Minimum Shift Keying (MSK) MCQ Quiz - Objective Question with Answer for Minimum Shift Keying (MSK) - Download Free PDF

• Gaussian Minimum Shift Keying, GMSK is a form of modulation based on frequency shift keying that has no phase discontinuities and provides efficient use of spectrum as well as enabling high-efficiency radio power amplifiers.
• GMSK is probably most widely associated with the 2G GSM mobile communications system where it proved to be an effective form of modulation.
• It was one of the reasons that GSM cellphones had a long battery life in view of the high efficiency that could be obtained from the RF power amplifiers.

Concept:

• Gaussian Minimum Shift Keying, GMSK is a form of modulation based on frequency shift keying that has no phase discontinuities and provides efficient use of spectrum as well as enabling high-efficiency radio power amplifiers.
• GMSK is probably most widely associated with the 2G GSM mobile communications system where it proved to be an effective form of modulation.
• It was one of the reasons that GSM cellphones had a long battery life in view of the high efficiency that could be obtained from the RF power amplifiers.

 Application:  In view of the concept the modulation scheme commonly used for transmission from GSM mobile terminals is Gaussian Minimum Shift Keying (GMSK)

• Gaussian Minimum Shift Keying, GMSK is a form of modulation based on frequency shift keying that has no phase discontinuities and provides efficient use of spectrum as well as enabling high-efficiency radio power amplifiers.
• GMSK is probably most widely associated with the 2G GSM mobile communications system where it proved to be an effective form of modulation.
• It was one of the reasons that GSM cellphones had a long battery life in view of the high efficiency that could be obtained from the RF power amplifiers.

Concept:

• Gaussian Minimum Shift Keying, GMSK is a form of modulation based on frequency shift keying that has no phase discontinuities and provides efficient use of spectrum as well as enabling high-efficiency radio power amplifiers.
• GMSK is probably most widely associated with the 2G GSM mobile communications system where it proved to be an effective form of modulation.
• It was one of the reasons that GSM cellphones had a long battery life in view of the high efficiency that could be obtained from the RF power amplifiers.

 Application:  In view of the concept the modulation scheme commonly used for transmission from GSM mobile terminals is Gaussian Minimum Shift Keying (GMSK)

• Gaussian Minimum Shift Keying, GMSK is a form of modulation based on frequency shift keying that has no phase discontinuities and provides efficient use of spectrum as well as enabling high-efficiency radio power amplifiers.
• GMSK is probably most widely associated with the 2G GSM mobile communications system where it proved to be an effective form of modulation.
• It was one of the reasons that GSM cellphones had a long battery life in view of the high efficiency that could be obtained from the RF power amplifiers.

Concept:

• Gaussian Minimum Shift Keying, GMSK is a form of modulation based on frequency shift keying that has no phase discontinuities and provides efficient use of spectrum as well as enabling high-efficiency radio power amplifiers.
• GMSK is probably most widely associated with the 2G GSM mobile communications system where it proved to be an effective form of modulation.
• It was one of the reasons that GSM cellphones had a long battery life in view of the high efficiency that could be obtained from the RF power amplifiers.

 Application:  In view of the concept the modulation scheme commonly used for transmission from GSM mobile terminals is Gaussian Minimum Shift Keying (GMSK)

From the given data the MSK waveform is inform $v_s\left(t\right)=\sqrt{2P_s}\left[\frac{b_0\left(t\right)+b_e\left(t\right)}{2}\right]\sin \left(5\pi \times {10}^7+\frac{\pi }{6}\right)+\sqrt{2P_s}\left[\frac{b_0\left(t\right)-b_e\left(t\right)}{2}\right]\sin \left({\omega }_{c}t-\varphi \right)$

$\Rightarrow \sqrt{2P_S}=4$

P_s = Power/symbol = 8

⇒ Energy per symbol = 8 × bit duration

f_b = 10⁷ S^-1

Energy per bit E_b = ½ Energy per symbol

= 4 × 10^-7 w

Noise power N_D = P.S.D × B

$=1.34\times {10}^{-15}\times \left(1.5\times {10}^7\right)\left(\therefore B_{MSK}=1.5f_B\right)$

= 2.01 × 10^-8 w

Probability of error $P_e=\frac{1}{2}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{c}\left(\sqrt{\frac{E_b}{N_o}}\right)$

$=\frac{1}{2}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{c}\left(\sqrt{19.9}\right)$

