|Year : 2009 | Volume
| Issue : 6 | Page : 304-308
Metrics to Define Probability of Interception of Conventional, Frequency-hopping, Spread Spectrum Radars
Sanjay Rajgopal, OP Sahu
Department of E and CE, NIT Kurukshetra, Kurukshetra, India
|Date of Web Publication||18-Jan-2010|
Department of E and CE, NIT Kurukshetra, Kurukshetra
| Abstract|| |
Low probability of interception (LPI) is an important characteristic, especially for military radars. Manufacturers boast of the LPI performance of their radar but in the absence of a quantifiable metric, there is no method to compare the LPI characteristics of different radars. This paper proposes a novel method of defining metrics for the probability of interception (PI) of conventional, frequency hopping and Spread Spectrum radars. The PI of conventional radar depends on Azimuth beam width, pulse repetition frequency (PRF) and pulse width. The PI of frequency hopping radar is defined in terms of the bandwidth of transmission in each hop and the band of operation. The PI of spread spectrum radar is evaluated by comparing power spectral density (PSD) of the transmitted waveform with that of a random binary wave of similar time period.
Keywords: Low probability of interception, p0 robability of interception, Spread spectrum radar.
|How to cite this article:|
Rajgopal S, Sahu O P. Metrics to Define Probability of Interception of Conventional, Frequency-hopping, Spread Spectrum Radars. IETE J Res 2009;55:304-8
| 1.Introduction|| |
Low probability of interception (LPI) is one major characteristic that sets apart military radars from their civilian counter parts. In a military scenario, the current and perceived battlefields are monitored by electronic intelligence (ELINT) equipment to detect the presence of radar activity. More often than not, static radars get detected over a period of time and thus mobile radars with reasonable LPI characteristics become a good sensor on any military inventory. Manufacturers of mobile radars boast of LPI performance of their products. Despite the importance of LPI, there has been no standard method of quantifying the probability of interception (PI) of radar. This paper attempts to define metrics for quantifying the PI characteristic of different types of radars. Reference  had defined a metric for probability of detection in a conventional communication system. It defines a detect-ability distance to compare communication system of GSM, IS-54, IS-95 and a generic wideband CDMA communication system. This kind of metric intrinsically deals with the power measured at a particular distance and can be applied to conventional communication systems. It is silent about the specific characteristics of a radar system like the revolution per minute (RPM), pulse repetition frequency (PRF), pulse width (PW) and beam width (BW); which are the key constituents of LPI characteristics of a radar.
Spread Spectrum (SS) systems are usually interference limited. Cases of multi-user SS environment have been presented extensively by  and  . Reference  has given an analysis of Frequency Hopping SS. The superior stealthiness of SS radar has been mentioned by ,, . Direct sequence (DS) SS and multi carrier (MC) DS SS are some of the types of SS which have been evaluated extensively for use in mobile multi-user communication in  . A metric to define the probability of interception of SS radars is, however, not found in any of these references.
This paper analyses the LPI characteristics of conventional surveillance radars, radars with frequency hopping and SS radars. Conventional radar manufacturer improves the LPI characteristics of his product by reducing the beam width, reducing the side lobes, reducing side lobe width, narrowing the pulse width and employing frequency agility among other methods. In SS radar, the stealth ness improves as the spread factor of the chip sequence. This analogy is similar to that of conventional communication system where SS spread factor is also called the spreading gain  .
The paper is organized as follows: In section 2, the PI of conventional surveillance radar is presented. Here, the metric defined has been used to evaluate the PI of a few radars manufactured in India and abroad. This is done without prejudice towards other methods used by the manufacturers towards improving the LPI characteristics. Moreover, modern radars are not considered in the comparative study to avoid controversy. Section 3 defines the metric for PI of frequency hopping radar. This metric is verified with the help of a computer simulation and the results are presented in section 3. Section 4 uses a simplistic model for radar using spread spectrum to define the metric for PI. It is defined as a ratio of power of the SS radar with that of a random binary wave. Finally conclusions are drawn in section 5.
| 2.Probability of Interception-Conventional Surveillance Radar|| |
Conventional surveillance radars are pulsed radars with the antenna rotating in azimuth. Most radars have a fan shaped beam or an equivalent of a fan shaped beam in the elevation. Following notations are used to calculate probability of interception:
The number of pulses (N) intercepted by a point interceptor depends on the duration that it is illuminated by the beam of the rotating antenna of the radar. This in turn is dependent on BW, RPM and the PRF of operation of the radar. It can be shown that
- PRF: Average pulse repetition frequency in pulses per second (most radars operate at a fixed PRF or have a set of fixed PRF. Certain modern radars have varying PRF for better space time management. Thus the average PRF is considered for evaluating the probability of interception).
