Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > A rate 1/2 convolution code with dfrec = 10 i...
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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 coding gain is
- a)7 dB
- b)12 dB
- c)14 dB
- d)24 dB
Correct answer is option 'A'. 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...
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A rate 1/2 convolution code with dfrec = 10 is used to encode a data r...
Given information:
- Convolution code rate: 1/2
- Data rate: 1 kbps
- DS spread spectrum chip rate: 10 MHz
To calculate:
- Coding gain
Formula:
Coding gain (in dB) = 10 * log10(data rate / chip rate)
Solution:
Given that the convolution code rate is 1/2, it means that for every 2 input bits, the encoder produces 1 output bit.
- The data rate is given as 1 kbps (kilobits per second).
- The DS spread spectrum chip rate is given as 10 MHz (megahertz), which means that it is generating 10 million chips per second.
To calculate the coding gain, we will use the formula:
Coding gain (in dB) = 10 * log10(data rate / chip rate)
Let's substitute the values into the formula:
Coding gain (in dB) = 10 * log10(1 kbps / 10 MHz)
Calculation:
1 kbps = 1000 bits per second
10 MHz = 10,000,000 chips per second
Coding gain (in dB) = 10 * log10(1000 / 10,000,000)
= 10 * log10(0.0001)
Using a calculator or logarithmic tables, we find:
Coding gain (in dB) ≈ 10 * (-4)
= -40 dB
Answer:
The coding gain is approximately -40 dB.
- Convolution code rate: 1/2
- Data rate: 1 kbps
- DS spread spectrum chip rate: 10 MHz
To calculate:
- Coding gain
Formula:
Coding gain (in dB) = 10 * log10(data rate / chip rate)
Solution:
Given that the convolution code rate is 1/2, it means that for every 2 input bits, the encoder produces 1 output bit.
- The data rate is given as 1 kbps (kilobits per second).
- The DS spread spectrum chip rate is given as 10 MHz (megahertz), which means that it is generating 10 million chips per second.
To calculate the coding gain, we will use the formula:
Coding gain (in dB) = 10 * log10(data rate / chip rate)
Let's substitute the values into the formula:
Coding gain (in dB) = 10 * log10(1 kbps / 10 MHz)
Calculation:
1 kbps = 1000 bits per second
10 MHz = 10,000,000 chips per second
Coding gain (in dB) = 10 * log10(1000 / 10,000,000)
= 10 * log10(0.0001)
Using a calculator or logarithmic tables, we find:
Coding gain (in dB) ≈ 10 * (-4)
= -40 dB
Answer:
The coding gain is approximately -40 dB.
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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 coding gain isa)7 dBb)12 dBc)14 dBd)24 dBCorrect answer is option 'A'. Can you explain this answer?
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