$=\frac{1}{2}\frac{e^{\left(-19.9\right)}}{\sqrt{\pi \sqrt{19.9}}}$

= 1.44 × 10^-10

Given the duration of bit T_b = 0.1 ml

⇒ f_b = 10 kHz

If the sure bits are modulated

Using BPSK and MSK

for BPSK bandwidth B = 2f_b

= 20 kHz

for MSK bandwidth B = 1.5 f_b

= 15 kHz

Explanation:

For the signals to be orthogonal, the cross correlation between ${\mathrm{f}}_1\left(\mathrm{t}\right)$ and ${\mathrm{f}}_2\left(\mathrm{t}\right)$ should be zero, i.e,

 $\underset{0}{\overset{\mathrm{T}}{\int }}{\mathrm{f}}_1\left(\mathrm{t}\right){\mathrm{f}}_2\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}=0$

$$\begin{gathered} \Rightarrow \underset{0}{\overset{\mathrm{T}}{\int }}{\mathrm{A}}^2\mathrm{c}\mathrm{o}\mathrm{s}\left(2\pi {\mathrm{f}}_1\mathrm{t}+{\varphi }_1\right)\mathrm{c}\mathrm{o}\mathrm{s}\left(2\pi {\mathrm{f}}_2\mathrm{t}+{\varphi }_2\right)\mathrm{d}\mathrm{t} \\ \Rightarrow \frac{{\mathrm{A}}^2}{2}\left[\underset{0}{\overset{\mathrm{T}}{\int }}\mathrm{c}\mathrm{o}\mathrm{s}\left[2\pi ({\mathrm{f}}_1+{\mathrm{f}}_2)\mathrm{t}+{\varphi }_1+{\varphi }_2\right]\mathrm{d}\mathrm{t} \\ +\underset{0}{\overset{\mathrm{T}}{\int }}\mathrm{c}\mathrm{o}\mathrm{s}\left[2\pi ({\mathrm{f}}_1-{\mathrm{f}}_2)\mathrm{t}+{\varphi }_1-{\varphi }_2\right]\mathrm{d}\mathrm{t}\right] \\ \Rightarrow \frac{{\mathrm{A}}^2/2}{2\pi ({\mathrm{f}}_1+{\mathrm{f}}_2)}\left[\mathrm{s}\mathrm{i}\mathrm{n}\left[2\pi ({\mathrm{f}}_1+{\mathrm{f}}_2)\mathrm{T}+{\varphi }_1+{\varphi }_2\right]-\mathrm{s}\mathrm{i}\mathrm{n}\left[{\varphi }_1+{\varphi }_2\right]\right] \\ +\frac{{\mathrm{A}}^2/2}{2\pi ({\mathrm{f}}_1-{\mathrm{f}}_2)}\left[\mathrm{s}\mathrm{i}\mathrm{n}\left[2\pi ({\mathrm{f}}_1-{\mathrm{f}}_2)\mathrm{T}+{\varphi }_1-{\varphi }_2\right]-\mathrm{s}\mathrm{i}\mathrm{n}\left[{\varphi }_1-{\varphi }_2\right]\right] \end{gathered}$$

Now, the first term is zero as ${\mathrm{f}}_1$ and ${\mathrm{f}}_2$ are integral multiples of $\frac{1}{\mathrm{T}}$ So, ${\mathrm{f}}_1+{\mathrm{f}}_2=\frac{\mathrm{r}}{\mathrm{T}}\left(\mathrm{l}\mathrm{e}\mathrm{t}\right)$ where $\mathrm{r}$ is an integer.

$\Rightarrow \mathrm{s}\mathrm{i}\mathrm{n}\left[2\pi ({\mathrm{f}}_1+{\mathrm{f}}_2)\mathrm{T}+{\varphi }_1+{\varphi }_2\right]-\mathrm{s}\mathrm{i}\mathrm{n}\left[{\varphi }_1+{\varphi }_2\right]=0$

Now, for the second term to be zero, $2\pi ({\mathrm{f}}_1-{\mathrm{f}}_2)\mathrm{T}+{\varphi }_1-{\varphi }_2={\varphi }_1-{\varphi }_2+2\pi \mathrm{n}$

$\Rightarrow {\mathrm{f}}_1-{\mathrm{f}}_2=\frac{\mathrm{K}}{\mathrm{T}}$

$\Rightarrow {\left|{\mathrm{f}}_1-{\mathrm{f}}_2\right|}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}=\frac{1}{\mathrm{T}}$

In MSK, $\left|{\mathrm{f}}_1-{\mathrm{f}}_2\right|=\frac{{\mathrm{R}}_{\mathrm{b}}}{2}$

This is the minimum frequency spacing while maintaining the orthogonality of signals.