- BW: Average azimuth beam width (most radars have a constant value of beam width in azimuth. However radars using electronic beam steering have varying azimuth beam widths for different values of phase shift introduced. Thus the average azimuth beam width is considered for this evaluation).
- PW: Average pulse width (in most radars, a constant value of pulse width is used. However radars using advanced pulse shapes have different pulse widths for different types of pulses. Thus the average pulse width is considered for this evaluation).
Then the probability of interception would be the ratio of time that the interceptor is illuminated and the total time of observation. Thus, PI is given by
Substituting the expression for N from (1) into (2), we get
It is worth noting that the PI is independent of the RPM.
This metric is useful in evaluating the LPI characteristics of most conventional radars. The values of PI for some of the radars are given in [Table 1]. The parameters required for the calculation of PI are taken from  . Certain parameters, wherever not given, have been assumed.
Factors like power output, side lobe illumination and radar silence mode also contribute to the PI of the radar. These have not been included in the metric defined in equation (3). However, Equation (1) can be suitably modified to include these.
Certain surveillance radars use electronic beam steering in elevation. Such radars generally have one beam which is steered vertically in elevation, while the antenna rotates mechanically in the azimuth. For such radars the interceptor is illuminated for a much lesser duration than is done by a fan shaped beam. The probability of interception of such radar would reduce by the ratio of elevation beam width to elevation coverage. Thus PI for such a radar is given by:
BWelev = average beam width in elevation.
covelev = coverage of radar in elevation.
| 3.Probability of Interception-Frequency Hopping Radar|| |
Modern military radar operates over a band of frequency. At any given moment it operates at a carrier frequency (say f1 ) with a band width of λ. For the next Pulse Repetition Time (PRT), the radar operates at another frequency f 2 with similar bandwidth λ (or a slightly different band width). This carrier frequency can be chosen over a band called the band of operation of the radar.
For this section, the model of radar considered has an average bandwidth of l and transmits over a band of operation B r. The number of carrier frequencies, also called hops, that are possible by the radar is B r /l. The interceptor model, considered in this section, listens over a band of operation B i. The interceptor is monitoring the band width l for a period of the average PRT of the radar. This assumption is made because the interceptor will generally have a priori knowledge of l and PRT of the radar based on the ELINT collected over a period of time, but not of the band of operation of the radar. The interceptor is sweeping the band B i sequentially from the lower end to the upper end where as the radar is choosing the carrier frequency from a random set in band B r.
The probability of a particular carrier frequency f 1 being transmitted by the radar is given by
The probability that the interceptor is listening to a particular carrier frequency fx is given by
Though the two events look seemingly independent, the probability of interception of radar by the interceptor is the probability that the radar transmits a frequency that is listened to by the interceptor. (This is assuming that the interceptor has no a priori knowledge of the radar transmission frequency). This is given by
This indicates that the PI decreases with band width λ. In case the radar manufacturer reduces λ, to improve his LPI characteristics, then it will have many consequences on the performance of radar. (Notably, reducing λ would mean use of wider pulse widths which in turn affects the radar resolution in range. It also means restricting the spread of frequency in frequency modulated pulses used for pulse compression.). Yet the radar designer would do well to keep λ as low as possible.
Let us consider a frequency-hopping radar with a band of operation of 200 MHz and an interceptor with a band of operation of 300 MHz. The simulated results, along with the expected results, for the PI of such frequency-hopping radars are shown in [Figure 1]. The expected result is the value obtained from eqn (7). Simulated results are obtained by simulating the operation of a radar and interceptor. The radar is hopping over the band of 200 MHz at random. [Figure 1]a shows the results of a case when the interceptor is sweeping the band of 300 MHz sequentially. [Figure 1]b indicates the PI of the same radar when the interceptor chooses at random the carrier frequency to listen.
What emerges from the simulated results shown above is that the PI formula, as defined above, is correct. Moreover, from [Figure 1]b it is clear that the interceptor gains no advantage by choosing the frequency band either sequentially or at random.
In [Figure 1]c the probability of interception is plotted for varying values of the radar band. It can be inferred that the PI reduces as the radar band increases beyond the band of operation of the interceptor. This may seem only of academic interest for conventional frequency hopping radars, but it proves that the PI can be reduced by increasing the band of operation.
| 4.Probability of Interception - Spread Spectrum Radar|| |
The model of spread spectrum (SS) radar considered in this section has a master oscillator generating a basic signal cos2πfct where fc is the basic frequency of operation. This signal is modulated by a product signal c(t)p(t). Here, p(t) is a pulse whose duration defines the range resolution of the radar and c(t) is a pseudo random noise (PN) sequence, having a chip duration that is a sub-multiple of the pulse duration p(t).
