CRLB for DOA Estimation
Start with a five-element ULA with half-wavelength element spacing. The ULA receives a signal from a target at a direction of arrival of 45 degrees. The signal is contained in complex Gaussian white noise. Calculate the DOA estimation CRLB via two ways:
Compute the CRLB using existing the
steervecfunction.Compute the CRLB using an anonymous function.
The two formulations should lead to the same estimated DOA CRLB. The estimate is in degrees squared.
Set up the ULA with equally spaced elements.
N = 5; elementPos = (0:N-1)/2;
Set the known noise power.
noise_level = 0.1; ncov = noise_level^2;
The target DOA is 45 degrees azimuth.
ang = 45;
Create a function handle from using the steervec function.
sig_steervec = @(ang)steervec(elementPos,ang);
Create a function handle from an anonymous function.
sig_anonymous = @(ang)exp(1j*(2*pi*sind(ang)*elementPos'));
Find the numerical CRLB of DOA estimation computed using the two approaches.
crlb_steervec = crlb(sig_steervec,ncov,ang)
crlb_steervec = 0.1109
crlb_anonymous = crlb(sig_anonymous,ncov,ang, ... DataComplexity = "Complex")
crlb_anonymous = 0.1109
