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An m =10 ML shift register is used to generate the pre hdarandlm sequence in a DS spread spectrum system. The chip duration is Tc = ℓμs and the bit duration is Tb, = NTc, where N is the length (period of the m sequence).
Que: The processing gain of the system is
- a)10 dB
- b)20 dB
- c)30 dB
- d)40 dB
Correct answer is option 'C'. Can you explain this answer?
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An m =10 ML shift register is used to generate the pre hdarandlm seque...
The period of the maximum length shift register sequence is
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An m =10 ML shift register is used to generate the pre hdarandlm seque...
Explanation:
1. Introduction:
- In a DS (Direct Sequence) spread spectrum system, a pre-hadarandlm sequence is generated using an m = 10 ML (Maximum Length) shift register.
- The chip duration is given as Tc = s, and the bit duration is given as Tb = NTc, where N is the length or period of the m sequence.
2. Definition of Processing Gain:
- Processing gain is a measure of the improvement in signal-to-noise ratio (SNR) achieved by spreading the signal across a wider bandwidth in a spread spectrum system.
- It is defined as the ratio of the total bandwidth to the bandwidth of the original signal.
3. Calculation of Processing Gain:
- The processing gain can be calculated using the formula: PG = 10 * log10(Bt/Bc), where Bt is the total bandwidth and Bc is the bandwidth of the original signal.
- In a DS spread spectrum system, the total bandwidth is equal to the chip rate, which is the reciprocal of the chip duration (Bt = 1/Tc).
- The bandwidth of the original signal is equal to the reciprocal of the bit duration (Bc = 1/Tb).
4. Calculation:
- Given that Tc = s and Tb = NTc, we can substitute these values into the formulas for Bt and Bc.
- Bt = 1/Tc = 1/s
- Bc = 1/Tb = 1/(NTc) = 1/(Ns)
- Simplifying the expressions for Bt and Bc, we get:
- Bt = s
- Bc = 1/(Ns)
- Substituting these values into the formula for processing gain, we get:
- PG = 10 * log10(s/(1/(Ns))) = 10 * log10(s * Ns) = 10 * log10(Ns^2) = 20 * log10(Ns)
5. Conclusion:
- The processing gain of the system is given by PG = 20 * log10(Ns), where N is the length or period of the m sequence.
- In this case, the length of the m sequence is given as m = 10, so N = 2^m - 1 = 2^10 - 1 = 1023.
- Substituting this value into the formula, we get:
- PG = 20 * log10(1023 * s)
- Therefore, the correct answer is option 'C', which corresponds to a processing gain of 30 dB.
1. Introduction:
- In a DS (Direct Sequence) spread spectrum system, a pre-hadarandlm sequence is generated using an m = 10 ML (Maximum Length) shift register.
- The chip duration is given as Tc = s, and the bit duration is given as Tb = NTc, where N is the length or period of the m sequence.
2. Definition of Processing Gain:
- Processing gain is a measure of the improvement in signal-to-noise ratio (SNR) achieved by spreading the signal across a wider bandwidth in a spread spectrum system.
- It is defined as the ratio of the total bandwidth to the bandwidth of the original signal.
3. Calculation of Processing Gain:
- The processing gain can be calculated using the formula: PG = 10 * log10(Bt/Bc), where Bt is the total bandwidth and Bc is the bandwidth of the original signal.
- In a DS spread spectrum system, the total bandwidth is equal to the chip rate, which is the reciprocal of the chip duration (Bt = 1/Tc).
- The bandwidth of the original signal is equal to the reciprocal of the bit duration (Bc = 1/Tb).
4. Calculation:
- Given that Tc = s and Tb = NTc, we can substitute these values into the formulas for Bt and Bc.
- Bt = 1/Tc = 1/s
- Bc = 1/Tb = 1/(NTc) = 1/(Ns)
- Simplifying the expressions for Bt and Bc, we get:
- Bt = s
- Bc = 1/(Ns)
- Substituting these values into the formula for processing gain, we get:
- PG = 10 * log10(s/(1/(Ns))) = 10 * log10(s * Ns) = 10 * log10(Ns^2) = 20 * log10(Ns)
5. Conclusion:
- The processing gain of the system is given by PG = 20 * log10(Ns), where N is the length or period of the m sequence.
- In this case, the length of the m sequence is given as m = 10, so N = 2^m - 1 = 2^10 - 1 = 1023.
- Substituting this value into the formula, we get:
- PG = 20 * log10(1023 * s)
- Therefore, the correct answer is option 'C', which corresponds to a processing gain of 30 dB.
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An m =10 ML shift register is used to generate the pre hdarandlm sequence in a DS spread spectrum system. The chip duration is Tc=ℓμsand the bit duration is Tb,= NTc,where N is the length (period of the m sequence).Que: The processing gain of the system isa)10 dBb)20 dBc)30 dBd)40 dBCorrect answer is option 'C'. Can you explain this answer?
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