matlab noise level,phase noise相位噪声matlab
该文本描述了一个MATLAB函数addphasenoise用于在输入信号中添加相位噪声。该函数接受五个参数：输入信号Sin、采样频率Fs、相位噪声的频率偏移phasenoisefreq、相位噪声的功率phasenoisepower以及一个验证标志VALIDATION_ON。
函数通过插值方法在对数尺度上对给定的SSB相位噪声功率谱进行平滑处理，并结合加性白高斯噪声（AWGN）生成具有指定特性（如最小相位噪声水平）的复数信号。此外，该函数还提供了验证功能以比较生成与预期的相位噪声谱特性。
函数 Sout = add_phase_noise(Sin, Fs, phase_noise_freq, phase_noise_power, VALIDATION_ON)
%
% function Sout = add_phase_noise( Sin, Fs, phase_noise_freq, phase_noise_power, VALIDATION_ON )
%
% Oscillator Phase Noise Model
%
% INPUT:
% Sin - input COMPLEX signal
% Fs - sampling frequency ( in Hz ) of Sin
% phase_noise_freq - frequency offsets where the SSB Phase Noise is specified (in Hz)
% phase_noise_power - SSB Phase Noise power ( in dBc/Hz )
% VALIDATION_ON - 1 - perform validation, 0 - don't perfrom validation
%
% OUTPUT:
% Sout - output COMPLEX phase noised signal
%
% NOTE:
% Input signal should be complex
%
% EXAMPLE ( How to use add_phase_noise ):
% Assume SSB Phase Noise is specified as follows:
% -------------------------------------------------------
% | Offset From Carrier | Phase Noise |
% -------------------------------------------------------
% | 1 kHz | -84 dBc/Hz |
% | 10 kHz | -100 dBc/Hz |
% | 100 kHz | -96 dBc/Hz |
% | 1 MHz | -109 dBc/Hz |
% | 10 MHz | -122 dBc/Hz |
% -------------------------------------------------------
%
% Assume that we have 10000 samples of complex sinusoid of frequency 3 KHz
% sampled at frequency 40MHz:
%
% Fc = 3e3; % carrier frequency
% Fs = 40e6; % sampling frequency
% t = 0:9999;
% S = exp(j2piFc/Fst); % complex sinusoid
%
To generate the phase-noised signal S_1 from the original signal S, the following procedure is executed.
%
% Fs = 40e6;
% phase_noise_freq = [ 1e3, 10e3, 100e3, 1e6, 10e6 ]; % Offset From Carrier
% phase_noise_power = [ -84, -100, -96, -109, -122 ]; % Phase Noise power
% S1 = add_phase_noise( S, Fs, phase_noise_freq, phase_noise_power );
% Version 1.0
% Alex Bur-Guy, October 2005
%
% Revisions:
% Version 1.5 - Comments. Validation.
% Version 1.0 - initial version
% NOTES:
The proposed model is a straightforward VCO phase noise model derived from the following considerations.
% If the output of an oscillator is given as V(t) = V0 * cos( w0*t + phi(t) ),
% then phi(t) is defined as the phase noise. In cases of small noise
% sources (a valid assumption in any usable system), a narrowband modulation approximation may be employed as a suitable approximation technique for analysis purposes
% be used to express the oscillator output as:
%
% V(t) = V0 * cos( w0*t + phi(t) )
%
% = V0 * [cos(w0*t)cos(phi(t)) - sin(w0t)*sin(phi(t)) ]
%
% ~ V0 * [cos(w0t) - sin(w0t)*phi(t)]
%
This demonstrates that phase noise will interact with the carrier to result in sidebands around it.
%
%
% 2) In other words, exp(jx) ~ (1+jx) for small x
%
% 3) Phase noise = 0 dBc/Hz at freq. offset of 0 Hz
%
The minimum phase noise level value is determined by the maximal input SSB phase noise power.
% freq. offset from DC. (IT DOES NOT BECOME EQUAL TO ZERO )
%
% The generation process is as follows:
First, we perform interpolation on a logarithmic scale to obtain the SSB phase noise power spectrum, which is then stored as variable M.
% equally spaced points (on the interval [0 Fs/2] including bounds ).
%
By means of determining the desired frequency profile of phase noise, we utilize the formula X(m) = \sqrt{P(m) \cdot dF(m)} to compute it.
After implementing this, I will subsequently counterbalance it with the symmetrical negative portion of the spectrum.
%
随后我们合成单位功率的AWGN在频域并对其应用点状乘法。
% the calculated shape
%
% Finally we perform 2*M-2 points IFFT to such generated noise
% ( See comments inside the code )
%
% 0 dBc/Hz
% \ /
% \ /
% \ /
% \P dBc/Hz /
% .\ /
% . \ /
% . \ /
改写说明
% . \
% || _||||||||||||||||||| (N points)
% 0 dF Fs/2 Fs
% DC
%
%
if nargin < 5
VALIDATION_ON = 0;
end
% Check Input
error( nargchk(4,5,nargin) );
if ~any( imag(Sin(:)) )
error( 'Input signal should be complex signal' );
end
if max(phase_noise_freq) >= Fs/2
error( 'Maximal frequency offset should be less than Fs/2');
end
% Make sure phase_noise_freq and phase_noise_power are the row vectors
phase_noise_freq = phase_noise_freq(:).';
phase_noise_power = phase_noise_power(:).';
if length( phase_noise_freq ) ~= length( phase_noise_power )
error('phase_noise_freq and phase_noise_power should be of the same length');
end
% Sort phase_noise_freq and phase_noise_power
[phase_noise_freq, indx] = sort( phase_noise_freq );
phase_noise_power = phase_noise_power( indx );
% Add 0 dBc/Hz @ DC
if ~any(phase_noise_freq == 0)
phase_noise_power = [ 0, phase_noise_power ];
phase_noise_freq = [0, phase_noise_freq];
end
% Calculate input length
N = prod( size( Sin ) );
Define M as the number of points (within the positive spectrum) for frequency resolution.
