GAUSSIAN MINIMUM SHIFT KEYING (GMSK) full form in digital communication gmsk vs msk difference between gmsk vs msk signals.

**GAUSSIAN MINIMUM SHIFT KEYING (I.e., GMSK) **

Like Minimum shift keying (MSK), Gaussian MSK (GMSK) yields a constant amplitude and continuous phase RF carrier signal. It only differs in use of a Gaussian baseband pulse shape in place of square pulse shape for MSK. Because, the Gaussian pulse rises and decays asymptotically with respect to a zero response level, it has a much more constrained bandwidth. A typical GMSK system has been shown in figure 8.36 along with an unfiltered MSK system.

**diagram**

**FIGURE 8.36*** GMSK as unfiltered MSK.*

The unfiltered MSK is generated by direct FSK modulation of a carrier with a baseband signal which is scaled in amplitude to produce a modulation index of 0.5. This value of modulation index produces a difference of 180° phase shift for the two data values. However, in GMSK, there is ISI (Inter symbol interference) which is a bandwidth limiting factor. GMSK is employed in GSM digital cellular radios and cellular digital packet data (CDPD) applications.

Gaussian Minimum Shift Keying (GMSK) is a modification of MSK. A filter used to reduce the bandwidth of a baseband pulse train prior to modulation is called a pre-modulation filter. The Gaussian pre-modulation filter smooths the phase trajectory of the MSK signal and hence limiting the instantaneous frequency variations. The result is an FM modulated signal with a much narrower bandwidth. This bandwidth reduction does not come for free since the pre-modulation filter smears the individual pulses in pulse train. As a consequence of this smearing in time, adjacent pulses interfere with each other generating what is commonly called inter-symbol interference or ISI. In the applications, where GMSK is used, the trade-off between power efficiency and bandwidth efficiency is well worth the cost.

Bit Error Rate (BER) for GMSK is given by

P* _{e}* = Q …(8.101)

where α is a constant related to BT

*,*

_{b}

**Table. 8.8. GMSK Parameter a Rslated to BT**

*.*_{b}S.No. |
The value of BT_{b} |
The values of α |

1. | 0.25 | 0.68 |

2. | 0.85 |

It may be noted that the case where BT → corresponds to MSK (i.e. the filter is all pass for a fixed symbol interval T* _{s}*).

Recall that the probability of error for plain MSK is given by

P

*Q …(8.102)*

_{e}Here, we can conclude that This arises from the trade off between power and bandwidth efficiency. GMSK achieves a better bandwidth efficiency than MSK at the expense of power efficiency.

**8.16 GMSK FOR WIRELESS DATA TRANSMISSION**

DO YOU KNOW? |

Gaussian minimum-shift keying is a special case of FSK that achieves the minimum bandwidth possible for a two-frequency FSK system at a given data rate. |

The proliferation of computers in today’s society has increased the demand for transmission of data over wireless links. Binary data, composed of sharp “one to zero” and “zero to one” transitions, results in a spectrum rich in harmonic content that is not well suited to RF transmission. Hence, the field of digital modulation has been flourishing. Recent standards such as Cellular Digital Packet Data (CDPD) and Mobitex specify Gaussian Filtered Minimum Shift keying (GMSK) for their modulation method.

GMSK is a simple yet effective approach to digital modulation for wireless data transmission. To provide a good understanding of GMSK, we shall review the basics of MSK and GMSK, as well as how GMSK is implemented in CDPD and Mobitex systems.

GMSK modems reduce system complexity, and in turn lower system cost. There are, however, some important implementation details to be considered.

If we look at Fourier series expansion of a data signal, we observe harmonics extending to infinity. When these harmonics are summed, they give the data signal and its sharp transitions. Hence, an unfiltered NRZ data stream used to modulate an RF carrier will produce an RF spectrum of considerable bandwidth. The FCC has strict regulations about spectrum usage and such a system is generally considered impractical. But if we start to remove the high frequency harmonics from the Fourier series (i.e. pass the data signal through a lowpass filter), the transitions in the data will become progressively less sharp. This suggests that premodulation filtering is an effective method for reducing the occupied spectrum for wireless data transmission. In addition to a compact spectrum, a wireless data modulation scheme must have good bit error rate (BER) performance under noisy conditions. Its performance should also be independent of power amplifier linearity to allow the use of class *C* power amplifiers.

The academic field of ‘Data Transmission’ is full of modulation strategies that attempt to meet the above criteria. Most of them involve translation of data bits or patterns into a particular Combination of phase, frequency or amplitude. Some of the more notable techniques are listed in Table 8.9.

