**8. (a) Draw and Explain block diagram of GSM system. [6M]**

GSM stands for Global System for Mobile communication.

In GSM, geographical area is divided into hexagonal cells whose side depends upon power of transmitter and load on transmitter (number of end user). At the center of cell, there is a base station consisting of a transceiver (combination of transmitter and receiver) and an antenna.

**GSM Architecture :-**

Fig. GSM Architecture

**Function of Components :-
**i) MS : It refers for mobile station. Simply, it means a mobile phone.

ii) BTS : It maintains the radio component with MS.

iii) BSC : Its function is to allocate necessary time slots between the BTS and MSC.

iv) HLR : It is the reference database for subscriber parameter ike subscriber’s ID, location, authentication key etc.

v) VLR : It contains copy of most of the data stored in HLR which is temporary and exist only until subscriber is active.

vi) EIR : It is a database which contains a list of valid mobile equipment on the network.

vii) AuC : It perform authentication of subscriber.

**Working:-
**i) GSM is combination of TDMA (Time Division Multiple Access), FDMA (Frequency Division Multiple Access) and Frequency hopping.

ii) Initially, GSM use two frequency bands of 25 MHz width : 890 to 915 MHz frequency band for up-link and 935 to 960 MHz frequency for down-link. Later on, two 75 MHz band were added. 1710 to 1785 MHz for up-link and 1805 to 1880 MHz for down-link.

iii) up-link is the link from ground station to a satellite and down-link is the link from a satellite down to one or more ground stations or receivers. GSM divides the 25 MHz band into 124 channels each having 200 KHz width and remaining 200 KHz is left unused as a guard band to avoid interference.

**Amplitude modulation (AM):** Modulation in which the amplitude of a carrier wave is varied in accordance with some characteristic of the modulating signal.

i) Amplitude modulation implies the modulation of a coherent carrier wave by mixing it in a nonlinear device with the modulating signal to produce discrete upper and lower sidebands, which are the sum and difference frequencies of the carrier and signal.

i) The envelope of the resultant modulated wave is an analog of the modulating signal.

**Expression of amplitude modulation:-
**1. Carrier signal equations

it is possible to describe the carrier in terms of a sine wave as follows:

$latex C(t)\;=\;C\sin\;\left(\omega_c\;+\;\phi\right)$

Where:

carrier frequency in Hertz is equal to $latex \frac{\omega_c}{2\mathrm\pi}$

C is the carrier amplitude

$latex \phi$ is the phase of the signal at the start of the reference time

Both C and $latex \phi$ can be omitted to simplify the equation by changing C to “1” and $latex \phi$ to “0”.

2. Modulating signal equations

The modulating waveform can either be a single tone. This can be represented by a cosine waveform, or the modulating waveform could be a wide variety of frequencies – these can be represented by a series of cosine waveforms added together in a linear fashion.

$latex m(t)\;=\;M\sin\;\left(\omega_m\;+\;\phi\right)$

Where:

modulating signal frequency in Hertz is equal to $latex \frac{\omega_m}{2\mathrm\pi}$

M is the carrier amplitude

$latex \phi$ is the phase of the signal at the start of the reference time

Both C and $latex \phi$ can be omitted to simplify the equation by changing C to “1” and $latex \phi$ to “0”.

3. Overall modulated signal for a single tone

The equation for the overall modulated signal is obtained by multiplying the carrier and the modulating signal together.

y (t) = [ A + m (t) ] . c (t)

The constant A is required as it represents the amplitude of the waveform.

Substituting in the individual relationships for the carrier and modulating signal, the overall signal becomes:

$latex y\;(t)\;=\;\lbrack\;A\;+\;M\;\cos\;(\omega_m\;t\;+\;\phi\;\rbrack\;.\;\sin(\omega_c\;t)$

This can be expanded out using the standard trigonometric rules:

$latex y\;(t)\;=\;A\;.\;\sin\;(\omega c\;t)\;+\;M/2\;\lbrack\;\sin\;((\omega c\;+\;\omega m)\;t\;+\;\phi)\;+\;M/2\;\lbrack\;\sin\;((\omega c\;-\;\omega m)\;t\;-\;\phi)$

In this theory, three terms can be seen which represent the carrier, and upper and lower sidebands:

Carrier: $latex A\;.\;\sin\;(\omega_c\;t)$

Upper sideband: $latex \frac M2\;\lbrack\;\sin\;((\omega_c\;+\;\omega_m)\;t\;+\;\phi)$

Lower sideband: $latex \frac M2\;\lbrack\;\sin\;((\omega_c\;-\;\omega_m)\;t\;-\;\phi)$

**Modulation Index in AM
**The modulation index is ratio of modulating signal voltage(V

m = V_{m}/V_{c}

The modulation index should be a number between 0 and 1.

Modulation index can be calculated by knowing modulating voltage and carrier voltage. But it is very common to measure the modulation index from the modulated waveform.

After the modulated envelope, Vmax and Vmin is noted down.

Using this Vm and Vc is derived using following formulas or equations.

$latex \begin{array}{l}V_m\;=\;(V_{max}-V_{min})/2\;….\left(1\right)\;\;\\\\V_c\;=\;(V_{max}+V_{min})/2\;…..\left(2\right)\end{array}$

Now modulation index is calculated either taking ratio of Vm by Vc as mentioned above.

$latex \begin{array}{l}m\;=\;V_m/V_c\;\;\\\\m\;=\;\left(V_{max}-V_{min}\right)/\left(V_{max}+V_{min}\right).\end{array}$

Waveforms of amplitude modulation:-

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