Principles of Modern Radar - Volume 2 1891121537

3.6 Adaptive MIMO Radar 109Magnitude (dB)Instantaneous Frequency(Normalized)151050−5−10−15−20−0.5ω0.50.0Optimum Pulse Spectrum0Frequency0.5FIGURE 3-17Illustration of the useof the method ofstationary phase tocreate a constantmodulus NLFMpulse whosespectral magnitudematches that of theoptimum pulse. TheNLFM pulse wasable to achieve anoutput SINR thatwas within 6.0 dBof the optimumcompared with a24 dB loss using anLFM waveform ofsame energy andduration.−0.50.0 T twhere Y (ω), H(ω), and S(ω) denote the Fourier transforms of the channel output, channelimpulse response, and input pulse, respectively. Note that the output energy in (3.64)depends on the spectral magnitude of the input pulse (steady-state)—not the phase. Thus,in theory an NLFM waveform that exactly matches the optimum pulse magnitude spectrumwill achieve the same matching gains in the steady-state limit (infinite pulse duration) forall square integrable (finite norm) functions.3.6 ADAPTIVE MIMO RADARSection 3.2 derived the optimal multidimensional transmit/receive (i.e., MIMO) designequations that assumed exact knowledge (deterministic or statistical) of the channel (targetand interference). However, as those familiar with real-world radar are well aware, channelcharacterization in large part must be performed on the fly, or adaptively. This is simplya result of the dynamic nature of real-world targets and especially interference.While a plethora of techniques have been developed for radar receiver adaptivity, estimatingrequisite channel characteristics for adapting the transmit function—especiallyfor transmit-dependent interference such as clutter—is a relatively new endeavor. In thischapter, we explore several approaches for addressing the adaptive MIMO optimizationproblem.