# What is GFSK Modulation?

What is Gaussian Frequency Shift Keying or GFSK Modulation?

#### Editorial Team - everything RF

Dec 13, 2022

Gaussian Frequency Shift Keying or GFSK is an extension of the FSK modulation scheme where the frequency of the modulated signal will not instantaneously change at the beginning of each symbol period of the binary data. As a result, the transition from bit 0 to bit 1 or vice-versa becomes smoother. In other words, the amplitude and phase variations of the modulated signal will be relatively less compared to traditional FSK. In principle, FSK is implemented using independent local oscillators separately for in-phase and Quadrature components and the oscillators will be switched at the beginning of each symbol period to generate the carrier frequency for modulation. In general, all independent oscillators will not be at the same amplitude and phase at the beginning of symbol period, and therefore this causes sudden and abrupt changes in frequency for every bit change of the transmitted signal. Thus, the modulated FSK signal will be very wide with non-negligible side-lobes. Figure 1 illustrates this point.

Figure 1: FSK modulated signal for a given digital signal

If such a signal is received at the receiver, the distortion caused by the wireless channel along with other effects such as interference, thermal regeneration in receiver and others will degrade the performance of FSK, which does not allow the signal to be correctly decoded with precise and accurate amplitude and phase values after every symbol period.

In the GFSK modulation scheme, a Gaussian filter is included before the baseband waveform signal, i.e. the data signal such as in Figure 1, is modulated by the FSK modulator circuit. The inclusion of this Gaussian filter before modulation is the difference between GFSK and FSK. A typical Gaussian filter is a filter whose impulse response is a Gaussian function as shown in Figure 2.

Figure 2: Impulse response of a Gaussian filter

Since the Gaussian function in time is still Gaussian in frequency domain, the frequency response of this filter is very narrow. When an input signal is passed through such a filter, the resulting spectral width of the filtered signal is reduced compared to FSK scheme with no filtering involved. As a result, any abrupt changes in frequency in FSK are filtered out, which make the transitions at the beginning of each symbol period relatively smoother than FSK. Figure 3 illustrates the response of GFSK signal.

Figure 3: Gaussian filtered signal and GFSK modulated signal response

This method of filtering reduces sideband power or out-of-band spectrum, interference due to adjacent channels and the spectral width or bandwidth of FSK signal. However, this reduction in spectral width causes a spread in the time domain, thereby making it more likely to face intersymbol interference (ISI). Therefore, an careful design of Gaussian filter with optimal cut-off frequencies is very important to ensure that ISI-related effects can be minimized. Additionally, other robust signal processing and channel equalization techniques can also be used to overcome the effects of ISI.

This filtering stage before modulating the signal is also called pulse shaping as the data pulses are filtered out to produce a clean output signal with sharp rise and fall times, which helps in accurately determining the carrier frequency of the received signal. GFSK technique is useful and used in a wide range of wireless systems and technologies such as the Improved Layer 2 protocol, Bluetooth, IEEE 802.15.4, and Z-wave.