Principles of Modern Radar - Volume 2 1891121537

42 CHAPTER 2 Advanced Pulse Compression Waveform Modulationsin Section 2.2.2, a lower sampling rate implies that the ADC is capable of supporting ahigher ENOB. Sampling the continuous signal in equation (2.58) yields(x BB (m) = exp (− j2π f 0 t d ) exp (− j2π pf 0 t d ) exp jπ β (( ) m− t d − τ ) 2 )τ F s 2(2.59)where ⌈F S t d ⌉ ≤ m ≤ [F S (τ + t d )]. The signal in equation (2.59) contains two phaseterms, 2π f 0 t d and 2π pf 0 t d , that are constant over a pulse. The second term, 2π pf 0 t d ,varies pulse to pulse and must be accounted for when reconstructing the wider bandwidthsignal within the signal processor.The discussion has focused on a point target located at a particular time delay; however,a radar collects returns over a range window. To accumulate these returns, the receiver isactive over the time intervalT c = τ + 2Rc(2.60)The samples collected over the range window from the n-th pulse are y n (m) where(m = 0,...,[F S τ + 2R )](2.61)cand include the return collected from the point target in equation (2.59).2.3.4 Processing OptionsThe objective is to create, within the signal processor, a composite waveform that exhibitsa range resolution commensurate with composite waveform’s transmit bandwidthby properly combining the N sc baseband returns in equation (2.59). A means for interpolatingin time and shifting in frequency the received pulses is required. In addition,careful consideration must be given to coherently combining the returns and accountingfor phase differences between pulses. Both time-domain (TD) and frequency-domain (FD)approaches are described in the literature [7, 8, 10, 11] and are covered in subsequent sections.An example of a stepped chirp waveform processed in the frequency domain is alsopresented. The analysis focuses on the return from a point target, but the process is linearand is applicable to a superposition of returns at different delays.2.3.4.1 Time DomainThe TD approach for processing a stepped chirp waveform is discussed in [7, 8], and thesteps are outlined here for completeness:1. When implementing the TD approach, it is assumed that the frequency step size isequal to the pulse bandwidth (i.e., f = β).2. In the signal processor, the first step is to up-sample (i.e., interpolate) the basebandsignals in equation (2.59) by a factor of N sc . The interpolation may be implementedusing a finite impulse response (FIR) filter. The interpolated signal is required to supportthe composite waveform bandwidth and is denoted y n ′ (m). The interpolated pulses havea frequency support defined by −π N sc F s ≤ ≤ π N sc F s .