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Simulating Minimum Shift Keying Transmitter

Posted By __Krishna Sankar__ On January 19, 2008 @ 5:51 am In __Modulation__ | __17 Comments__

**Minimum shift keying (MSK)** is an important concept to learn in digital communications. It is a form of continuous phase frequency shift keying ^{[1]}. In minimum phase shift keying, two key concepts are used.

(a) The frequency separation of the sinusoidals used for representing bits 1′s and 0′s are , where is the symbol period.

(b) It is ensured that the resulting waveform is phase continuous.

In a previous post (here), ^{[2]}we have understood that the minimum frequency separation for two sinusoidals having zero phase difference to be orthogonal is , where is the symbol period. However, it can be observed that at each symbol boundary, there is a phase discontinuity. The presence of phase discontinuities can result in large spectral side lobes outside the desired bandwidth. Hence the need for having a frequency modulated signal which is phase continuous.

To ensure continuous phase, the phase of the carrier of the MSK signal is

, where

is the symbol period,

corresponds to -1 for bit 0, +1 for bit 1 respectively.

The corresponding carrier signal is

.

**Figure: Phase transition diagram for MSK (Ref: Fig10.22 in [COMM-PS ^{[3]}]**

Simple Octave/Matlab code for simulating and plotting binary Minimum Shift Keying is kept here ^{[4]}.

We have observed that bit error probability of classical coherent binary frequency shift keying ^{[1]} is 3dB poorer compared to bit error probability of binary phase shift keying ^{[5]}. However, in minimum shift keying, using the knowledge of the phase transitions, we should be able to **recover the 3dB loss associated with FSK and get a performance comparable to BPSK**. We will hopefully discuss that in a future post.

[COMM-PS] Communication Systems Engineering, John G. Proakis, Masoud Salehi ^{[3]}

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URL to article: **http://www.dsplog.com/2008/01/19/simulating-minimum-shift-keying-transmitter/**

URLs in this post:

[1] frequency shift keying : **http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/**

[2] here), : **http://www.dsplog.com/2007/12/31/minimum-frequency-spacing-for-having-orthogonal-sinusoidals/**

[3] COMM-PS: **http://www.amazon.com/Communication-Systems-Engineering-John-Proakis/dp/0130617938**

[4] here: **http://www.dsplog.com/db-install/wp-content/uploads/2008/01/scriptmsktx.m**

[5] bit error probability of binary phase shift keying: **http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/**

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