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A wireless digital transmission scheme is using 16-QAM over an additive white Gaussian noise channel ...

 


Given Information

  • Modulation scheme: 16-QAM
  • Bit rate: Rb = 4 × 106 bits/sec
  • Channel: Additive White Gaussian Noise (AWGN)
  • Receiver: Maximum-Likelihood Receiver

Step 1: Calculate Bits per Symbol

For M-ary QAM, the number of bits transmitted per symbol is:

Bits per symbol = log2(M)

= log2(16) = 4 bits/symbol

Step 2: Calculate Symbol Rate

Symbol rate is calculated by dividing the bit rate by the number of bits per symbol.

Rs = Rb / log2(M)

= (4 × 106) / 4

= 106 symbols/sec

Step 3: Calculate Minimum Bandwidth

For ideal Nyquist transmission with zero roll-off factor:

Bmin = Rs

= 106 Hz

= 1 MHz

Final Answer

1.00 MHz

Minimum transmission bandwidth required

Note: AWGN and maximum-likelihood detection do not change the minimum Nyquist bandwidth. The calculation assumes ideal zero-roll-off pulse shaping.

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