Communication systems and modulation
Communication systems and modulation
This domain tests analog and digital modulation, bandwidth, symbol rate, SNR, Eb/N0, and multiple-access choices. You should be able to move between bit rate, symbol rate, occupied bandwidth, and error-performance metrics.
Core rules
- AM with a single tone has bandwidth 2fm; SSB uses fm. FM Carson's rule: BW approximately 2(Delta f+fm).
- For M-ary signaling, symbol rate Rs=Rb/log2M. With raised-cosine filtering, occupied bandwidth is approximately Rs(1+alpha).
- Shannon capacity: C=B log2(1+S/N), with linear power ratio. Eb/N0(dB)=SNR(dB)+10log(B/Rb).
- Coherent PSK/QAM needs carrier recovery; noncoherent FSK is simpler but less efficient. OFDM uses many subcarriers and a cyclic prefix to absorb delay spread.
- Processing gain for direct-sequence spread spectrum is about 10log(chip rate/bit rate).
Worked example
A 16-QAM link carries 24 Mbit/s. Each symbol carries log2 16=4 bits, so Rs=24/4=6 Msym/s. With alpha=0.25, the occupied bandwidth is 6(1.25)=7.5 MHz, giving 24/7.5=3.2 bit/s/Hz. If the received SNR in that bandwidth is 20 dB, Eb/N0=20+10log(7.5/24)=20-5.05=14.95 dB. That value, not raw SNR, is compared with the modulation's required Eb/N0.
Traps
Confusing bit rate with symbol rate, using log10 instead of log2 for M, applying Carson's rule to AM, and inserting a dB SNR directly into Shannon's linear formula. Also check whether bandwidth means occupied, channel, or noise bandwidth.