Dear Dr. Ahmed,

If i understood you, you distribute the signal states of the QAM symbols by means of the constellation diagram or phasor diagram, where one plot the state points on a two intentional diagram. It is so that the states at best distributed regularly in a square mesh with equal distance between the state points in the horizontal x direction and vertical y -direction.

In case of 16 QAM one has 16 symbols distributed homogeneously an a square whose half diagonal length is equal to the maximum symbol strength. Twice its projection distance on the x or the y direction has equidistant four points representing 4 states. In this way one divides the square into square mesh with distance dx=dy= 2 projection distance/3.

For the figure please follow the link: http://ecelabs.njit.edu/ece489v2/lab5.php

So given the coordinates of the points one can calculate its angle and the magnitude of the vector connecting this point to the point of origin.

Best wishes

Thanks a lot Dr. Zekry for your helpful explaination.

Dear Ahmed,

The basic way in which a QAM signal can be generated is to generate two signals that are 90° out of phase with each other and then sum them. This will generate a signal that is the sum of both waves, which has a certain amplitude resulting from the sum of both signals and a phase which again is dependent upon the sum of the signals.

If the amplitude of one of the signals is adjusted then this affects both the phase and amplitude of the overall signal, the phase tending towards that of the signal with the higher amplitude content.

As there are two RF signals that can be modulated, these are referred to as the I - In-phase and Q - Quadrature signals.

The I and Q signals can be represented by the equations below:

I = A cos(Ψ) and Q = A sin(Ψ)

It can be seen that the I and Q components are represented as cosine and sine. This is because the two signals are 90° out of phase with one another.

Using the two equations it is possible to express the signal as:.

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

Using the expression A cos(2πft + Ψ) for the carrier signal.

A cos(2πft + Ψ) = I cos(2?ft) - Q sin(2πft)

Where f is the carrier frequency.

This expression shows the resulting waveform is a periodic signal for which the phase can be adjusted by changing the amplitude either or both I and Q. This can also result in an amplitude change as well.

Accordingly it is possible to digitally modulate a carrier signal by adjusting the amplitude of the two mixed signals.

By Ian Poole

Thank you very much Dear Khalid for your help and explanation...