Signal power ....A confusion

Hi there, I have confusion about computation of signal power in matlab. Suppose i generate binary data of 1s and -1s ....once i transmit the data on a carrier as data.*carrier; ......% doing Bandpass

i would like to compute noise power so that i could add noise in my signal (talking about AWGN addition). So to compute noise we have noise_power = signal_power/SNR;

how would i calculate signal power? should i take signal before modulating carrier or after modulation i.e. with carrier...

Also sometimes i have seen codes in which the programmer took signal power Sp =1 .....why?

Answer 1

[Rick Rosson]

In this specific case, the probabilities of the outcomes do not actually matter; the only reason that I asked is that the probabilities do sometimes matter in the general case.

The reason they don't matter here is that the complex magnitude ( abs ) of each of the two outcomes in this specific case is always the same, which is exactly 1. So regardless of the individual probabilities, the average of the complex magnitudes across all of the outcomes is the magnitude of any one of the outcomes, which is exactly 1.

In other words, we can compute this average distance metric in MATLAB as follows:

   % Alphabet of possible symbols:
   a = [ +1 ; -1 ];

   % Probability of each symbol:
   p = [ 0.5 ; 0.5 ];

   % Average distance from the origin in the complex plane:
   A = (p.')*abs(a);

At this point, the value of A should be exactly 1:

   disp(A);

The only other thing we need to find is the power of the carrier wave. That is why I asked for the amplitude of the carrier. Let's represent the carrier amplitude in MATLAB as:

   % Amplitude of the carrier:
   V = 1;

so that the carrier itself is:

   % Carrier signal:
   x = V*cos(2*pi*Fc*t);

where t is some appropriate discrete representation of the time domain (in seconds), and Fc is the carrier frequency (in hertz).

So, how do we compute the power in the carrier signal, which is simply a pure-tone cosine wave? Well, power in any signal is simply the time average of the square of the signal. In the case of any unity amplitude pure tone sine or cosine wave, the time average of the square of the signal is simply 1/2. So for a carrier with amplitude of V, the time average is:

   % Carrier power:
   Pc = V^2/2;

So the overall signal power is:

   % Signal power:
   Ps = A*Pc;

HTH.

Rick

Answer 2

[Rick Rosson]

1. What is the amplitude of the carrier?
2. What is the probability of each outcome {+1 versus -1} in the data stream?

Answer 3

[Talha Rahman]

Amplitude of carrier ...is 1 ...

probability is 0.5.

???

Answer 4

[Talha Rahman]

Thanks Alot ...for the description ..... Indeed it helps...

Thank You..

Talha