I have a question regarding the concept of carrier power, output power and power relative to carrier (dBc). Suppose I have a carrier frequency of 4Hz and signal bandwidth = 4 Hz. The signal span is from [2Hz 6Hz].
My indexing starts at 0 for simplicity.
I have 7 samples with sampling frequency 7 Hz such that:
x(n)=[1+1j 2-2j 1+3j 3+j 4 5 2+2j]; % Time domain signal
Representing the signal into frequency domain by taking the FFT with 7 points (each frequency bin is 1 Hz range 0-6 Hz) and normalizing for power,
X[n]=[2.6+0.7j -0.56+0.54j -0.99-0.52j -0.5+0.07j 0.38+0.69j 0.7+0.2j -0.63-0.7j].
The output power in dBm within the Bandwidth from 2Hz to 6Hz (for simplicity we are considering up to only 4 samples excluding 6Hz sample) is:
OutPow=10*log10(sum(abs(X[:,2:5]).^2))+30; % in dBm
Therefore, the signal power is 34.34 dBm. Note: I don't think this is the average power.
I would like to generate a noise with -20 dBc. Here are two methods to generate noise power with -20dBc in frequency domain.
Method 1 (the idea is Wanted Signal Power (BW 4 Hz) -Noise at the carrier = 20 dBc):
SigPow=34.34 ; %dBm TargetNoisePower=(34.34-20)=5.66; % Its down to 20 dBc NoiseCarrierMagnitude=sqrt(1/1000)*10^(5.66/20)=0.0607; % Noise amplitude for carrier Noise(n)=[0 0 0 0 0.0607 0 0]; % A single sample at frequency domain
Method 2 (The idea is Sample Power at carrier ($f_c=4$ Hz) -Noise at the carrier =20 dBc):
FcPow=27.93 ; %dBm At 4Hz the sample is 0.38+0.69j TargetNoisePower=(27.93-20)=7.93; % at the carrier NoiseCarrierMagnitude=sqrt(1/1000)*10^(7.93/20)=0.079; % Noise amplitude for carrier Noise(n)=[0 0 0 0 0.079 0 0]; % A single sample at frequency domain
My questions are the following:
- Which method is right for generating a noise signal in dBc?
- The channel might not be occupied with signal at the carrier frequency. For example within the signal BW the exact carrier frequency ($f_c=4$ Hz) sample might be 0 or have only some noise (AWGN) sample.
- When we say signal power within the bandwidth, do we mean the total power within the bandwidth?