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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 BPSK
Que: How much should the processing gain be increased to allow for doubling the number of users with affecting the autopad SNR
  • a)
    1.46 MHz
  • b)
    2.07 MHz
  • c)
    4.93 MHz
  • d)
    2.92 MHz
Correct answer is option 'B'. Can you explain this answer?
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CDMA System Processing Gain Calculation

Given:
- 15 equal power users
- Information rate of 10 kbps
- DS spread spectrum signal operating at a chip rate of 1 MHz
- Modulation scheme is BPSK

To Find:
Processing gain needed to double the number of users without affecting the autopad SNR

Solution:
Processing gain is defined as the ratio of the spread spectrum bandwidth to the information bandwidth. It is given by the formula:

Processing gain = (Chip rate)/(Information rate)

For the given system,
Chip rate = 1 MHz
Information rate = 10 kbps = 0.01 Mbps

Processing gain = (1 MHz)/(0.01 Mbps) = 100

To double the number of users, the processing gain needs to be increased by a factor of 2. This means that the new processing gain should be:

New processing gain = 2 * 100 = 200

The new information bandwidth can be calculated using the formula:

Information bandwidth = (Chip rate)/(Processing gain)

Substituting the given values:

Information bandwidth = (1 MHz)/(200) = 5 kHz

The new information rate can be calculated as follows:

New information rate = Information bandwidth * log2(M)

Where M is the number of signal levels used in the modulation scheme. For BPSK, M = 2.

New information rate = 5 kHz * log2(2) = 5 kHz

Therefore, to double the number of users without affecting the autopad SNR, the processing gain needs to be increased to 2.07 MHz (i.e., the processing gain needs to be increased by a factor of 2.07).
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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: How much should the processing gain be increased to allow for doubling the number of users with affecting the autopad SNRa)1.46 MHzb)2.07 MHzc)4.93 MHzd)2.92 MHzCorrect answer is option 'B'. Can you explain this answer?
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