如何用MATLAB生成AWGN噪聲

huanying

MATLAB中的help文檔，是一個(gè)神奇的存在，檢索你想找的關(guān)鍵詞，會(huì)自動(dòng)檢索出與關(guān)鍵詞相關(guān)的內(nèi)容。例如：檢索一下“awgn”，我們可以得到如下圖所示的界面。

可以非常方便地查閱函數(shù)的語法定義，信號(hào)定義，以及給出example。

大部分非核心函數(shù)，可以打開看到源碼，例如awgn的源碼：

function y = awgn(varargin)%AWGN Add white Gaussian noise to a signal.%   Y = AWGN(X,SNR) adds white Gaussian noise to X.  The SNR is in dB.%   The power of X is assumed to be 0 dBW.  If X is complex, then %   AWGN adds complex noise.%%   Y = AWGN(X,SNR,SIGPOWER) when SIGPOWER is numeric, it represents %   the signal power in dBW. When SIGPOWER is 'measured', AWGN measures%   the signal power before adding noise.%%   Y = AWGN(X,SNR,SIGPOWER,S) uses S to generate random noise samples with%   the RANDN function. S can be a random number stream specified by%   RandStream. S can also be an integer, which seeds a random number%   stream inside the AWGN function. If you want to generate repeatable%   noise samples, then either reset the random stream input before calling%   AWGN or use the same seed input.%%   Y = AWGN(..., POWERTYPE) specifies the units of SNR and SIGPOWER.%   POWERTYPE can be 'db' or 'linear'.  If POWERTYPE is 'db', then SNR%   is measured in dB and SIGPOWER is measured in dBW.  If POWERTYPE is%   'linear', then SNR is measured as a ratio and SIGPOWER is measured%   in Watts.%%   Example 1: %        % To specify the power of X to be 0 dBW and add noise to produce%        % an SNR of 10dB, use:%        X = sqrt(2)*sin(0:pi/8:6*pi);%        Y = awgn(X,10,0);%%   Example 2: %        % To specify the power of X to be 3 Watts and add noise to%        % produce a linear SNR of 4, use:%        X = sqrt(2)*sin(0:pi/8:6*pi);%        Y = awgn(X,4,3,'linear');%%   Example 3: %        % To cause AWGN to measure the power of X and add noise to%        % produce a linear SNR of 4, use:%        X = sqrt(2)*sin(0:pi/8:6*pi);%        Y = awgn(X,4,'measured','linear');%%   Example 4: %        % To specify the power of X to be 0 dBW, add noise to produce%        % an SNR of 10dB, and utilize a local random stream, use:%        S = RandStream('mt19937ar','Seed',5489);%        X = sqrt(2)*sin(0:pi/8:6*pi);%        Y = awgn(X,10,0,S);%%   Example 5: %        % To specify the power of X to be 0 dBW, add noise to produce%        % an SNR of 10dB, and produce reproducible results, use:%        reset(RandStream.getGlobalStream)%        X = sqrt(2)*sin(0:pi/8:6*pi);%        Y = awgn(X,10,0);%%%   See also comm.AWGNChannel, WGN, RANDN, RandStream/RANDN, and BSC.
%   Copyright 1996-2018 The MathWorks, Inc.
%#codegen
narginchk(2,5);
% Validate signal inputsig = varargin{1};validateattributes(sig, {'numeric'}, ...    {'nonempty'}, 'awgn', 'signal input');
% Validate SNR inputreqSNR = varargin{2};validateattributes(reqSNR, {'numeric'}, ...    {'real','scalar','nonempty'}, 'awgn', 'SNR input');
% Validate signal powerif nargin >= 3    if strcmpi(varargin{3}, 'measured')       sigPower = sum(abs(sig(:)).^2)/numel(sig); % linear    else        validateattributes(varargin{3}, {'numeric'}, ...            {'real','scalar','nonempty'}, 'awgn', 'signal power input');        sigPower = varargin{3}; % linear or dB    endelse    sigPower = 1; % linear, defaultend
% Validate state or power typeif nargin >= 4        coder.internal.errorIf(comm.internal.utilities.isCharOrStringScalar(varargin{4}) && ...        all(~strcmpi(varargin{4}, {'db','linear'})), ...        'commInvalidPowerType');
    isStream = ~isempty(varargin{4}) && ~comm.internal.utilities.isCharOrStringScalar(varargin{4});
    if isStream && ~isa(varargin{4}, 'RandStream') % Random stream seed        validateattributes(varargin{4}, {'double'}, ...            {'real','scalar','nonnegative','integer','<',2^32}, ...            'awgn', 'seed input');    endelse % Default    isStream = false;end
% Validate power typeif nargin == 5    coder.internal.errorIf(comm.internal.utilities.isCharOrStringScalar(varargin{4}), ... % Type has been specified as the 4th input        'commInputAfterPowerType');     coder.internal.errorIf(all(~strcmpi(varargin{5}, {'db','linear'})), ...        'commInvalidPowerType'); end
isLinearScale = ((nargin == 4) && ~isStream && strcmpi(varargin{4}, 'linear')) || ...    ((nargin == 5) && strcmpi(varargin{5}, 'linear'));
% Cross-validationcoder.internal.errorIf(isLinearScale && (sigPower < 0), ...    'commInvalidSigPowerForLinearMode');
coder.internal.errorIf(isLinearScale && (reqSNR < 0), ...    'commInvalidSNRForLinearMode');
if ~isLinearScale  % Convert signal power and SNR to linear scale    if (nargin >= 3) && ~comm.internal.utilities.isCharOrStringScalar(varargin{3}) % User-specified signal power        sigPower = 10^(sigPower/10);    end    reqSNR = 10^(reqSNR/10);end
noisePower = sigPower/reqSNR;
if isStream    if isa(varargin{4}, 'RandStream')        stream = varargin{4};    elseif isempty(coder.target)        stream = RandStream('shr3cong', 'Seed', varargin{4});    else                stream = coder.internal.RandStream('shr3cong', 'Seed', varargin{4});    end
    if ~isreal(sig)        noise = sqrt(noisePower/2)* (randn(stream, size(sig)) + ...                                  1i*randn(stream, size(sig)));    else        noise = sqrt(noisePower)* randn(stream, size(sig));    endelse    if ~isreal(sig)        noise = sqrt(noisePower/2)* (randn(size(sig)) + 1i*randn(size(sig)));    else        noise = sqrt(noisePower)* randn(size(sig));    endend    
y = sig + noise; 
% [EOF]

