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A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ?
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A binary digital communication system tranamits the signala uning o n...
Optimal Detection Rule
To design the optimal detection rule for a binary digital communication system using on-off signaling over an AWGN channel, the following steps are taken:
- Signal Representation: The two signals transmitted are:
- s0(t) = 0, for 0 ≤ t ≤ Ts (representing the absence of a signal)
- s1(t) = 2, for 0 ≤ t ≤ Ts (representing the presence of a signal)
- Correlator Demodulation: The receiver uses a correlator to compute the decision statistic:
- Y = ∫ (r(t) * s1(t)) dt for 0 ≤ t ≤ Ts, where r(t) is the received signal.
- Detection Rule: The optimal detection rule can be expressed as:
- If Y > threshold, decide s1 (signal present).
- If Y ≤ threshold, decide s0 (signal absent).
The threshold is typically set at zero for equally probable signals, leading to a decision boundary.
Average Probability of Error
To determine the average probability of error in terms of SNR:
- SNR Definition: The SNR is defined as the ratio of the signal power to the noise power. For on-off signaling, the average SNR can be expressed as:
- SNR = (Signal Power) / (Noise Power) = (E[|s1(t)|^2]) / (N0/2)
- Error Probability Calculation: The average probability of error for this binary system under AWGN can be derived using the Q-function:
- P_e = Q(√(2 * SNR))
This equation arises from the Gaussian nature of the noise and the properties of the decision statistic.
- Interpretation: As SNR increases, the probability of error decreases, indicating better performance of the communication system under lower noise conditions.
This concise approach details the optimal detection rule and error probability, ensuring clarity and visual appeal for understanding in the context of digital communication systems.
To design the optimal detection rule for a binary digital communication system using on-off signaling over an AWGN channel, the following steps are taken:
- Signal Representation: The two signals transmitted are:
- s0(t) = 0, for 0 ≤ t ≤ Ts (representing the absence of a signal)
- s1(t) = 2, for 0 ≤ t ≤ Ts (representing the presence of a signal)
- Correlator Demodulation: The receiver uses a correlator to compute the decision statistic:
- Y = ∫ (r(t) * s1(t)) dt for 0 ≤ t ≤ Ts, where r(t) is the received signal.
- Detection Rule: The optimal detection rule can be expressed as:
- If Y > threshold, decide s1 (signal present).
- If Y ≤ threshold, decide s0 (signal absent).
The threshold is typically set at zero for equally probable signals, leading to a decision boundary.
Average Probability of Error
To determine the average probability of error in terms of SNR:
- SNR Definition: The SNR is defined as the ratio of the signal power to the noise power. For on-off signaling, the average SNR can be expressed as:
- SNR = (Signal Power) / (Noise Power) = (E[|s1(t)|^2]) / (N0/2)
- Error Probability Calculation: The average probability of error for this binary system under AWGN can be derived using the Q-function:
- P_e = Q(√(2 * SNR))
This equation arises from the Gaussian nature of the noise and the properties of the decision statistic.
- Interpretation: As SNR increases, the probability of error decreases, indicating better performance of the communication system under lower noise conditions.
This concise approach details the optimal detection rule and error probability, ensuring clarity and visual appeal for understanding in the context of digital communication systems.
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A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ?
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A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ? 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 A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ?.
A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ? 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 A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binary digital communication system tranamits the signala uning o n - off algnaling over the AWGN channel with zero mean and vartance N 0 2 s 0 ( t ) = 0 , 0 ≤ t ≤ T s 1 ( t ) = 2 , 0 ≤ t ≤ T The receiver employs the correlator demodulator followed b y the detector. ( i n ) Design the optimal detection rule i f signals are equally probabable. ( 4 M ) ( b ) Determine the average probability o f error i n terms o f S N R ? ( 4 M ?.
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