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A slow FH binary FSK system with non coherent detection operates at ε0/J0 10, with hopping bandwidth of 2 GHz, and a bit rate of 10 kbps.
Que: The probability of error for the worst-case partial band jammer is
- a)0.2996
- b)0.1496
- c)0.0368
- d)0.0298
Correct answer is option 'C'. Can you explain this answer?
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A slow FH binary FSK system with non coherent detection operates at ...
The probability of error with worst-case partial-band jamming is
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A slow FH binary FSK system with non coherent detection operates at ...
Given Parameters
- Center frequency, f0 = 10 GHz
- Hopping Bandwidth, Δf = 2 GHz
- Bit rate, Rb = 10 kbps
Approach
- For slow FH binary FSK, the frequency shift can be calculated as Δf = Rb/2
- Hence, frequency deviation, Δf = 5 kHz
- Probability of error can be calculated using the equation,
P(e) = 1/2 erfc[√(Eb/N0)]
- where erfc is the complementary error function and Eb/N0 is the signal-to-noise ratio (SNR) per bit
- The SNR per bit can be expressed as,
Eb/N0 = (Ps/2) / (N0B + I)
- where Ps/2 is half of the signal power, N0 is the power spectral density of the noise, B is the bandwidth of the signal and I is the interference power
- For a partial band jammer, the interference power can be expressed as I = (Δf/B)N0
- The worst-case scenario occurs when the jammer occupies the entire hopping bandwidth
- Therefore, I = (Δf/B)N0 = (2/10)N0 = 0.2N0
- Substituting the values in the equation for Eb/N0, we get,
Eb/N0 = (Ps/2) / (1.2N0)
- The probability of error can now be calculated using the above equations
Calculation
- Δf = Rb/2 = 5 kHz
- I = (Δf/B)N0 = (2/10)N0 = 0.2N0
- Eb/N0 = (Ps/2) / (1.2N0)
- P(e) = 1/2 erfc[√(Eb/N0)]
- P(e) = 0.0368
Therefore, the probability of error for the worst-case partial band jammer is 0.0368 or 3.68%. Option (C) is the correct answer.
- Center frequency, f0 = 10 GHz
- Hopping Bandwidth, Δf = 2 GHz
- Bit rate, Rb = 10 kbps
Approach
- For slow FH binary FSK, the frequency shift can be calculated as Δf = Rb/2
- Hence, frequency deviation, Δf = 5 kHz
- Probability of error can be calculated using the equation,
P(e) = 1/2 erfc[√(Eb/N0)]
- where erfc is the complementary error function and Eb/N0 is the signal-to-noise ratio (SNR) per bit
- The SNR per bit can be expressed as,
Eb/N0 = (Ps/2) / (N0B + I)
- where Ps/2 is half of the signal power, N0 is the power spectral density of the noise, B is the bandwidth of the signal and I is the interference power
- For a partial band jammer, the interference power can be expressed as I = (Δf/B)N0
- The worst-case scenario occurs when the jammer occupies the entire hopping bandwidth
- Therefore, I = (Δf/B)N0 = (2/10)N0 = 0.2N0
- Substituting the values in the equation for Eb/N0, we get,
Eb/N0 = (Ps/2) / (1.2N0)
- The probability of error can now be calculated using the above equations
Calculation
- Δf = Rb/2 = 5 kHz
- I = (Δf/B)N0 = (2/10)N0 = 0.2N0
- Eb/N0 = (Ps/2) / (1.2N0)
- P(e) = 1/2 erfc[√(Eb/N0)]
- P(e) = 0.0368
Therefore, the probability of error for the worst-case partial band jammer is 0.0368 or 3.68%. Option (C) is the correct answer.
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A slow FH binary FSK system with non coherent detection operates atε0/J010, with hopping bandwidth of 2 GHz, and a bit rate of 10 kbps.Que: The probability of error for the worst-case partial band jammer isa)0.2996b)0.1496c)0.0368d)0.0298Correct answer is option 'C'. Can you explain this answer?
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