MSK and GMSK Modulation Techniques Explained

This page delves into the MSK (Minimum Shift Keying) and GMSK (Gaussian Minimum Shift Keying) modulation techniques. We’ll explore the intricacies of the GMSK modulator and demodulator, focusing on implementations based on the QPSK modulation method.

MSK Modulation

GMSK is a derivative of the MSK modulation scheme, which itself is derived from Offset QPSK modulation. In MSK, a half-cycle sine wave is used instead of a rectangular pulse wave. The frequency difference between a logical zero and a logical one is half the data rate. The modulation index is 0.5.

The mathematical representation of MSK modulation is given by:

Fig.1 MSK Equation

The MSK modulation waveform for an NRZ (Non-Return-to-Zero) data signal is depicted below:

Fig.2 MSK modulation signal in time domain

GMSK Modulation

Gaussian Minimum Shift Keying, or GMSK, is employed in GSM (Global System for Mobile Communications) and CDPD (Cellular Digital Packet Data) technologies. There are two primary methods for generating GMSK: FSK modulation and QPSK modulation.

While the FSK-based GMSK VCO architecture exists, it’s not ideal for coherent demodulation. We will focus on the QPSK-based method used in GSM, as illustrated in Figures 3 and 4. Figure 3 shows the GMSK modulator and figure 4 shows the GMSK demodulator.

Fig.3 GMSK Modulation Block Diagram

As seen in the GMSK modulator diagram, a Gaussian filter is applied to the NRZ signal after it passes through an integrator block. This produces Φ (phase). Applying cosine (COS) and sine (SIN) functions to Φ generates the I (In-phase) and Q (Quadrature) components, which are then mixed with cos and sin functions, respectively. Both chains are summed to produce S(n). The trigonometric equations included in Fig.3 describe this process in mathematical detail.

Fig.4 GMSK Demodulator Block Diagram

The GMSK demodulator (Fig.4) essentially retrieves Φ using the arctangent (arctan) function. This is then passed to a derivator block to recover the NRZ signal. Before this, mixing and low-pass filtering are applied to obtain the I and Q components from two chains. Again, the trigonometric equations in Fig. 4 illustrate the underlying mathematics.

The bandwidth efficiency for both MSK and GMSK is 1 bit/s/Hz, also known as spectral efficiency.

Figure 5 depicts typical MSK and GMSK waveforms:

Fig. 5 MSK/GMSK spectral density

Advantages

• In MSK, the modulated carrier has no phase discontinuities, and frequency changes occur at the zero-crossings of the carrier. This helps keep the PAPR (Peak-to-Average Power Ratio) low, reducing the need for highly linear power amplifiers.
• GMSK offers better spectral efficiency compared to MSK (as shown in Figure 5).
• GMSK demodulation has reasonably low complexity.

Disadvantages

• The power spectral density of MSK doesn’t decay quickly enough, which can lead to interference between adjacent channels.
• GMSK addresses this by using various BT (Bandwidth-Time product) factors. A BT of 0.3 provides good rejection against adjacent channels because the curve falls more rapidly (as shown in Figure 5).