## Amplitude and Phase Modulation

Amplitude and phase modulation is a linear baseband modulation technique in which the message modulates the amplitude and phase of a constant frequency signal. Two carrier signals of the same frequency are out of phase with each other by 90°, a condition known as orthogonality or quadrature. The transmitted signal is created by adding the two carrier signals together. At the receiver, the two signals can be coherently separated (demodulated) because of their orthogonality property.

Communications Toolbox™ software includes these modulation and demodulation functions and blocks to model amplitude phase shift keying (APSK) and MIL-188-QAM.

Functions | System objects | Blocks |
---|---|---|

None | M-APSK Modulator Baseband, M-APSK Demodulator Baseband MIL-188 QAM Modulator Baseband, MIL-188 QAM Demodulator Baseband |

### APSK

A pure M-APSK constellation is composed of
*N*_{C} concentric rings or contours, each with
uniformly spaced PSK points. The M-APSK constellation set is

$$\chi =\{\begin{array}{cc}{R}_{1}\mathrm{exp}\left(j\left(\frac{2\pi}{{M}_{1}}i+{\varphi}_{1}\right)\right),& i=0,\dots ,{M}_{1}-1,\\ {R}_{2}\mathrm{exp}\left(j\left(\frac{2\pi}{{M}_{2}}i+{\varphi}_{2}\right)\right),& i=0,\dots ,{M}_{2}-1,\\ \vdots & \vdots \\ {R}_{{N}_{\text{C}}}\mathrm{exp}\left(j\left(\frac{2\pi}{{M}_{{N}_{\text{C}}}}i+{\varphi}_{\text{Nc}}\right)\right),& i=0,\dots ,{M}_{{N}_{\text{C}}}-1,\end{array}$$

where:

The modulation order is equal to the sum of all

*M*_{l}for*l*= 1, 2, ... ,*N*_{C}.*N*_{C}is the number of concentric rings.*N*_{C}≥ 2.*M*_{l}is the number of constellation points in the*l*th ring.*R*_{l}is the radius of the*l*th ring.ϕ

_{l}is the phase offset of the*l*th ring.$$j=\sqrt{-1}$$

### MIL-STD-188-110

MIL-STD-188-110 is a US Department of Defense standard for HF communications using serial PSK mode of both data and voice signals.

The standard specifies physical layer modulation schemes for tactical and long-haul communications. The modulation scheme specified by the standard is a mix of QAM and APSK. For a detailed description of the modulation scheme, see MIL-STD-188-110B & C [2].

## References

[1] Sebesta, J. “Efficient Method for APSK Demodulation.” *Selected Topics on Applied Mathematics, Circuits, Systems, and Signals* (P. Pardalos, N. Mastorakis, V. Mladenov, and Z. Bojkovic, eds.). Vouliagmeni, Athens, Greece: WSEAS Press, 2009.

[2] MIL-STD-188-110B & C: "Interoperability and Performance Standards for Data Modems." Department of Defense Interface Standard, USA.

## See Also

### Functions

### Objects

### Blocks

- Raised Cosine Transmit Filter | Raised Cosine Receive Filter | M-APSK Modulator Baseband | M-APSK Demodulator Baseband | MIL-188 QAM Modulator Baseband | MIL-188 QAM Demodulator Baseband