Principles of Modern Radar - Volume 2 1891121537

496 CHAPTER 10 Clutter Suppression Using Space-Time Adaptive Processing[30] Hersey, R.K., Melvin, W.L., McClellan, J.H., and Culpepper, E., “Adaptive Ground ClutterSuppression for Conformal Array Radar Systems,” IET Journal on Radar, Sonar, and Navigation,vol. 3, no. 4, pp. 357–372, 2009.[31] Melvin, W.L., “Adaptive Moving Target Indication,” Ch. 11 in Advances in Bistatic Radar,N. Willis and H. Griffiths, Ed., SciTech Publishing, Raleigh, NC, 2007.10.11 PROBLEMSThe interested reader should accomplish the following problem set in the order givenusing a suitable numerical simulation capability, such as the MATLAB programmingenvironment.1. Based on the discussion in Section 10.2, generate a matrix of space-time steeringvectors covering ±90 ◦ in angle and ±1000 Hz in Doppler, where each column isa space-time steering vector. The resulting matrix is known as the steering matrix.Assume an 11-element, uniform linear array with half-wavelength spacing receiving32 pulses. Take the wavelength to be 0.3 m and the PRF to be 2 kHz. Choose anarbitrary space-time test steering vector (any column of the steering matrix, preferablystarting with the steering vector at 0 ◦ angle and 0 Hz Doppler), manipulate into theform of (10.35), and take the two-dimensional FFT. Compare this result with thecomplex inner product of the steering matrix and the test vector. After evaluatingseveral test cases, next duplicate Figure 10-5.2. Using the steering matrix of problem 1, generate a simple, space-time covariancematrix comprised of receiver noise and three unity amplitude space-time signals withthe following characteristics: (1) –200 Hz Doppler frequency and 20 ◦ DOA; (2) 200 HzDoppler frequency and –20 ◦ DOA; and (3) 0 Hz Doppler frequency and 0 ◦ DOA. Setthe receiver noise to 1 watt/channel. Using the steering matrix, calculate the MVDRspectra, thereby reproducing Figure 10-7.3. Using the space-time covariance matrix from problem 2, generate 3520 IID datarealizations by multiplying the matrix square root of the covariance matrix by unitypower, complex white noise. If R test is the covariance matrix, the corresponding MAT-LAB command is x = sqrtm(R test)*(randn(N*M, 3520) + sqrt(–1)*randn(N*M,3520))/sqrt(2), where N = 32, M = 11, and 3520 IID realizations represents trainingsupport equal to 10 times the processor’s DoFs. Using the IID data, calculate theperiodogram estimate via (10.40).4. Using the covariance matrix from problem 2 and the IID data from problem 3, calculatethe eigenspectra for known and unknown covariance matrices of varying samplesupport. Regenerate the space-time covariance matrix and IID data with variable signalamplitude (to vary the SNR) and recompute the eigenspectra. Compare the eigenvaluesto the calculated, matched filtered SNR. The eigenvalues should be equal to theintegrated signal power plus the single-element noise power; alternately, the differencebetween a given eigenvalue and the noise floor eigenvalue level is the integrated SNR.5. Take the eigenvectors from problem 4 corresponding to the dominant subspace (thoseeigenvalues above the noise floor). Then, apply the two-dimensional Fourier transformto each of the three dominant eigenvectors; use the space-time steering vectorsgenerated in problem 1 to accomplish this task. Compare the resulting spectrum with