Online Simulator for MSK (Minimum Shift Keying)

MSK Waveform Generator

Standard: Minimum Shift Keying

Input Bitstream

Baud Rate ($R_b$)

Mod. Index ($h$)

Carrier (Hz)

Step 1: NRZ Encoding
$m(t) = \sum a_n \cdot rect(t-nT)$

Step 2: Frequency Pulse (Rectangular)
$g(t) = m(t)$

Step 3: Linear Phase Trajectory
$\phi(t) = \frac{\pi}{2T} \int m(\tau) d\tau$

Step 4: MSK Carrier Waveform
$s(t) = \cos(2\pi f_c t + \phi(t))$

Theory: Understanding MSK Modulation

Minimum Shift Keying (MSK) is a type of continuous-phase frequency shift keying. The frequency spacing is the minimum required to keep the symbols orthogonal ($1/2T$).

• Phase: Shifts exactly $\pm 90^\circ$ ($\pi/2$ radians) over each bit period.

What is MSK?

Minimum Shift Keying (MSK) is a type of continuous-phase frequency shift keying (CPFSK). In standard FSK, abrupt frequency changes cause phase jumps. MSK ensures the phase remains perfectly smooth.

The frequency spacing between '0' and '1' is exactly $1/2T$, which is the minimum spacing required for the two signals to remain orthogonal (detectable without interference).

Mathematical Form

$$s(t) = \cos \left( 2\pi f_c t + \Phi(t) \right)$$

Where the phase $\Phi(t)$ evolves linearly:

$$\Phi(t) = b(t) \frac{\pi t}{2T} + \phi_0$$

Key Advantages

• Spectral Efficiency: Lower sidebands than standard FSK due to continuous phase.
• Constant Amplitude: Allows use of efficient non-linear amplifiers without signal distortion.

GMSK Variant

In Gaussian MSK (GMSK), the NRZ pulses are passed through a Gaussian filter to "round off" edges, further narrowing the spectrum (used in GSM cellular standards).

Simulator Guide:
1. NRZ Signal: Raw data pulses (-1 and +1).
2. Phase Plot: Observe how the phase climbs for '1's and falls for '0's.
3. MSK Carrier: The final wave with no sudden "breaks" in the signal.

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