QAM: need, generation and detection

Quadrature Amplitude Modulation (QAM) sends two independent message signals on the same carrier frequency, using two carriers of the same frequency that are $90^\circ$ apart (cos and sin). It is also called quadrature-carrier multiplexing. In digital form (M-ary QAM) both amplitude and phase change from symbol to symbol.

$$s(t)=A_c\,m_1(t)\cos 2\pi f_ct+A_c\,m_2(t)\sin 2\pi f_ct$$

Why QAM is necessary

• Bandwidth saving: two DSB-SC signals occupy the bandwidth of one, i.e. $2W$ for two messages. Its spectral efficiency equals SSB without needing sharp sideband filters.
• Higher data rate: in digital form, M-ary QAM carries $\log_2 M$ bits per symbol (16-QAM: 4 bits), so more data fits a band-limited channel.
• Better noise performance than M-ary PSK for the same $M$, because points are spread over the whole plane, not only a circle.
• Used in colour TV (chrominance), telephone modems, Wi-Fi, cable TV, LTE.

Generation

 m1(t) ---------->(X)<--- Ac cos wc t
                   |
                  (+)-------> s(t) QAM
                   |
 m2(t) ---------->(X)<--- Ac sin wc t
                        (-90 deg shift of
                         the same oscillator)

Two product modulators share one oscillator; one gets the carrier directly and the other through a $-90^\circ$ phase shifter. Their outputs are added. In digital QAM, $m_1$ and $m_2$ are multi-level signals $a_k$, $b_k$ produced by splitting the bit stream (serial-to-parallel) and converting groups of bits to levels.

Detection (coherent)

        +->(X)->[LPF]-> (Ac/2) m1(t)
        |   ^ cos wc t
 s(t) --+
        |   v sin wc t
        +->(X)->[LPF]-> (Ac/2) m2(t)

In-phase branch:

$$\begin{aligned} s(t)\cos\omega_ct &= A_cm_1\cos^2\omega_ct+A_cm_2\sin\omega_ct\cos\omega_ct\\ &=\frac{A_c}{2}m_1(t)+\frac{A_c}{2}m_1\cos 2\omega_ct+\frac{A_c}{2}m_2\sin 2\omega_ct \end{aligned}$$

The LPF removes the $2\omega_c$ terms, leaving $\tfrac{A_c}{2}m_1(t)$. Similarly the quadrature branch gives $\tfrac{A_c}{2}m_2(t)$.

The local carrier must have exactly the right phase and frequency. A phase error $\phi$ gives $\tfrac{A_c}{2}[m_1\cos\phi - m_2\sin\phi]$, i.e. cross-talk between channels. So a pilot or carrier recovery circuit (e.g. Costas loop) is used. In digital QAM the LPFs are replaced by integrate-and-dump correlators followed by multi-level decision devices.