**Table 8.9. Modulation Formats**

S.No. | Modulation technique | Common Acronym |

1. | Frequency Shift Keying | FKS |

2. | Multi-level Frequency Shift Keying | MFSK |

3. | Continuous Phase Frequency Shift Keying | CPFSK |

4. | Minimum Shift Keying | MSK |

5. | Gaussian Minimum Shift Keying | GMSK |

6. | Tamed Frequency Modulation | TFM |

7. | Phase Shift Keying | PSK |

8. | Quadrature Phase Shift Keying | QPSK |

9. | Differential Quadrature Phase Shift Keying | DQPSK |

10. | π/4 Differential Quadrature Phase Shift Keying | π/4 DQPSK |

11. | Quadrature Amplitude Modulation | QAM |

Each of the modulation formats listed in Table 8.6 is suited to specific applications. In general, schemes that rely on more than two levels (e.g. QAM, QPSK) require better signal to noise ratios (SNR) than two-level schemes for similar BER perfomance. Additionally, in a wireless environment, multi-level schemes generally require greater power amplifier linearity than two-level schemes. The fact that GMSK uses a two-level continuous phase modulation (CPM) format has contributed to its popularity. Another point in its favour is that it allows the use of class C power amplifiers (relatively non-linear) and data rates approaching the channel BW (dependent on filter bandwidth and channel spacing).

**8.17 GMSK FROM MSK **

Prior to discussing GMSK in detail, we need to review MSK, from which GMSK is derived. MSK is a continuours phase modulation scheme where the modulated carrier contains no phase discontinuities and frequency changes occur at the carrier zero crossings. MSK is unique due to the relationship between the frequency of a logical zero and one the difference between the frequency of a logical zero and a logical one is always equal to half the data rate. In other words, the modulation index is 0.5 for MSK, and is defined as

m = D*f* x T

where Df = |f_{logic-1} – *f*_{logic0} |

T = 1/bit rate

For example, a 1200 bit per second baseband MSK data signal could be composed of 1200 Hz and 1800 Hz frequencies for a logical one and zero respectively as shown in figure 8.37.

**diagram**

**FIGURE 8.37** *1200 band MSK Data Signal; (a) NRZ Data (b) Signal*

Baseband MSK, as shown in figure 8.37, is a robust means of transmitting data in wireless systems where the data rate is relatively low compared to the channel BW.

An alternative method for generating MSK modulation can be realized by directly injecting NRZ data into a frequency modulator with its modulation index set for 0.5 as shown in figure 8.38. This approach is essentially equivalent to baseband MSK. However, in the direct approach, the VCO is part of the RF/IF section, whereas in baseband MSK, the voltage to frequency conversion takes place at baseband.

**diagram**

**FIGURE 8.38*** Direct MSK modulation*

The fundamental problem with MSK is that the spectrum is not compact enough to realize data rates approaching the RF channel BW. A plot of the spectrum for MSK reveals sidelobes extending well above the data rate. For wireless data transmission system, which require more efficient use of the RF channel BW, it is necessary to reduce the energy of the MSK upper sidelobes. Earlier, we stated that straightforwared means of reducing this energy is lowpass filtering the data stream prior to presenting it to the modulator (pre- modulation filtering). The pre-modulation lowpass filter must have a narrow BW with a sharp cutoff frequency and very little overshoot in its impulse response. This is where the Gaussian filter characteristic comes in. It has an impulse response characterized by a classical Gaussian distribution (bell shaped curve), as shown in figure 8.39. The absence of overshoot or ringing may be clearly observed.

**diagram**

**FIGURE 8.39** *Gaussian Filter Impulse Response for BT= 0.3 and BT = 0.5.*

Figure 8.39 depicts the impulse response of a Gaussian filter for BT = 0.3 and 0.5. *BT* is related to the filter’s 3 dB BW and data rate by

BT =

Hence, for a data rate of 9.6 kbps and a BT of 0.3, the filter’s – 3 dB cutoff frequency is 2880 Hz.

Again from figure 8.39, it may be noted that a bit is spread over approximately 3 bit periods for BT = 0.3 and two bit periods for BT = 0.5. This gives rise to a phenomena called inter-symbol interference (ISI). For BT = 0.3 adjacent symbols or bits will interfere with each other more than for BT = 0.5. GMSK with BT = is equivalent to MSK.

In other words, MSK does not intentionally introduce ISI. Greater ISI allows the spectrum to be more compact, making demodulation more difficult. Hence, spectral compactness is the primary trade-off in going from MSK to Gaussian pre-modulation filtered MSK. Figure 8.40 displays the normalized spectral densities for MSK and GMSK. It may be observed that the sidelobe energy for GMSK is reduced. Ultimately, this means that channel spacing can be tighter for GMSK compared to MSK for the same adjacent channel interference.

**diagram**

**FIGURE 8.40*** Spectral Density for MSK and GMSK.*