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?

Question

Answer

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.

Similar Electronics and Communication Engineering (ECE) Doubts

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 is

A CDMA system consist of 15 equal power user that transmit information at a rate of 10 kbps, each using a DS spread spectrum signal operating at chip rate of 1 MHz. The modulation scheme is BPSKQue: The Processing gain is

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=sand the bit duration is Tb,= NTc,where N is the length (period of the m sequenc e).Que: The processing gain of the system is

A CDMA system is designed based on DS spread spectrum with a processing gain of 1000 and BPSK modulation scheme. If user has equal power and the desired level of performance of an error probability of 10-6, the number of user will be

Top Courses for Electronics and Communication Engineering (ECE)View all

GATE ECE (Electronics) Mock Test Series 2025

Network Theory (Electric Circuits)

General Aptitude for GATE

Crash Course: Electronic Communication Engineering (ECE)

Signals and Systems

Top Courses for Electronics and Communication Engineering (ECE)

Top Courses for Electronics and Communication Engineering (ECE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company