The model of the receiver used by an interceptor considered for this section receives c(t) p(t) cosωc t at the antenna. This signal is mixed with cosωi t, where vi is the closest approximation of radar frequency ωc made by the interceptor with apriori knowledge (based on ELINT). The mixed signal is passed through a low pass filter (LPF) such that the complete radar band is passed to the integrator. At the integrator the energy is calculated over the average pulse repetition time (PRT) of the radar.
The power spectral density Sc (f) of a unit energy PN sequence c(t) is given by 
where, N is the length of the PN sequence, δ(f) is the delta function of f, Tc is the chip time period, n is a non zero integer, and sin c(x) is as defined below
The total energy received by an interceptor depends on the amount of energy in the band of reception of the interceptor. This amount would determine whether the radar can be intercepted. The one sided energy of the SS signal intercepted by a receiver over a band of 0 to B would be given by
The one sided energy intercepted over a band of 300 MHz is evaluated by a computer and is presented in [Figure 2]. It is evident that the value saturates beyond an approximate value of 63. It can be inferred that, for LPI characteristics, there is no advantage in increasing N beyond a limit of 63.
The PI of SS radar would depend on how less the power intercepted is. Since the random binary wave is the best approximation of a SS signal, the ratio of the energy of the radar to the ratio of a comparable random binary wave would define the relative PI of the radar. Thus, metric for PI for SS radar is defined as the ratio of the energy of SS signal in the bandwidth of the interceptor to the energy of a random binary wave calculated over the same bandwidth.
The total energy of SS signal can be calculated by integrating Sc(f) for the PN sequence over the defined band. In a similar way the energy of the random binary wave can also be calculated over the band. Notably, the S c (f) of random binary wave is 
Tc is the period of the random binary wave.
A simulation for calculating one sided energy in Sc (f) is done for the PN sequence and that for the random binary wave for different values of time period Tc . The results are plotted in [Figure 3]. The values considered for simulations are
Band width of receiver = 300 MHz
N = 31
0.1 μ sec < Tc < 1 μ sec
It can be inferred from this graph that the energy content of the PN sequence, in the band of interest, is lower than that of the random binary wave. This is because of the frequency impulses of the Sc (f) of the PN sequence. Secondly, the energy of PN sequence is considerably close to that of the random binary wave, when measured over a large band. Thirdly, the LPI performance of the PN sequence is better for lower values of T.
Practical SS radar would use a code sequence different from a pn sequence and thus the energy of such a sequence would be higher than the energy of a pn sequence. The PI as per equation (11) for such a sequence would thus be higher.
| 5.Conclusion|| |
LPI is an important characteristic for military radars. This paper defines the PI of conventional radar in terms of the Azimuth beam width, PRF and its pulse width. It is shown that the PI is further reduced if the radar uses electronic scanning in the elevation using a single beam. The paper also establishes that the PI of frequency-hopping radar reduces if the number of hops increases. It is also established that for frequency hopping radar the PI is independent of the manner in which the interceptor scans the band of interest. A simple model of SS radar is considered for evaluation of PI in SS radars. Here, the metric is defined in terms of the power spectral density of the PN sequence. A simulation of the energy calculation over a desired bandwidth shows that the PI reduces as the Tc reduces. The metrics defined in this paper can be suitably modified for radar performance evaluation.
| Authors|| |
Sanjay Rajgopal received BE in Electronics and Telecomn Engg from Govt Engg College, Jabalpur, India in 1989 and M Tech in Comn Systems from IIT Madras, India in 1999. He also received MSc degree from Madras University, India and a Masters Diploma in Business Administration from Symbiosis, Pune, India. He is also a Fellow of IETE. He has an experience of over 20 years in Surveillance Radars. His fields of interest include Digital Communication, Radar and Spread Spectrum applications. He is presently pursuing his Ph D from NIT Kurukshetra, India.
O. P. Sahu received his B.E. degree in 1989 and M.Tech degree in 1991 both in Electronics and Communication Engineering from Rani Durgavati Vishvavidyalaya Jabalpur and Kurukshetra University Kurukshetra respectively. He received his PhD degree in 2005 from Kurukshetra University Kurukshetra in the area of Multirate Filter Banks. He joined NIT (then REC) Kurukshetra as a Lecturer in 1991 in the department of Electronics and Communication Engineering and was promoted as an Assistant Professor in 1999 and is still working there. He has more than 25 papers in his credit in National and International Conferences and Journals. His Research interests include Signals and Systems, Digital Signal Processing, Digital Communication and Fuzzy Systems.
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[Figure 1], [Figure 2], [Figure 3]