MSK and GMSK | Teleinf Edu

Minimum Shift Keying (MSK): continuous-phase binary FSK

Minimum Shift Keying (MSK) is a binary continuous-phase form of Frequency Shift Keying (FSK). It uses a constant envelope and a selected frequency deviation, so nonlinear amplification can be used without encoding information in amplitude. The phase remains continuous at symbol boundaries, which generally reduces sidelobes compared with independently switched FSK. MSK's occupied spectrum still depends on pulse shape, filtering, and the bandwidth definition.

Continuous phase in CPFSK

MSK is a type of . MSK applies this principle with binary frequency pulses and $h=0.5$ . The phase trajectory is continuous, while instantaneous frequency follows the selected tone. This reduces sidelobes relative to discontinuous FSK; the occupied bandwidth remains dependent on pulse shaping and the measurement definition.

Minimum shift and modulation index

The name "Minimum Shift" refers to the relationship between the two frequencies ( $f_1$ and $f_2$ ) used for the binary symbols and the bit rate ( $R_b$ ). Let $T_b=1/R_b$ . In this definition, $\Delta f$ denotes the deviation from the center frequency, so the tone separation is $2\Delta f$ :

$\Delta f_{\mathrm{tone}} = |f_1 - f_2| = 0.5 \cdot R_b,\qquad \Delta f = \frac{R_b}{4}$

For rectangular binary FSK with coherent correlation over one bit interval, this tone separation makes the two signals . With the deviation notation defined above, MSK has $h=2\Delta f T_b=0.5$ , where $h$ is the modulation index.

How MSK is generated: relation to OQPSK

MSK can be represented as a special case of Offset QPSK (OQPSK). Like OQPSK, it offsets one of the two signal components, the 'Q' channel, to prevent simultaneous changes that would create a 180° phase reversal. MSK also uses a defined pulse shape for the I and Q branches.

In the rectangular-pulse QPSK representation, MSK uses half-sine shaped pulses on the I and Q branches. The pulse shape gives a continuous phase trajectory and a constant envelope in the resulting signal.

With $h=0.5$ , half-sine pulse shaping gives MSK a narrow main lobe and lower sidelobes than discontinuous binary FSK, reducing . Exact adjacent-channel performance depends on filtering and channel spacing.

Gaussian MSK (GMSK): Gaussian pulse shaping

Gaussian Minimum Shift Keying (GMSK) is MSK with Gaussian filtering of the data or frequency pulse before modulation. It was specified for the Global System for Mobile Communications (GSM) and used in its 2G radio interface. GMSK retains a constant envelope and continuous phase while the filter changes the pulse shape and spectrum.

Gaussian pre-filtering

GMSK adds a before the MSK modulator. The stream of rectangular data pulses first passes through this filter, which smooths their transitions and produces pulses with temporal tails.

Filtering changes the frequency-pulse shape and therefore the phase trajectory; continuity remains a property of the CPFSK modulator. Lower sidelobes can make the spectrum more compact, with the result depending on the filter parameter and measurement definition. This supports systems with closely spaced frequency channels, including GSM.

The BT Product

The amount of smoothing is controlled by the BT product, where 'B' is the 3-dB bandwidth of the Gaussian filter and 'T' is the bit period. A smaller BT product narrows the spectrum and increases temporal overlap between adjacent bits, producing more controlled inter-symbol interference. In GSM, the specified value is $BT = 0.3$ , a compromise between spectral occupancy and detection performance.

GMSK trade-off: controlled ISI

Gaussian filtering narrows the spectrum but introduces .

A filtered pulse extends beyond the interval of its bit and overlaps neighboring intervals. This is a controlled form of ISI: its response is known from the filter and can be included in receiver design. Depending on the receiver architecture, an equalizercan compensate for the overlap and improve bit decisions. The added processing is the trade-off for GMSK's spectral containment.