## How Gross Trasmission Rate of 270Kbps calculate in GSM?

Dear Experts,

The amount of information transmitted over a radio channel over a period of time is known as the transmission rate. Transmission rates is expressed in bits per second or bits/s. in GSM the net bit rate over the air interface is 270 kbit/s.

Lets See how it is calculated....

The modulation technique used in GSM is Gaussian Minimum Shift Keying (GMSK). GMSK enables the transmission of 270 kbit/s within a 200 kHz channel. This gives a bitrate of 1.3 bit/s per Hz.

In GSM, a TDMA frame consists of 8 time slots.

Now, Human speech is first converted from analog to digital then to reduce effect of trasmission problems speech coding,interleaving,antenna diversity,space diversity,polarization diversity,frequency hopping etc are used.

Normal speech is sampled by twice the voice frequency as per sampling theory to analog speech signals.Telecommunication systems use a sampling frequency of 8 kHz, which is acceptable based on the sampling theory.

The next step is to give each sample a value for quantization.Within common telephony, 256 levels are used while in GSM 8,192 levels are used.

Then Coding is done for the quantized values into binary.Every value is represented by a binary code of 13 bits (213 = 8192). Foe example, a quantized value of 2,157 would have a bit pattern of 01000011011101:
The result from the process of A/D conversion is 8,000 samples per second of 13 bits each. This is a bit rate of 104 kbits/s.When it is considered that 8 subscribers use one radio channel, the overall bit rate would be 8× 104 kbits/s = 832 kbits/s. recalling the general rule of 1 bit per Hertz, this bit rate would not fit into the 200 kHz available for all 8 subscribers. The bit rate must be reduced somehow- this is achieved using segmentation and speech coding.

In GSM each 20 ms of speech is sampled at the rate of 50 times per second(beacuse out of 260 bits from speech coding 50 are most important bits) instead of the 8,000 used by A/D.instead of using 13 bits per sample as in A/D conversion, GSM speech coding uses 260 bits. This calculates as 50× 260=13 kbits/s. this provides a speech quality which is acceptable for mobile telephony and comparable with wire line PSTN phones.

The GSM speech coder produces a bit rate of 13 kbits/s per subscriber. When it is considered that 8 subscribers use one radio channel, the overall bit rate would be 8×13 kbits/s =104 kbits/s. this compares favorably with the 832 kbits/s from A/D conversion.

Channel coding in GSM uses the 260 bits from speech coding as input to channel coding and outputs 456 encoded bits.In GSM, the input to burst formatting is the 456 bits received from ciphering. Burst formatting adds a total of 136 bits per block of 20 ms, bringing the overall total to 592.However, each time slot a TDMA frame is 0.577 ms long. This provides enough time for 156.25 bits to be transmitted (each bit takes 3.7µs).

In 0.577 ms 156.25 bits or 1250 (8 subscribers in 1 TDMA frame of 4.615 ms)will be trasmitted so trasmission rate would be 270.9Kbps.