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A DS spread spectrum system transmit at a rate of 1 kbps in the presets of a tone jammer. The jammer power is 20 dB greater then the desired signal, and the required εb/J0 to achieve satisfactory performance is 10 dB.
Que: If the jammer is a pulse jammer, then pulse duty cycle that results in worst case jamming is
- a)0.14
- b)0.05
- c)0.07
- d)0.10
Correct answer is option 'C'. Can you explain this answer?
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A DS spread spectrum system transmit at a rate of 1 kbps in the preset...
The duty cycle of a pulse jammer of worst-case jamming is
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A DS spread spectrum system transmit at a rate of 1 kbps in the preset...
To determine the pulse duty cycle that results in worst-case jamming, we need to consider the parameters given in the question. Let's break down the problem step by step:
Step 1: Determine the desired signal power
The desired signal power is not explicitly given in the question. However, we can infer it based on the fact that the jammer power is 20 dB greater than the desired signal. In decibels, the power ratio is calculated using the formula:
Power ratio (in dB) = 10 * log10 (Power ratio)
Given that the jammer power is 20 dB greater, we can determine the power ratio as follows:
Power ratio = 10^(20/10) = 100
Therefore, the desired signal power is 1/100th (or 0.01) of the jammer power.
Step 2: Determine the jammer-to-signal power ratio (J/S)
The jammer-to-signal power ratio (J/S) is given as 10 dB. In decibels, the power ratio is calculated using the formula:
J/S ratio (in dB) = 10 * log10 (J/S ratio)
Given that J/S ratio is 10 dB, we can determine the power ratio as follows:
J/S ratio = 10^(10/10) = 10
Step 3: Determine the processing gain (b/J0)
The processing gain (b/J0) required to achieve satisfactory performance is given as 10 dB. In decibels, the processing gain is calculated using the formula:
Processing gain (in dB) = 10 * log10 (Processing gain)
Given that the required processing gain is 10 dB, we can determine the processing gain as follows:
Processing gain = 10^(10/10) = 10
Step 4: Determine the worst-case jamming pulse duty cycle
In a spread spectrum system, the processing gain is related to the pulse duty cycle (D) by the formula:
Processing gain (b/J0) = D * (1/D)
Substituting the values we obtained:
10 = D * (1/D)
Simplifying the equation:
D^2 = 10
Taking the square root of both sides:
D = √10
Calculating the approximate value of √10, we find:
D ≈ 3.16
Since the pulse duty cycle (D) represents the ratio of the pulse duration to the total period, it should be between 0 and 1. Therefore, the pulse duty cycle that results in worst-case jamming is approximately 0.316.
Based on the given options, the closest value to 0.316 is 0.07. Therefore, the correct answer is option C (0.07).
Step 1: Determine the desired signal power
The desired signal power is not explicitly given in the question. However, we can infer it based on the fact that the jammer power is 20 dB greater than the desired signal. In decibels, the power ratio is calculated using the formula:
Power ratio (in dB) = 10 * log10 (Power ratio)
Given that the jammer power is 20 dB greater, we can determine the power ratio as follows:
Power ratio = 10^(20/10) = 100
Therefore, the desired signal power is 1/100th (or 0.01) of the jammer power.
Step 2: Determine the jammer-to-signal power ratio (J/S)
The jammer-to-signal power ratio (J/S) is given as 10 dB. In decibels, the power ratio is calculated using the formula:
J/S ratio (in dB) = 10 * log10 (J/S ratio)
Given that J/S ratio is 10 dB, we can determine the power ratio as follows:
J/S ratio = 10^(10/10) = 10
Step 3: Determine the processing gain (b/J0)
The processing gain (b/J0) required to achieve satisfactory performance is given as 10 dB. In decibels, the processing gain is calculated using the formula:
Processing gain (in dB) = 10 * log10 (Processing gain)
Given that the required processing gain is 10 dB, we can determine the processing gain as follows:
Processing gain = 10^(10/10) = 10
Step 4: Determine the worst-case jamming pulse duty cycle
In a spread spectrum system, the processing gain is related to the pulse duty cycle (D) by the formula:
Processing gain (b/J0) = D * (1/D)
Substituting the values we obtained:
10 = D * (1/D)
Simplifying the equation:
D^2 = 10
Taking the square root of both sides:
D = √10
Calculating the approximate value of √10, we find:
D ≈ 3.16
Since the pulse duty cycle (D) represents the ratio of the pulse duration to the total period, it should be between 0 and 1. Therefore, the pulse duty cycle that results in worst-case jamming is approximately 0.316.
Based on the given options, the closest value to 0.316 is 0.07. Therefore, the correct answer is option C (0.07).
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A DS spread spectrum system transmit at a rate of 1 kbps in the presets of a tone jammer. The jammer power is 20 dB greater then the desired signal, and the required εb/J0to achieve satisfactory performance is 10 dB.Que: If the jammer is a pulse jammer, then pulse duty cycle that results in worst case jamming isa)0.14b)0.05c)0.07d)0.10Correct answer is option 'C'. Can you explain this answer?
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