ecorrm.m

阵列信号处理的工具箱

function Rout  = ecorrm(inData, method, rangeIx, cpiIx, in5, in6, in7, dimensions)

%ECORRM Estimates the antenna signal correlation matrix or modifies the estimate.
%
%--------
%Synopsis:
%  Rout = ecorrm(inData, method, rangeIx, cpiIx, ...)
%
%Description:
%  Estimates the antenna signal correlation matrix or modifies the estimate.
%  If the input parameter "inData" is of data type RxRadarSigT, then
%  samples used for the estimation are taken from all pulses at a certain
%  range bin (specified by "rangeIx") and CPI (specified by "cpiIx").
%  If the input parameter "inData" is of data type RxCorrMatT the input
%  parameters "rangeIx" and "cpiIx" are not used.
%
%  The base of all estimates of the correlation matrix is a maximum
%  likelihood (ML) estimate and this is what is
%  returned if nothing else is requested. The ML-estimate can be modified
%  in different ways, see the "method" input parameter. The estimation
%  and modification can be done in one call or two, where the first
%  calculate the ML-estimate and the second does the modification.
%  If the input is already a correlation matrix and "method" = [], then
%  nothing is done but returning the input as output.
%
%  Modifications to the help text of this function should also be done
%  to the function "modcorrmkernel".
%
%Output and Input:
%  Rout (RxCorrMatT): The estimated antenna signal correlation matrix
%    or a modification of the estimate. This output parameter always
%    contains only one correlation matrix.
%  inData (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  method [D](StringT): Type of correlation matrix estimation. See below for
%    sections about each method.
%    = 'ml': ML-estimate (default). See below.
%    = 'forback': Forward-backward averaging. See below.
%    = 'spatsmooth': Spatial smoothing. See below.
%    = 'diagload': Diagonal loading. See below.
%    = 'diagloadeig': Diagonal loading relative noise eigenvalues. See below.
%    = 'equeig': Equal Noise Eigenvalues. See below.
%    = 'normeig': Norming relative the noise eigenvalues. See below.
%  rangeIx [D](IntScalarT): Specify the range bin to use in the radar
%    signal when estimating the correlation matrix. Default range bin is 1.
%    This input parameter is only applicable when the input parameter
%    "inData" is of data type RxRadarSigT.
%  cpiIx [D](IntScalarT): Like "rangeIx" but for CPI. Default CPI is 1.
%  dimensions [D] (IndexT): The used index in the data (a RxRadarSigT 
%    variable), e.g = [ 3] for a space correlation matrix and = [1 3] for
%    a space-time (slow-time) correlation matrix. Not implemented.
%
%--------
%Maximum Likelihood
%Synopsis:
%  Rout = ecorrm(inData)
%  Rout = ecorrm(inData, 'ml')
%  Rout = ecorrm(inData, 'ml', rangeIx, cpiIx)
%
%Description:
%  Calculates the maximum likelihood correlation matrix estimate of the
%  received signals from different channels.
%
%Algoritm:
%  R = 1/L * X*X', where R is the correlation matrix,
%  L is the number of snapshots,
%  X is the data matrix with different channels as different
%  rows and different snapshots as different columns.
%
%--------
%Forward-Backward Averaging
%Synopsis:
%  Rout = ecorrm(inData, 'forback')
%  Rout = ecorrm(inData, 'forback', rangeIx, cpiIx)
%
%Description:
%  This method requires an ULA. When used on the 'expAnt' antenna type
%  this probably means that the calibration and near field compensations
%  must be performed on the signals (with "sigcomp2") and not on the
%  steering matrix (with "setcal1"). This method can only handle two
%  coherent signals. For more information about this method, see [2] p. 75-76.
%
%Algoritm:
%  Rfb = 0.5*(R+J*conj(R)*J);
%  where J is a (L x L) exchange matrix, whose components are zero except for
%  ones in the anti-diagonal, R is the ML-estimate, and Rfb is the modified
%  estimate.
%
%--------
%Spatial Smoothing
%Synopsis:
%  Rout = ecorrm(inData, 'spatsmooth', [], [], noElemSub)
%  Rout = ecorrm(inData, 'spatsmooth', [], [], noElemSub, channelIx)
%  Rout = ecorrm(inData, 'spatsmooth', rangeIx, cpiIx, noElemSub, channelIx)
%
%Output and Input:
%  noElemSub (IntScalarT): Number of elements in the subarrays.
%  channelIx [D](IndexT): Specifies which channels of the original steering
%    vector to use. The number of channels to use must be equal to
%    "noElemSub". If all channels are equal, which is a requirement for
%    this method, it does not matter which channels are chosen.
%    Default value is (1:noElemSub).
%
%Description:
%  In this method the array antenna is split into a number of overlapping
%  subarrays whose correlation matrices are averaged. The number K of
%  subarrays used is K = N - noElemSub +1, where N is the total number
%  of channels (elements) in the array. For each additional subarray the
%  method can handle one extra coherent source signal. A drawback with this 
