## 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), digital video broadcast system APSK (DVBS-APSK), and MIL-188-QAM.

### APSK

A pure M-APSK constellation is composed of NC concentric rings or contours, each with uniformly spaced PSK points. The M-APSK constellation set is

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

where:

• The modulation order is equal to the sum of all Ml for l = 1, 2, ... , NC.

• NC is the number of concentric rings. NC ≥ 2.

• Ml is the number of constellation points in the lth ring.

• Rl is the radius of the lth ring.

• ϕl is the phase offset of the lth ring.

• $j=\sqrt{-1}$

### DVBS APSK

Digital video broadcasting (DVB) standards specify S2 [1], S2X [2], and SH [3] standard-specific amplitude phase shift keying (APSK) modulation.

• DVB-S2 standard specifies QPSK modulation and concatenated convolutional and Reed-Solomon channel coding, and is now used by most satellite operators worldwide for television and data broadcasting services.

• DVB-S2X standard based systems offer the ability to operate with very low carrier-to-noise and carrier-to-interference ratios (SNR down to -10 dB), to serve markets such as airborne (business jets), maritime, civil aviation internet access, VSAT terminals at higher frequency ranges or in tropical zones, small portable terminals for journalists and other professionals. Furthermore, the S2X system provides transmission modes offering significantly higher capacity and efficiency to serve professional links characterized by very high carrier-to-noise and carrier-to-interference ratios conditions.

• DVB-SH standard provides an efficient transmission system using frequencies below 3 GHz suitable for satellite services to handheld devices, in terms of reception threshold and resistance to mobile satellite channel impairments.

### 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 [5].

## References

[1] ETSI Standard EN 302 307 V1.4.1: Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S2), European Telecommunications Standards Institute, Valbonne, France, 2005-03.

[2] ETSI Standard EN 302 307-2 V1.1.1: Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S2X), European Telecommunications Standards Institute, Valbonne, France, 2015-02.

[3] ETSI Standard EN 302 583 V1.1.1: Digital Video Broadcasting (DVB); Framing structure, channel coding and modulation for Satellite Services to Handheld devices (SH), European Telecommunications Standards Institute, Valbonne, France, 2008-03.

[4] 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.

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