of the synthesizer is B divided, for example, into 50 frequency slots, so, we have to choose the rate of selecting the carrier frequency slot from the total 50 slots of the bandwidth. Now, the output from the radar modulator will be a train of pulsed frequency slots as will be selected by the simulator. Figure 9 illustrates the simulator of the radar receiver autocorrelator. Assuming a train of 5 pulses is studied for every pulse the carrier frequency may occupy any frequency slot(s) from 1 up to 50 frequency slots. The normalized ambiguity function AMF(τ), and f(τ) of such a train is illustrated in Figure 10 (a,b). From Figure 10(a), the AMF(τ) could reach the optimum, [5,6] i.e one part (frequency slot) of a pulse may be missing from pulse to pulse all-over the whole train. Thus, even if a part of a received pulse (frequency slot) is lost, the target is still observed. From Figure 10(b), it is shown that only a single slot (f=50) is shared all-over the five pulses. Figures 11 a,b illustrate the crossambiguity function (CAF (τ), and f (τ)) of the prescribed pulse train with a different pulse train having the same parameters, but is not synchronized. It is clear from the figure that the maximum value of the cross-correlation function peaks could reach the optimum, i.e one frequency slot may be lost if any pulse train, except the transmitted one is received. Figures 12a,b illustrate the CCF of the prescribed 5 pulses radar system and interfered signals of heavy interference conditions. Figure 12(a) is an 100 pulse train, with ebs=1 µsec., T=100 µsec. and number of frequency slots =50. The second example Figure 12(b), is the will known type of interference that is the active jamming. A selected frequency inside the system bandwidth is continuously transmitted for few seconds to saturate the
radar receiver, i.e the radar display is almost blind. It is seen from Figure 12 that the FFH radar system is sensitive for such interferers, i.e the maximum side lobes level of the CCF is considered low (about 10% of the maximum level of the ACF main lobe).
Figure 9: Simulator of the auto-correlator.
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Figure 10: Ambiguity function of 5-pulses FFH radar pulse train example (a) AMF(τ), (b) f(τ).
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Figure 11: Cross-ambiguity function of 5- pulses FFH radar pulse train example.(a) CAMF(τ), (b) f(τ).
References [1] J. G. Proakis, " Digital Communications ", 4th Edition, McGraw-Hill, 2001.
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[2] M. K. Simon, J. K. Omura, R. A. Scholtz, B. K. Lvitt, " Spread Spectrum Communications Handbook " , McGraw-Hill, New York, 1994.
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Figure 12: CCF of two interferer signals (a) 100 pulse train signal, (b)Single frequency interference al l-over the bandwidth of the radar system(active jamming).
Conclusions and Future Work The FFH radar system is discussed and evaluated. It is proved that the Matlab random generator could be used with reasonable performance, i.e there is no need to design a separate PN generator. The Ambiguity and cross-ambiguity properties of the FFH radar system proved that the system is resistive to interference and jamming. Figure 13 shows that even for high pulse transmission rates and high hopping rate the ambiguity properties of the FFH radar system is still satisfactory. The present work could be extended to discuss the FFH radar system resolvability and multi-target radar signals. More accurate PN generators and faster computers with larger memory capacities could achieve better results.
A utocorrelation Function of FFH Radar S ys tem 1 0.9 Transm ission rate= 500 p/s slots selection rate= 2000 slot/s No. of slots = 50 slot pulse width= 4 us
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Figure 13: Ambiguity function of high density radar pulse train.
[3] Joha Costas, " A Study of a Class of Detection Waveforms Having Nearly Ideal Range-Doppler Ambiguity Properties ", Proceedings of the IEEE Vol. 72, No. 8, August 1984, pp 996-1009. [4] Svetislav V. Maric and Edward L. Titlebaum, " A class of frequency hop codes with nearly ideal characteristics for use in multiple-access a spread-spectrum communications and radar and sonar systems ", IEEE Transactions on Communications, COM-40(9):1442-1447, September 1992. [5] Salwa El Ramly, Ezat Garas, Sami Ali Mostafa, " Random Pulse Radar Signal Analysis and Evaluation ", ICSPAT, 1996, USA, pp 1484-1488. [6] Sami A. Mostafa, S. El Ramly, " Random Pulse Train Signals in Long Range Radar Systems ", ICSPAT, October 16-18, 2000, Tx, USA. [7] Joseph L. Hammond, Harlan B. Russell, "Properties of a transmission assignment algorithm for multiple-hop packet radio networks", IEEE Transactions on Wireless Communications, vol. 3, no. 4, Jul 2004 pp. 1048-1052 .