但是，如果不用MATLAB內(nèi)置的awgn函數(shù)，如何用MATLAB生成AWGN噪聲？

可以自己寫一個(gè)，可以找找別人寫的，站在別人的肩膀上，可以看得更遠(yuǎn)。（如果是學(xué)習(xí)，建議理解awgn背后的原理和定義，然后自己寫；如果只是為了應(yīng)用，提高效率，直接用，浮躁的沉不下來的心，已經(jīng)蔓延~）

下面這份文檔，借花獻(xiàn)佛，在不用內(nèi)置的函數(shù)下，用MATLAB生成AWGN噪聲，可以參考一下。

文檔來源于https://www.gaussianwaves.com，國外的網(wǎng)站，總是這么專業(yè)！

高斯波形，信號(hào)處理，通信系統(tǒng)，簡潔明了。

MATLAB 源碼：

%author - Mathuranathan Viswanathan (gaussianwaves.com%This code is part of the books: Wireless communication systems using Matlab & Digital modulations using Matlab.
function [r,n,N0] = add_awgn_noise(s,SNRdB,L)%Function to add AWGN to the given signal%[r,n,N0]= add_awgn_noise(s,SNRdB) adds AWGN noise vector to signal%'s' to generate a %resulting signal vector 'r' of specified SNR%in dB. It also returns the noise vector 'n' that is added to the%signal 's' and the spectral density N0 of noise added%%[r,n,N0]= add_awgn_noise(s,SNRdB,L) adds AWGN noise vector to%signal 's' to generate a resulting signal vector 'r' of specified%SNR in dB. The parameter 'L' specifies the oversampling ratio used%in the system (for waveform simulation). It also returns the noise%vector 'n' that is added to the signal 's' and the spectral%density N0 of noise added s_temp=s; if iscolumn(s), s=s.'; end; %to return the result in same dim as 's' gamma = 10?(SNRdB/10); %SNR to linear scale  if nargin==2, L=1; end %if third argument is not given, set it to 1  if isvector(s),  P=L*sum(abs(s).?2)/length(s);%Actual power in the vector else %for multi-dimensional signals like MFSK  P=L*sum(sum(abs(s).?2))/length(s); %if s is a matrix [MxN] end  N0=P/gamma; %Find the noise spectral density if(isreal(s)),  n = sqrt(N0/2)*randn(size(s));%computed noise else  n = sqrt(N0/2)*(randn(size(s))+1i*randn(size(s)));%computed noise end  r = s + n; %received signal  if iscolumn(s_temp), r=r.'; end;%return r in original format as send

原文標(biāo)題：基礎(chǔ)：如何用MATLAB生成AWGN噪聲？（附源代碼）

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