% (M equally spaced points on the interval [0 Fs/2] including bounds),
% then the number of points in the negative spectrum will be M-2
% ( interval (Fs/2, Fs) not including bounds )
%
% The total number of points in the frequency domain will be 2*M-2, and if we want
% to get the same length as the input signal, then
% 2*M-2 = N
% M-1 = N/2
% M = N/2 + 1
%
% So, if N is even then M = N/2 + 1, and if N is odd we will take M = (N+1)/2 + 1
%
if rem(N,2), % N odd
M = (N+1)/2 + 1;
else
M = N/2 + 1;
end
% Equally spaced partitioning of the half spectrum
F = linspace( 0, Fs/2, M ); % Freq. Grid
dF = [diff(F) F(end)-F(end-1)]; % Delta F
% Perform interpolation of phase_noise_power in log-scale
intrvlNum = length( phase_noise_freq );
logP = zeros( 1, M );
for intrvlIndex = 1 : intrvlNum,
leftBound = phase_noise_freq(intrvlIndex);
t1 = phase_noise_power(intrvlIndex);
if intrvlIndex == intrvlNum
rightBound = Fs/2;
t2 = phase_noise_power(end);
inside = find( F>=leftBound & F<=rightBound );
else
rightBound = phase_noise_freq(intrvlIndex+1);
t2 = phase_noise_power(intrvlIndex+1);
inside = find( F>=leftBound & F
end
logP( inside ) = ...
该计算结果等于初始时间与从内部功能值加实数最小值减去左边界加实数最小值得到的对数值之差，
再除以右边界加实数最小值减左边界加实数最小值得到的对数值之差，
最后乘以最终时间减初始时间的结果。
end
P = 10.^(real(logP)/10); % Interpolated P ( half spectrum [0 Fs/2] ) [ dBc/Hz ]
Now, to achieve this goal, we will synthesize an additive white Gaussian noise (AWGN) signal with a power level of one in the frequency domain and reshape it into the target configuration.
% as follows:
%
DC附近的频率偏移F(m)，我们的目标是获得所需功率Ptag(m)，以实现P(m)=Ptag/dF(m)。
% that is we have to choose X(m) = sqrt( P(m)*dF(m) );
%
% Due to the normalization factors of FFT and IFFT defined as follows:
% For length K input vector x, the DFT is a length K vector X,
% with elements
% K
% X(k) = sum x(n)exp(-j2pi(k-1)*(n-1)/K), 1 <= k <= K.
% n=1
% The inverse DFT (computed by IFFT) is given by
% K
% x(n) = (1/K) sum X(k)exp( j2pi(k-1)*(n-1)/K), 1 <= n <= K.
% k=1
%
% we have to compensate normalization factor (1/K) multiplying X(k) by K.
% In our case K = 2*M-2.
% Generate AWGN of power 1
if ~VALIDATION_ON
awgn_P1 = ( sqrt(0.5)(randn(1, M) +1jrandn(1, M)) );
else
awgn_P1 = ( sqrt(0.5)(ones(1, M) +1jones(1, M)) );
end
% Shape the noise on the positive spectrum [0, Fs/2] including bounds ( M points )
X = (2M-2) * sqrt( dF . P ) .* awgn_P1;
A fully symmetric negative spectrum spanning from Fs/2 to Fs is excluded at the boundaries, comprising M-2 points.
X( M + (1:M-2) ) = fliplr( conj(X(2:end-1)) );
% Remove DC
X(1) = 0;
% Perform IFFT
x = ifft( X );
% Calculate phase noise
phase_noise = exp( j * real(x(1:N)) );
% Add phase noise
if ~VALIDATION_ON
Sout = Sin .* reshape( phase_noise, size(Sin) );
else
Sout = 'VALIDATION IS ON';
end
if VALIDATION_ON
figure;
plot( phase_noise_freq, phase_noise_power, 'o-' ); % Input SSB phase noise power
hold on;
grid on;
plot( F, 10log10(P),'r-'); % Input SSB phase noise power
X1 = fft( phase_noise );
plot( F, 10log10( ( (abs(X1(1:M))/max(abs(X1(1:M)))).^2 ) ./ dF(1) ), 'ks-' );% generated phase noise exp(jx)
X2 = fft( 1 + j*real(x(1:N)) );
plot( F, 10log10( ( (abs(X2(1:M))/max(abs(X2(1:M)))).^2 ) ./ dF(1) ), 'm>-' ); % approximation ( 1+jx )
xlabel('Frequency [Hz]');
ylabel('dBc/Hz');
legend( ...
'Input SSB phase noise power', ...
'Interpolated SSB phase noise power', ...
'Positive spectrum of the generated phase noise exp(j*x)', ...
'Positive spectrum of the approximation ( 1+j*x )' ...
);
end