Hello Kassem,

If you have your signal sequence in matlab, say:

x(n) = [ 1 -1 1 -1]

The average power of this signal is it's variance which is its' variance which is var(x)=1.3333 in our assumed case.

Once you normalize x(n) by the square root of the power (i.e. standard deviation) you get the same signal of unit power, that is 

x1 = sqrt(1/var(x)) * x 

Now that you've got your signal with power 1 Watt (or mW depending on the units of the vector x(n) ), you can generate your signal with a desired power P (which in your case is tuned to be 150mW) by 

x2= sqrt(P) * x1

Finally x2 is the same signal as x but with power P.

Hope this helps ;-D

Dear Kassem,

let x be your signal.

First you normalize by the square root of it's power (or square root of the variance) to get the same signal at unit power.

x1 = sqrt(1/var(x))*x;

Now x1 is of power 1 and you would like a signal at power P (which in your case is P = 150mW) so all you need to do is multiply x1 by sqrt(P)

x2 = sqrt(P)*x1;

Finally, x2 is the same signal as x but at power P.

Hope this helps ;-D

Mr. @Ahmad Bazzi, for x2, should i convert P=150 mW to watts?

Hello again Kassem,

Well since x1 is now unit less, if you'd leave P as 150 then the total power is measured in mW but if you convert P to 150*10^-3 then the total power is measured in Watt.

You can generate a Gaussian signal via randn(1,10000) in MATLAB. This signal show you variance equal to 1 (1W power). To find 150W, you have to scale your generated data by sqrt(150).