## 3 Modulation format for 8PSK

05.043GPPModulationTS

## 3.1 Modulating symbol rate

The modulating symbol rate is 1/T = 1 625/6 ksymb/s (i.e. approximately 270.833 ksymb/s), which corresponds to 3*1 625/6 kbit/s (i.e. 812.5 kbit/s).

## 3.2 Symbol mapping

The modulating bits are Gray mapped in groups of three to 8PSK symbols by the rule

where l is given by table 1.

Table 1: Mapping between modulating bits and the 8PSK symbol parameter l.

 Modulating bits d3i,, d3i+1, d3i+2 Symbol parameter l (1,1,1) 0 (0,1,1) 1 (0,1,0) 2 (0,0,0) 3 (0,0,1) 4 (1,0,1) 5 (1,0,0) 6 (1,1,0) 7

This is illustrated in figure 2.

Figure 2: Symbol mapping of modulating bits into 8PSK symbols.

## 3.3 Start and stop of the burst

Before the first bit of the bursts as defined in GSM 05.02 [3] enters the modulator, the state of the modulator is undefined. Also after the last bit of the burst, the state of the modulator is undefined. The tail bits (see GSM 05.02) define the start and the stop of the active and the useful part of the burst as illustrated in figure 3. Nothing is specified about the actual phase of the modulator output signal outside the useful part of the burst.

Figure 3: Relation between active part of burst and tail bits.
For the normal burst the useful part lasts for 147 modulating symbols

## 3.4 Symbol rotation

The 8PSK symbols are continuously rotated with 3/8 radians per symbol before pulse shaping. The rotated symbols are defined as:

## 3.5 Pulse shaping

The modulating 8PSK symbols as represented by Dirac pulses excite a linear pulse shaping filter. This filter is a linearised GMSK pulse, i.e. the main component in a Laurant decomposition of the GMSK modulation. The impulse response is defined by:

where

and

.

T is the symbol period.

The base band signal is

The time reference t’ = 0 is the start of the active part of the burst as shown in figure 3. This is also the start of the bit period of bit number 0 (the first tail bit) as defined in GSM 05.02 [2].

## 3.6 Modulation

The modulated RF carrier during the useful part of the burst is therefore:

where Es is the energy per modulating symbol, f0 is the centre frequency and 0 is a random phase and is constant during one burst.

Annex A (informative):
Change control history

 SMG# SPEC VERS NEW_VERS PHASE SUBJECT S27 05.04 5.0.1 6.0.0 (Ph.2) R97 conversion to Release 97 EN S28 05.04 6.0.0 8.0.0 R99 Introduction of 8PSK for EDGE S30b 05.04 8.0.0 8.1.0 R99 Correction of mistake for range alpha-sub-i in clause 2.3 05.04 8.1.0 8.1.1 Figure 3 replaced (as it was corrupted) 05.04 8.1.1 8.1.2 Update to Version 8.1.2 for Publication