Bandpass power spectrum density issue

I have a signal x with power 15 dB and carrier frequency 29.7 GHz. I want to draw the power spectral desnity (PSD) of the signal in bandpass from 0 to fs/2. I expected

• The main lobe of the PSD to be centered at 29.7 GHz

However, what I get

• The main lobe of the PSD is centered around 3 GHz

See the image

This is the code I am using

clearvars;
clc;

Wx = 50*10^6;               % Signal bandwidth
Tx = 1/Wx;                  % Symbol time

fs = 1*10^9;                % Sampling frequency
Ts = 1/fs;                  % Sampling time
fc = 29.7*10^9;             % Carrier frequency

J = Tx/Ts;                  % Number of samples per symbol

SNRdB = 15;                 % SNR in dB scale
SNR = 10^(SNRdB/10);        % SNR in linear scale

M = 32;                     % Number of BPSK symbols
S = M*J;                    % Total number of samples in M symbols

t=(0:S-1)*Ts;               % Time vector in sample time

d = 2.*(rand(M,1)>0.5)-1;   % Generating BPSK signal

dSamples = repelem(d,J);    % The equivalent signal in samples


dx = sqrt(SNR).*dSamples.*cos(2*pi*fc*t.');     % Scaling the power of the signal and frequency shift the frequency to fc
[psd,fr]=pwelch(dx,[],[],(0:10^6:fs/2),fs);     % Finding the PSD using pwelch MATLAB method between 0 and fs/2
plot(fr, 10*log10(psd), 'LineWidth',1);
ylabel('PSD (dBW/Hz)');
xlabel('Frequency');
grid on;

Why is the center frequency not correct? Am I using pwelch method incorrectly?

Answer 1

[Chunru]

You need fs >2*f_upper. Try fs = 80GHz

Wx = 50*10^6;               % Signal bandwidth
Tx = 1/Wx;                  % Symbol time
fs = 80*10^9;                % Sampling frequency  <==================
Ts = 1/fs;                  % Sampling time
fc = 29.7*10^9;             % Carrier frequency
J = Tx/Ts;                  % Number of samples per symbol
SNRdB = 15;                 % SNR in dB scale
SNR = 10^(SNRdB/10);        % SNR in linear scale
M = 32;                     % Number of BPSK symbols
S = M*J;                    % Total number of samples in M symbols
t=(0:S-1)*Ts;               % Time vector in sample time
d = 2.*(rand(M,1)>0.5)-1;   % Generating BPSK signal
dSamples = repelem(d,J);    % The equivalent signal in samples
dx = sqrt(SNR).*dSamples.*cos(2*pi*fc*t.');     % Scaling the power of the signal and frequency shift the frequency to fc
[psd,fr]=pwelch(dx,[],[],(0:1e5:fs/2),fs);     % Finding the PSD using pwelch MATLAB method between 0 and fs/2
plot(fr, 10*log10(psd), 'LineWidth',1);
ylabel('PSD (dBW/Hz)');
xlabel('Frequency');
grid on;

[MAWE]

My understanding is that the sampling rate has to be greater than twice the bandwidth, which is the case in my code. What's f_upper in this case?

[Chunru]

In passband, fs should be more than twice of the largest frequency of interest (f_upper).

In baseband, fs should be twice of the bandwidth.

(There are special scheme for bandpass sampling which is not discussed here).