Principles of Modern Radar - Volume 2 1891121537

3.4 Optimum MIMO Design for Target Identification 99where⎡E { ˜H c ′ ˜H} −1 1c = ⎢P c ⎣⎤d 1 0 ··· 00 d 2 . ..⎥⎦0 ··· d N(3.37)andd i= (N + i − 1)−1(3.38)It is readily verified that the solution to (3.36) yielding the maximum eigenvalue is given by⎡ ⎤10s = ⎢⎣⎥(3.39). ⎦0Thus the optimum pulse shape for detecting a point target is itself an impulse. This should beimmediately obvious since it is the shape that excites the range bin only with the target andzeros out all other range bin returns that contain competing clutter.Of course, transmitting a short pulse (much less an impulse) is problematic in the realworld (e.g., creating extremely high peak power pulses) thus an approximation to a short pulsein the form of a spread spectrum waveform (e.g., LFM) is often employed [12]. This examplealso illuminates that in uniform random clutter nothing is gained by sophisticated pulse shapingfor a point target other than to maximize bandwidth (i.e., range resolution) [21]. The interestedreader is referred to [19] for further examples of optimizing other DOF (e.g., angle-Doppler)for the clutter mitigation problem.Up to this point we have been focused on judiciously choosing the transmit/receiveDOF to maximize SINR or SCR. In the next section we will extend this framework to thetarget identification problem.3.4 OPTIMUM MIMO DESIGN FOR TARGETIDENTIFICATIONConsider the problem of determining target type when two possibilities exist (the multitargetcase is addressed later in this section). This can be cast as a classical binary hypothesistesting problem [7]:(Target 1) H 1 : y 1 + n = H T1 s + n(Target 2) H 2 : y 2 + n = H T2 s + n(3.40)where H T1 , H T2 denote the target transfer matrices for targets 1 and 2, respectively. Forthe AGCN case, the well-known optimum receiver decision structure consists of a bankof matched filters, each tuned to a different target assumption, followed by comparator asshown in Figure 3-7 [7]. Note that (3.40) presupposes that either Target 1 or 2 is present, but