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An FH binary orthogonal FSK system employs an m = 15 stage liner feedback shift register that generates an ML sequence. Each state of the shift register selects one of L non over lapping frequency bands in the hopping pattern. The bit rate is 100 bits/s. The demodulator employ non coherent detection
Que: Suppose the hop rate is increased to 2 hops/bit and the receiver uses square law combining the signal over two hops. The hopping bandwidth for this channel is
  • a)
    3.2767 MHz
  • b)
    13.1068 MHz
  • c)
    26.2136 MHz
  • d)
    1.6384 MHz
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
An FH binary orthogonal FSK system employs an m = 15 stage liner feedb...
If the hopping rate is 2 hops/bit and the bit rate is 100 bits/sec, then, the hop rate is 200 hops/sec. The minimum frequency separation for orthogonality 2/T =400 Hz. Since there are N = 2767 states of the shift register and for each state we select one of two frequencies separated by 400 Hz, the hopping bandwidth is 13.1068 MHz.
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Most Upvoted Answer
An FH binary orthogonal FSK system employs an m = 15 stage liner feedb...
Given information:
- The system employs an m = 15 stage linear feedback shift register (LFSR) that generates an ML sequence.
- Each state of the shift register selects one of L non-overlapping frequency bands in the hopping pattern.
- The bit rate is 100 bits/s.
- The demodulator employs non-coherent detection.

To find:
The hopping bandwidth for this channel when the hop rate is increased to 2 hops/bit and the receiver uses square law combining the signal over two hops.

Solution:
Step 1: Calculate the number of frequency bands (L) based on the given information.
The bit rate (Rb) is given as 100 bits/s.
For an FH binary orthogonal FSK system, the hopping bandwidth (B) is given by the formula:
B = Rb * (m/L)
where m is the number of stages in the linear feedback shift register (LFSR) and L is the number of frequency bands.

In this case, Rb = 100 bits/s and m = 15. We need to find the value of L.

Step 2: Calculate the value of L.
Given that the hop rate is increased to 2 hops/bit, it means that the number of hops per second is 2 * Rb = 200 hops/s.

The number of hops per second (Nh) is given by the formula:
Nh = L * Rb
200 = L * 100
L = 2

Step 3: Calculate the hopping bandwidth (B).
Using the formula B = Rb * (m/L), we can substitute the values:
B = 100 * (15/2) = 750 MHz

Step 4: Calculate the bandwidth per hop (Bh) when the receiver uses square law combining over two hops.
Since the hop rate is 2 hops/bit, the bandwidth per hop (Bh) can be calculated as:
Bh = B / (2 * Rb)
Bh = 750 MHz / (2 * 100) = 3.75 MHz

Step 5: Calculate the hopping bandwidth for this channel.
The hopping bandwidth for this channel is the total bandwidth spanned by all the frequency bands, which is L * Bh.
Hopping bandwidth = 2 * 3.75 MHz = 7.5 MHz

Conclusion:
The hopping bandwidth for this channel, when the hop rate is increased to 2 hops/bit and the receiver uses square law combining over two hops, is 7.5 MHz. However, none of the given options match this value. Therefore, the correct answer cannot be determined from the given options.
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An FH binary orthogonal FSK system employs an m = 15 stage liner feedback shift register that generates an ML sequence. Each state of the shift register selects one of L non over lapping frequency bands in the hopping pattern. The bit rate is 100 bits/s. The demodulator employ non coherent detectionQue: Suppose the hop rate is increased to 2 hops/bit and the receiver uses square law combining the signal over two hops. The hopping bandwidth for this channel isa)3.2767 MHzb)13.1068 MHzc)26.2136 MHzd)1.6384 MHzCorrect answer is option 'B'. Can you explain this answer?
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