List of Abbreviations
Chapter 2. Literature Review
2.5 Electronic Warfare
2.5.5 Jamming of Radio Communications
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2.7
If the received power is greater than the intercepting antenna's sensitivity, S (in dBm), then the signal can be successfully intercepted. Therefore, to calculate the maximum range a signal can be intercepted for a given sensitivity, the received power, PR, should be replaced by the sensitivity, S, and then solve for the distance, d. The formula to calculate maximum distance at which the signal can be successfully intercepted for line of sight propagation is then:
2.8
The equivalent formula for two-ray propagation becomes:
2.9
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relation to the communications signal, the more errors and the less likely the receiver will be able to recover the transmitted information. The jamming-to-signal ratio (in decibels) is determined by subtracting the power of the signal at the receiver from the power of the jamming at the receiver.
The received powers are calculated from the transmitting power, the loss due to the channel, and the gain of the receiving antenna in the direction of the signal or jamming. A general formula for calculating the JSR is (Adamy, 2009):
2.10
Where ERPj is the effective radiated power of the jammer (in dBm), ERPs is the effective radiated power of the desired signal transmitter (in dBm), Lj is the propagation loss from the jammer to the receiver (in dB), Ls in the propagation loss of the desired signal (in dB), Grj is the gain of the receiver in the direction of the jammer (in dBi), and Gr is the gain of the receiver in the direction of the desired transmitter (in dBi). The channel loss follows the same rules for line of sight and two- ray propagation as in Section 2.5.4.1.
There is some difference in jamming analogue signals to digital signals. Generally, a high JSR, in the region of 10dB, is required to effectively jam analogue signals, with 100% duty cycle (i.e.
continuously jammed). In the case of digital signals, the jammer attacks the digital modulation to make the signal unreadable by the demodulator; here a quantifiable measurement of jammer performance can be used: the bit error rate (BER), also known as the probability of error (Pe).
Generally, only 20% to 33% of a digital signal needs to be unreadable for it to be useless, however error correction codes may reduce the jammer performance (Adamy, 2009; Poisel, 2004). It should be noted that a BER of 50% is the worst achievable, as anything lower makes the signal more coherent (Adamy, 2009). This is equivalent to reducing the mutual information by increasing the noise levels (as described in Section 2.2), thereby introducing errors in the digital communications signal.
The probability of bit error for a basic binary phase shift key (BPSK) modulated signal in an additive white Gaussian noise (AWGN) channel is , where Eb is the bit energy and N0 is the power spectral density of the Gaussian noise. From this the equation for BER for BPSK under conditions of intentional jamming can be derived (Poisel, 2004):
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2.11
where J0 is the energy of the jamming signal. In general, J0 is much larger then N0, so the equation can be simplified to:
2.12
For Equations 2.11 and 2.12, the equality (Nicholson, 1998) is used.
If the jammer does not have enough power to jam the entire message, partial-message jamming, also called pulse jamming (Adamy, 2009), can be employed. The concept is that if the power is concentrated on a specific part of a message, that part will be destroyed, and if enough of the message is destroyed, then the message as a whole can be destroyed. A simple tactic for partial message jamming is to transmit band-limited white Gaussian noise with a power spectral density of J0/ρ for a time period ρ, and to transmit nothing for the remainder of the time. The parameter ρ is known as the duty factor of the jammer. As partial-message jamming creates blocks of errors, and some error correcting codes which can correct blocks of erroneous data, it may not be effective (ibid.).
Other jamming strategies include (Poisel, 2004):
Broadband jamming: where a large frequency spectrum is jammed;
Partial band jamming: where the jamming energy is focussed on specific channels of the frequency band;
Narrowband jamming: where the jamming energy is focussed on a small portion of the frequency band;
Multi-tone jamming: the jamming energy is focussed on certain specific frequencies; and Single-tone jamming: the jamming energy is focussed on a single frequency.
These strategies are particularly useful against spread-spectrum communications, which have inherent anti-jamming features; an example of such technology is the CDMA employed in 3G mobile communications, and frequency-hopping radios (Adamy, 2009; Poisel, 2004). The performance of the various types of spread spectrum communications are derived in Adamy (2009) and Poisel (2004) for each of the jamming strategies mentioned above. For the purposes of this
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dissertation, a basic description of direct-spread CDMA (DS-CDMA) communications, such as those used in 3G mobile networks will be presented here.
In spread-spectrum communications, the signal is distributed over a wider frequency range, as the name suggests. This is done by the means of a pseudo-random sequence, which spreads the data signal with bit rate Rb to a rate that is equal to the chip rate of the sequence, Rc (Adamy, 2009;
Poisel, 2004). When this signal is transmitted, the interference is introduced (as indicated by the dashed line in Figure 2.19); at the receiver, the received signal is de-spread using the same pseudo- random sequence, however as the interference has not been spread, the de-spreading process now does so, thereby reducing the spectral density of the interference (Adamy, 2009; Poisel, 2004).
Figure 2.19: The Effects of Spreading on Interference, adapted from (Nicholson, 1998)
This advantage over interference is known as the processing gain, Gp, and is a function of the rate of the pseudo-noise sequence divided by the original data rate, which is equivalent to the bandwidth of the spread signal divided by the bandwidth of the original signal; this can be calculated as, (Poisel, 2004):
2.13
where W is the original (non-spread) bandwidth and Wss is the spread bandwidth. Due to the spreading of the interference, in this case the jamming signal, it first needs to overcome the jamming margin, which is calculated as (Blahut, 1990):
2.14
which is the difference of the processing gain (in dB) and the minimum required SNR (in dB) for the receiver to detect the desired signal. This results in a probability of bit error of (Blahut, 1990):
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2.15
Figure 2.20 compares the theoretical performance of spread-spectrum communications signals against those of a common binary phase shift key (BPSK) communication system; the spread spectrum signal is not as badly affected by the jamming.
Figure 2.20: Comparing Theoretical Jammer Performance against Spread-Spectrum and Conventional Communications Signals
For the case where multiple users are present on a channel, such as for mobile communications, correlated jamming may be used to improve the performance of the jammer. Correlated jamming results when the jammer has some knowledge of the target signals, and can adjust the ERP of the jamming accordingly (Shafiee & Ulukus, 2009). This information about the target signal may be gained from SIGINT, as discussed in Section 2.5.4. Such a method of gaining information is proposed by Yao and Poor (2001), where an expectation-maximisation algorithm is used to estimate the spreading sequence of mobile CDMA systems in order to eavesdrop of the signals. Simulations in Chapter 7 will be done to illustrate potential limitations of this concept.
The BER equations (Equations 2.11 to 2.15) may be used to describe the theoretical performance of communication systems under jamming; these equations were used in the simulation presented in
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Section 7.6 and generate Figure 2.20. For the purposes of the dissertation, the dB equations (Equations 2.5 to 2.10) will be used to estimate the maximum distance for which jamming and signal interception is effective; this will be presented in Section 7.5.