Principles of Modern Radar - Volume 2 1891121537

402 CHAPTER 9 Adaptive Digital Beamforming9.1.1 OrganizationThe fundamentals of digital beamforming are covered in Section 9.2 including the keybenefits and implementation challenges. Section 9.3 introduces adaptive algorithms forjammer cancellation and derives the optimal solution for the adaptive weights. Section 9.4describes the sidelobe canceller, beamspace, and subarray space adaptive beamformingarchitectures and their relative performance. Section 9.5 extends the adaptive algorithmsfrom section 9.3 to operate over wide bandwidths and presents the special case of linearfrequency modulated (LFM) waveforms pulse compressed using stretch processing.9.1.2 Key Points• DBF enhances phased array radar functionality.• Element level DBF is often impractical for large arrays operating at high frequencies.• DBF at the subarray level reduces the receiver count for easier implementation.• The subarray architecture choice heavily impacts performance due to grating lobes andgrating nulls.• ADBF increases the input-output (I/O) throughput requirements linearly with the numberof spatial channels.• ADBF increases the computational requirements superlinearly with the total numberof both spatial and temporal degrees of freedom (DOF).• Various types of spatial DOF can be used for adaptive cancellation, and they each workbest for jamming located in specific regions of the antenna pattern.• When canceling interference over wide bandwidths, the adaptive filter needs to jointlyoptimize over both the spatial and frequency domains.• Cancellation performance is limited by the hardware errors in the array and receivers.9.1.3 NotationThe following lists many of the variable names found within this chapter:f 0 = center frequency (Hz)ω 0 = center frequency (rads/s)λ 0 = center wavelength (m)M = number of channelsN = number of pulsesL = number of available range binsT = pulse repetition interval (s)c = velocity of propagation (speed of light, m/s)s s = spatial steering vectorv s = hypothesized spatial steering vectors t = temporal steering vectorv t = hypothesized temporal steering vectors s − t = space-time steering vectorv s − t = hypothesized space-time steering vectorx s,k (n) = spatial data snapshot, k-th range cell, n-th pulsex t,k (m) = temporal data snapshot, k-th range cell, m-th channelx k = space-time data snapshot, k-th range cell