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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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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...
Given Information:
- FH spread spectrum system
- Non-coherent detection
- N = 3 hops/bit
- Hard decision decoding
- Channel is AWGN with power spectral density 0.5No
- SNR 20 ~ 13 dB (total SNR over the three hops)
Explanation:
To find the probability of error in this system, we need to consider the different sources of error in the system and calculate their individual probabilities.
1. Bit Error Probability in Each Hop:
Since each bit is transmitted over N = 3 hops, the probability of error in each hop can be calculated using the formula for bit error probability in FSK modulation:
P(error) = Q(sqrt(2 * SNR))
Given that the SNR is 20, we can calculate the bit error probability for each hop as:
P(error_hop) = Q(sqrt(2 * 20))
2. Probability of No Errors in All Hops:
Since the system uses hard decision decoding, an error will occur only if there is an error in all three hops. The probability of no errors in all hops can be calculated by taking the complement of the probability of error in each hop:
P(no_errors_all_hops) = (1 - P(error_hop))^N
Substituting the value of P(error_hop) calculated above:
P(no_errors_all_hops) = (1 - P(error_hop))^3
3. Probability of Error in All Hops:
The probability of error in all hops can be calculated by taking the complement of the probability of no errors in all hops:
P(error_all_hops) = 1 - P(no_errors_all_hops)
Substituting the value of P(no_errors_all_hops) calculated above:
P(error_all_hops) = 1 - (1 - P(error_hop))^3
4. Total Probability of Error in the System:
Since the system uses non-coherent detection, the probability of error in the system is the same as the probability of error in all hops:
P(error_system) = P(error_all_hops)
Calculations:
Substituting the value of P(error_hop) calculated above:
P(error_system) = 1 - (1 - Q(sqrt(2 * 20)))^3
Calculating the value using a calculator or software, we get:
P(error_system) ≈ 0.0013
Answer:
The probability of error for this system is approximately 0.0013, which corresponds to option B.
- FH spread spectrum system
- Non-coherent detection
- N = 3 hops/bit
- Hard decision decoding
- Channel is AWGN with power spectral density 0.5No
- SNR 20 ~ 13 dB (total SNR over the three hops)
Explanation:
To find the probability of error in this system, we need to consider the different sources of error in the system and calculate their individual probabilities.
1. Bit Error Probability in Each Hop:
Since each bit is transmitted over N = 3 hops, the probability of error in each hop can be calculated using the formula for bit error probability in FSK modulation:
P(error) = Q(sqrt(2 * SNR))
Given that the SNR is 20, we can calculate the bit error probability for each hop as:
P(error_hop) = Q(sqrt(2 * 20))
2. Probability of No Errors in All Hops:
Since the system uses hard decision decoding, an error will occur only if there is an error in all three hops. The probability of no errors in all hops can be calculated by taking the complement of the probability of error in each hop:
P(no_errors_all_hops) = (1 - P(error_hop))^N
Substituting the value of P(error_hop) calculated above:
P(no_errors_all_hops) = (1 - P(error_hop))^3
3. Probability of Error in All Hops:
The probability of error in all hops can be calculated by taking the complement of the probability of no errors in all hops:
P(error_all_hops) = 1 - P(no_errors_all_hops)
Substituting the value of P(no_errors_all_hops) calculated above:
P(error_all_hops) = 1 - (1 - P(error_hop))^3
4. Total Probability of Error in the System:
Since the system uses non-coherent detection, the probability of error in the system is the same as the probability of error in all hops:
P(error_system) = P(error_all_hops)
Calculations:
Substituting the value of P(error_hop) calculated above:
P(error_system) = 1 - (1 - Q(sqrt(2 * 20)))^3
Calculating the value using a calculator or software, we get:
P(error_system) ≈ 0.0013
Answer:
The probability of error for this system is approximately 0.0013, which corresponds to 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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 Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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 Electrical Engineering (EE) 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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 Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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 Electrical Engineering (EE) 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 0.5No and an SNR 20 ~13 dB (total SNR over the three hops). 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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