an averaged spatial covariance matrix,
RSM = spsmooth(
the full spatial covariance matrix,
R, using spatial
smoothing (see Van Trees , p. 605). Spatial smoothing
creates a smaller averaged covariance matrix over L maximum
overlapped subarrays. L is a positive integer less
than N. The resulting covariance matrix,
has dimensions (N–L+1)-by-(N–L+1).
Spatial smoothing is useful when two or more signals are correlated.
Construct a 10-element half-wavelength-spaced uniform line array receiving two plane waves arriving from 0° and -25° azimuth. Both elevation angles are 0°. Assume the two signals are partially correlated. The SNR for each signal is 5 dB. The noise is spatially and temporally Gaussian white noise. First, create the spatial covariance matrix from the signal and noise. Then, solve for the number of signals, using
rootmusicdoa. Next, perform spatial smoothing on the covariance matrix, using
spsmooth, and solve for the signal arrival angles again using
Set up the array and signals. Then, generate the spatial covariance matrix for the array from the signals and noise.
N = 10; d = 0.5; elementPos = (0:N-1)*d; angles = [0 -25]; ac = [1 1/5]; scov = ac'*ac; R = sensorcov(elementPos,angles,db2pow(-5),scov);
Solve for the arrival angles using the original covariance matrix.
Nsig = 2; doa = rootmusicdoa(R,Nsig)
doa = 1×2 0.2099 41.3166
The solved-for arrival angles are wrong - they do not agree with the known angles of arrival used to create the covariance matrix.
Next, solve for the arrival angles using a smoothed covariance matrix. Perform spatial smoothing to detect L-1 coherent signals. Choose L = 3.
Nsig = 2; L = 2; RSM = spsmooth(R,L); doasm = rootmusicdoa(RSM,Nsig)
doasm = 1×2 -25.0000 -0.0000
In this case, computed angles do agree with the known angles of arrival.
R— Spatial covariance matrix
Spatial covariance matrix, specified as a complex-valued, positive-definite N-by-N matrix. In this matrix, N represents the number of sensor elements.
Example: [ 4.3162, –0.2777 –0.2337i; –0.2777 + 0.2337i , 4.3162]
Complex Number Support: Yes
L— Maximum number of overlapped subarrays
Maximum number of overlapped subarrays, specified as a positive integer. The value L must be less than the number of sensors, N.
RSM— Smoothed covariance matrix
Smoothed covariance matrix, returned as a complex-valued, M-by-M matrix. The dimension M is given by M = N–L+1.
 Van Trees, H.L. Optimum Array Processing. New York, NY: Wiley-Interscience, 2002.
Usage notes and limitations:
Does not support variable-size inputs.