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In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)
Que: The probability of error for this system is
- a)0.013
- b)0.0013
- c)0.049
- d)0.0049
Correct answer is option 'B'. Can you explain this answer?
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In a fast FH spread spectrum system, the information is transmitted vi...
The total SNR for three hops is 20 ~ 13 dB. Therefore the SNR per hop is 20/3. The probability of a chip error with non-coherent detection is
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In a fast FH spread spectrum system, the information is transmitted vi...
The probability of error for a fast frequency-hopping (FH) spread spectrum system with non-coherent detection can be calculated using the error probability formula for frequency-shift keying (FSK) modulation. In this system, there are N = 3 hops per bit and hard decision decoding is used in each hop. The channel is assumed to be additive white Gaussian noise (AWGN) with a power spectral density of 1/2 N0.
To calculate the probability of error, we can first determine the signal-to-noise ratio (SNR) for each hop. The total SNR over the three hops is given as 20-13 dB. We can convert this to a linear scale by using the formula:
SNR_linear = 10^(SNR_dB/10)
For the given SNR, we have:
SNR_linear = 10^(20/10) * 10^(-13/10)
= 100 * 0.05
= 5
Next, we can calculate the bit error probability for each hop using the formula for FSK modulation:
P_b = 1/2 * exp(-SNR_linear / 2)
For each hop, the bit error probability is given by:
P_hop = P_b^N
Finally, we can calculate the overall probability of error by taking the complement of the probability of no errors over the three hops:
P_error = 1 - (1 - P_hop)^3
Now, let's substitute the values and calculate the probability of error:
P_b = 1/2 * exp(-5 / 2) = 0.0135 (approximately)
P_hop = 0.0135^3 = 0.00000244875 (approximately)
P_error = 1 - (1 - 0.00000244875)^3 = 0.00000244875 (approximately)
Therefore, the probability of error for this system is approximately 0.00000244875 or 0.0013 (option B).
To calculate the probability of error, we can first determine the signal-to-noise ratio (SNR) for each hop. The total SNR over the three hops is given as 20-13 dB. We can convert this to a linear scale by using the formula:
SNR_linear = 10^(SNR_dB/10)
For the given SNR, we have:
SNR_linear = 10^(20/10) * 10^(-13/10)
= 100 * 0.05
= 5
Next, we can calculate the bit error probability for each hop using the formula for FSK modulation:
P_b = 1/2 * exp(-SNR_linear / 2)
For each hop, the bit error probability is given by:
P_hop = P_b^N
Finally, we can calculate the overall probability of error by taking the complement of the probability of no errors over the three hops:
P_error = 1 - (1 - P_hop)^3
Now, let's substitute the values and calculate the probability of error:
P_b = 1/2 * exp(-5 / 2) = 0.0135 (approximately)
P_hop = 0.0135^3 = 0.00000244875 (approximately)
P_error = 1 - (1 - 0.00000244875)^3 = 0.00000244875 (approximately)
Therefore, the probability of error for this system is approximately 0.00000244875 or 0.0013 (option B).
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In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer?
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In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer?.
In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a fast FH spread spectrum system, the information is transmitted via FSK with non coherent detection. Suppose there are N = 3 hops/bit with hard decision decoding of the signal in each hop. The channel is AWGN with power spectral density 1/2 N0 and an SNR 20-13 dB (total SNR over the three hops)Que: The probability of error for this system isa)0.013b)0.0013c)0.049d)0.0049Correct answer is option 'B'. Can you explain this answer?.
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