Apparent Contradiction: Textbook $\beta < 0.3$ for NBFM vs. practical $\beta \approx 0.83$ in real systems.
Resolution:
1. "Narrowband" has two definitions:
  - Theoretical: $\beta < 0.3$, small angle approximation holds, exactly 3 spectral components.
  - Practical: $\beta < 1$, 2-3 significant sideband pairs, but still much narrower than WBFM. This is common industrial usage.
2. Actual Bandwidth: For $\beta = 0.83$, Bessel functions show the 2nd sidebands are marginal, 3rd negligible. Carson's rule: $BW = 2(\Delta f + f_m) = 2(2.5+3) = 11$ kHz, which fits in a 12.5 kHz channel.
3. Why $\beta = 0.83$ is "narrowband": It's a relative definition. Compared to WBFM ($\beta = 5$, BW $\approx 180$ kHz), 11 kHz is indeed narrow.
4. Historical Context: Early NBFM systems used $\beta = 0.8-1.0$ as a practical compromise for audio quality and bandwidth.
Conclusion: The $\beta < 0.3$ is a pedagogical simplification. In engineering practice, NBFM often refers to systems with $\beta < 1$, which are still "narrowband" relative to WBFM and meet channel spacing requirements. This highlights the difference between theoretical ideals and practical compromises.

Critical Distinction: Two different efficiencies:
1. Modulation Efficiency (what I meant): Percentage of RF power carrying information.
  - AM (DSB-FC): 33% (carrier wastes 2/3 power).
  - SSB-SC: 100% (all transmitted RF power carries information).
2. Power Amplifier (PA) Efficiency: Percentage of DC input converted to RF output. This depends on PA class, not modulation.
  - Class A: 25-30% (linear, for SSB, AM, QAM)
  - Class B: 50-60% (linear, for SSB)
  - Class C: 60-80% (non-linear, for NBFM, WBFM - constant envelope)
Where Wasted Power Goes: Mostly converted to heat in the PA transistors and other circuit components. This is why transmitters need cooling.
SSB requires Linear PA: SSB has a variable envelope, so it needs linear PAs (Class A/B) to avoid distortion, which are less efficient.
NBFM Advantage: NBFM has a constant envelope, allowing it to use highly efficient Class C PAs (75% efficient).
Overall Efficiency Comparison (DC input for 100W RF carrying information):
- AM: 400W DC (due to carrier waste and Class C PA)
- SSB: 167W DC (100% modulation efficient, but Class B PA)
- NBFM: 133W DC (100% modulation efficient, and Class C PA)
Conclusion: While SSB has 100% modulation efficiency, NBFM often has better overall DC-to-RF efficiency due to its ability to use more efficient Class C PAs. This is why handheld radios often use NBFM.

Your Proposal: Parallel BPSK (Frequency Division Multiplexing - FDM):
- Fails to achieve high throughput: e.g., 50 parallel BPSK channels in 100 MHz might only yield 50 Mbps, far from 1 Gbps.
Why Parallel BPSK Fails:
1. Guard Bands Waste Spectrum: Each BPSK channel needs separation, wasting significant bandwidth. QAM with OFDM uses orthogonal subcarriers, requiring no guard ban