In digital modulation two commonly used terms are **Symbols** n **Modulation order(M) ****Symbol:**

It is actually a combination of bits.For instance, So and S1 are two symbols.Where ,So=00,S1=11 etc

**Modulation order-M**:

It refers to the number of states used in modulation,or the number of symbols.If M=2 it means two distinct states are being used in modulation. States could be different frequencies, amplitudes, or phase angles.If **M** is represented in power of ‘2’, that shows the number of bits per symbol.

** **__For M=4__

There will be 4 symbols(S0, S1, S2, S3).4=2^2.Therefore ,each symbol will be represented by **Two** bits.S0=00,S1=01,S2=10,S3=11

Keeping in view the ‘M’ factor, let’s restate the modulations techniques as:

**M-PSK,M-FSK,M-ASK, and M-QAM**

__M-PSK:__

For M=2: It is called as BPSK,(where B stands for Binary).Number of symbols are two. S0 and S1.As 2=2^1, so each symbol is represented by a single bit, therefore we wil have, S0=0 and S1=1

For M=4: It is called as 4-PSK.Number of symbols are Four.S0,S1,S2,and S3.As 4= 2^2,so each symbol is a combination of two bits,so we will have,S0=00,s1=01,s2=10,s4=11

So on and so forth for M=8,16,32,64

As **PSK** is phase modulation ,therefore the __number of states__ actually refer to __distinct Phase angles__.These phase angles are used to modulate the carrier.

**For M=2 , we have 2 phases/states**

Total angle is 360 degree

360/M =180 deg

So.’S0’ will b represented by 0 degree and ‘S1’ will be represented by 180(phase difference of 180 between symbols).That is, if 0 bit appears in signal, it will modulate the carrier wave with 0 degree, and 1 bit will modulate the carrier with 180 deg phase.

** **** **__For M=4, we have 4 distinct phases__

360/4 =90

So, Symbols will be represented as:

S0=0 deg,S1=90 deg,S2=135 deg,S3=180 deg

As we have the following symbols ,S0=00,s1=01,s2=10,s4=11.So, if 00 bits appear in signal, they will modulate the carrier wave with 0 degree,01 will modulate the carrier with 90 deg phase.10 will modulate the carrier with 135 deg n 11 will modulate it with 180 deg.

**For M=8,we have 8 phases**

360/8=45 deg

So,So=0deg,S1=45 deg,S2=90 deg,S3=135 deg,S4=180 deg,S5=225 deg,S6=270deg deg,S7=360 deg

Each symbol is represented by three bits here,

S0=000,S1=001,S2=010,S3=011,S4=100,S5=101,S6=110,S7=111

So, 000 bits will indicate 0 degree phase shift ,001 will represent 90 deg phase.010 will modulate the carrier with 135 deg ,0 11 will refer to 180 deg, n so on .

Similarly, for M-FSK, M frequencies are used to modulate a carrier and for M-ASK , M amplitude levels will be used.