%  method is that the size of the antenna decreases, since the subarrays
%  are smaller than the original array.
%
%  This method requires a regular array antenna with a translational
%  invariant property, e.g. an ULA. When used on the 'expAnt' antenna type
%  this probably means that the calibration and near field compensations
%  must be performed on the signals (with "sigcomp2") and not on the
%  steering matrix (with "setcal1").
%
%  For more information about this method, see [2] p. 75-76.
%
%Algoritm:
%  Rss = zeros(noElemSub,noElemSub);
%  for n=1:noSubArray
%    Rss = Rss + R(n:n+noElemSub-1, n:n+noElemSub-1);
%  end
%  Rout = (1/noSubArray)*Rss;
%  where noSubArray is the number of subarrays.
%
%--------
%Diagonal Loading
%Synopsis:
%  Rout = ecorrm(inData, 'diagload', [], [], loadVal)
%  Rout = ecorrm(inData, 'diagload', rangeIx, cpiIx, loadVal)
%
%Output and Input:
%  loadVal (RealScalarT):
%
%Description:
%  An amount, which is determined by the input parameter "loadVal", of
%  the identity matrix is added to the correlation matrix. Diagonal loading
%  reduces the fluctuation of the small eigenvalues of the correlation
%  matrix [5,3,4]. A suitable size of "loadVal" is in the order of the noise
% variance [5].
%
%Algoritm:
%
%--------
%Diagonal Loading relative noise eigenvalues
%Synopsis:
%  Rout = ecorrm(inData, 'diagloadeig', [], [], relLoadVal)
%  Rout = ecorrm(inData, 'diagloadeig', [], [], relLoadVal, noSrc)
%  Rout = ecorrm(inData, 'diagloadeig', rangeIx, cpiIx, relLoadVal)
%  Rout = ecorrm(inData, 'diagloadeig', rangeIx, cpiIx, relLoadVal, noSrc)
%
%Output and Input:
%  relLoadVal (RealScalarT): Load relative the noise eigenvalues (noise power).
%  noSrc [D](IntScalarT): Number of signal sources. This means that there
%    are ((number-of-channels) - noSrc) noise eigenvalues. If this value
%    is too low, the estimated noise power will be somewhat too low. If
%    this value is too high, the estimated noise power will be too high
%    (maybe much too high). Default value is = 1, which means that only the
%    smallest eigenvalue is used.
%
%Description:
%  An amount, which is determined by the input parameter "relLoadVal"
%  multiplied with the noise power, of the identity matrix is added to the 
%  correlation matrix. Diagonal loading reduces the fluctuation of the small 
%  eigenvalues of the correlation matrix [5,3,4]. A suitable size of 
%  "loadVal" is in the order of the noise variance (power) [5]. The noise
%  power is calculated as the mean value of the smallest eigenvalues of the 
%  spatial correlation matrix
%
%Algoritm:
%
%--------
%Equal Noise Eigenvalues.
%Synopsis:
%  Rout = ecorrm(inData, 'equeig')
%  Rout = ecorrm(inData, 'equeig', [], [], [], noSrc)
%  Rout = ecorrm(inData, 'equeig', rangeIx, cpiIx)
%  Rout = ecorrm(inData, 'equeig', rangeIx, cpiIx, [], noSrc)
%
%Output and Input:
%  noSrc [D](IntScalarT): Number of signal sources. This means that there
%    are ((number-of-channels) - noSrc) noise eigenvalues. If this value
%    is too low, the estimated noise power will be somewhat too low. If
%    this value is too high, the estimated noise power will be too high
%    (maybe much too high). Default value is = 1, which means that only the
%    smallest eigenvalue is used.
%
%Description:
%  All noise eigenvalues, as determined by "noSrc", are set equal to the
%  noise power. The noise power is calculated as the mean value of the
%  smallest eigenvalues of the spatial correlation matrix.
%
%Algoritm:
%
%--------
%Norming relative the noise eigenvalues.
%Synopsis:
%  Rout = ecorrm(inData, 'normeig')
%  Rout = ecorrm(inData, 'normeig', [], [], [], noSrc)
%  Rout = ecorrm(inData, 'normeig', rangeIx, cpiIx)
%  Rout = ecorrm(inData, 'normeig', rangeIx, cpiIx, [], noSrc)
%
%Output and Input:
%  relLoadVal (RealScalarT):
%  noSrc [D](IntScalarT): Number of signal sources. This means that there
%    are ((number-of-channels) - noSrc) noise eigenvalues. If this value
%    is too low, the estimated noise power will be somewhat too low. If
%    this value is too high, the estimated noise power will be too high
%    (maybe much too high). Default value is = 1, which means that only the
%    smallest eigenvalue is used.
%
%Description:
%  All eigenvalues (both signal and noise) are set equal to the noise power.
%  The noise power is calculated as the mean value of the smallest eigenvalues 
%  of the spatial correlation matrix.
%
%Algoritm:
%
%--------
%Notations:
%  Data type names are shown in parentheses and they start with a capital
%  letter and end with a capital T. Data type definitions can be found in [1]
%  or by "help dbtdata".
%  [D] = This parameter can be omitted and then a default value is used.
%  When the [D]-input parameter is not the last used in the call, it must be
%  given the value [], i.e. an empty matrix.