ISB modulation; AM vs FM

ISB modulation

Independent Sideband (ISB) modulation transmits two different messages on the two sidebands of one carrier: message $m_1(t)$ on the USB and message $m_2(t)$ on the LSB. A reduced (pilot) carrier is usually sent for receiver synchronisation.

 m1(t) --> SSB modulator (USB) --+
                ^                |
 fc osc --------+---------------(+)--> ISB out
                v                |       (+ pilot carrier)
 m2(t) --> SSB modulator (LSB) --+

Derivation. Using the phase-shift form of SSB:

$$\begin{aligned} s_{USB}(t) &= \frac{A_c}{2}[m_1(t)\cos\omega_ct - \hat m_1(t)\sin\omega_ct] \\ s_{LSB}(t) &= \frac{A_c}{2}[m_2(t)\cos\omega_ct + \hat m_2(t)\sin\omega_ct] \end{aligned}$$ $$s_{ISB}(t) = \frac{A_c}{2}\{[m_1(t) + m_2(t)]\cos\omega_ct - [\hat m_1(t) - \hat m_2(t)]\sin\omega_ct\}$$

For single tones $m_1 = A_1\cos\omega_1t$, $m_2 = A_2\cos\omega_2t$:

$$s_{ISB}(t) = \frac{A_cA_1}{2}\cos(\omega_c+\omega_1)t + \frac{A_cA_2}{2}\cos(\omega_c-\omega_2)t$$

        m2 band  |  m1 band
       (LSB)     |   (USB)
   ----[////]----+----[\\\\]---->  f
      fc-W      fc       fc+W

Bandwidth $= 2W$ for two channels, same as one DSB channel. Used in HF point-to-point radio telephony to carry two voice channels.

AM vs FM