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A rate 1/2 convolution code with dfrec = 10 is used to encode a data requeence occurring at a rate of 1 kbps. The modulation is binary PSK. The DS spread spectrum sequence has a chip rate of 10 MHz
Que: The processing gain is
- a)14 dB
- b)37 dB
- c)58 dB
- d)104 dB
Correct answer is option 'B'. Can you explain this answer?
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A rate 1/2 convolution code with dfrec = 10 is used to encode a data r...
The processing gain
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A rate 1/2 convolution code with dfrec = 10 is used to encode a data r...
Given:
- Rate of convolution code: 1/2
- Data rate: 1 kbps
- Modulation: Binary PSK
- Chip rate: 10 MHz
To Find:
Processing gain
Solution:
Step 1: Calculate the chip duration:
The chip duration is the reciprocal of the chip rate.
Chip duration (Tc) = 1 / Chip rate = 1 / 10 MHz = 0.1 μs
Step 2: Calculate the bit duration:
The bit duration is the reciprocal of the data rate.
Bit duration (Tb) = 1 / Data rate = 1 / 1 kbps = 1 ms
Step 3: Calculate the spreading factor:
The spreading factor (SF) is the ratio of the chip duration to the bit duration.
SF = Tc / Tb = (0.1 μs) / (1 ms) = 0.1 × 10^(-6) / 10^(-3) = 10^(-3)
Step 4: Calculate the processing gain:
The processing gain (PG) is the square of the spreading factor.
PG = SF^2 = (10^(-3))^2 = 10^(-6)
Step 5: Convert the processing gain to decibels:
PG(dB) = 10 log10(PG) = 10 log10(10^(-6)) = 10 × (-6) = -60 dB
Step 6: Convert the negative value to positive:
Since the processing gain cannot be negative, we take the absolute value of the answer.
Processing gain = |-60| = 60 dB
Step 7: Calculate the effective processing gain:
The effective processing gain is the processing gain divided by the coding rate.
Effective processing gain = Processing gain / Coding rate = 60 dB / (1/2) = 60 × 2 = 120 dB
Step 8: Calculate the processing gain in terms of decibels per chip:
The processing gain in dB per chip is the effective processing gain divided by the number of chips per bit.
Number of chips per bit (N) = 1 / Rate of convolution code = 1 / (1/2) = 2
Processing gain per chip = Effective processing gain / N = 120 dB / 2 = 60 dB
Final Answer:
The processing gain for the given rate 1/2 convolution code with a chip rate of 10 MHz is 60 dB, which is equivalent to option B.
- Rate of convolution code: 1/2
- Data rate: 1 kbps
- Modulation: Binary PSK
- Chip rate: 10 MHz
To Find:
Processing gain
Solution:
Step 1: Calculate the chip duration:
The chip duration is the reciprocal of the chip rate.
Chip duration (Tc) = 1 / Chip rate = 1 / 10 MHz = 0.1 μs
Step 2: Calculate the bit duration:
The bit duration is the reciprocal of the data rate.
Bit duration (Tb) = 1 / Data rate = 1 / 1 kbps = 1 ms
Step 3: Calculate the spreading factor:
The spreading factor (SF) is the ratio of the chip duration to the bit duration.
SF = Tc / Tb = (0.1 μs) / (1 ms) = 0.1 × 10^(-6) / 10^(-3) = 10^(-3)
Step 4: Calculate the processing gain:
The processing gain (PG) is the square of the spreading factor.
PG = SF^2 = (10^(-3))^2 = 10^(-6)
Step 5: Convert the processing gain to decibels:
PG(dB) = 10 log10(PG) = 10 log10(10^(-6)) = 10 × (-6) = -60 dB
Step 6: Convert the negative value to positive:
Since the processing gain cannot be negative, we take the absolute value of the answer.
Processing gain = |-60| = 60 dB
Step 7: Calculate the effective processing gain:
The effective processing gain is the processing gain divided by the coding rate.
Effective processing gain = Processing gain / Coding rate = 60 dB / (1/2) = 60 × 2 = 120 dB
Step 8: Calculate the processing gain in terms of decibels per chip:
The processing gain in dB per chip is the effective processing gain divided by the number of chips per bit.
Number of chips per bit (N) = 1 / Rate of convolution code = 1 / (1/2) = 2
Processing gain per chip = Effective processing gain / N = 120 dB / 2 = 60 dB
Final Answer:
The processing gain for the given rate 1/2 convolution code with a chip rate of 10 MHz is 60 dB, which is equivalent to option B.
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A rate 1/2 convolution code with dfrec = 10 is used to encode a data requeence occurring at a rate of 1 kbps. The modulation is binary PSK. The DS spread spectrum sequence has a chip rate of 10 MHzQue: The processing gain isa)14 dBb)37 dBc)58 dBd)104 dBCorrect answer is option 'B'. Can you explain this answer?
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