413x0g2 - CCSDS

CCSDS REPORT CONCERNING BANDWIDTH-EFFICIENT MODULATIONS3 TECHNICAL DEFINITIONS3.1 PRECODED GMSK3.1.1 INTRODUCTIONGaussian Minimum Shift Keying (GMSK) is a constant envelope, continuous phasemodulation first introduced in 1981 by Murota and Hirade (reference [4]). It is derived fromMinimum Shift Keying (MSK) with the addition of a baseband Gaussian filter that furtherreduces sidelobe levels and spectral bandwidth. The product of the Gaussian filterbandwidth and the coded symbol period at the input to the modulator, referred to as the BT sfactor, is used to differentiate between GMSK modulations of varying bandwidthefficiencies. If there is no coding, BT s refers to the filter bandwidth times the bit period. 3 Ingeneral, a smaller BT s factor results in less spectral bandwidth occupancy but greaterintersymbol interference which can be compensated for using equalization or trellisdemodulation. GMSK has a constant envelope which reduces spectral regrowth and signaldistortion due to amplifier nonlinearity.Like MSK, GMSK is inherently a differential Continuous Phase Modulation (CPM) (i.e., theinformation is carried in the change of the phase rather than the phase itself). For a coherentin-phase/quatrature (I/Q) demodulator, at the receiver is needed a differential decoder whichincreases the BER by approximately a factor of two. By precoding the GMSK signal at thetransmitter to remove the inherent differential encoding, the BER can be halved. Figure 3-1d ∈ 1 .shows a block diagram of the precoder were { }k±Input NRZbit stream(-1) k to GMSK modulatorda kkz -1Figure 3-1: GMSK Precoder3.1.2 SIGNAL MODELMathematically, the precoded GMSK modulated RF carrier is expressed as:where:P is the power of the carrier;ƒ c is the center frequency;( 2πfτ + ϕ(τ ) 0)x ( τ ) 2Pcos+ ϕ=c3 See 2.4 for bit/symbol terminology definitions used in this Green Book.CCSDS 413.0-G-2 Page 3-1 October 2009