Principles of Modern Radar - Volume 2 1891121537

2.5 Stepped Frequency Waveforms 63where M ≥ N. This is equivalent to evaluating the response at equally spaced rangesdefined byR k =Inserting equation (2.119) into (2.113) yields the DFTck k = 0,...,(M − 1) (2.120)2f MX (k) =N−1∑n=0(x (n) exp − j 2πk )M nM ≥ N (2.121)which is often implemented using an FFT for computational efficiency. For a point targetlocated at range R 0 , the compressed response is a sampled instantiation of the digital sincin (2.114) or|X (k)| =∣sin( Nsin2( ))2πM k − ω R 0 (( )/ )2πM k − ω R 02∣k = 0,...,(M − 1) (2.122)The DFT is a linear operator; thus, the range profile associated with multiple scatterers issimply the superposition of the individual responses.Zero padding is often used in conjunction with a DFT to decrease the filter spacing,which reduces straddle loss. For M > N, the sequence is said to be zero padded withM − N zeros. For M = N, the filters or range bins are spaced by the nominal waveformresolution c/2Nf .2.5.4.3 Range Sidelobe SuppressionRange sidelobes associated with large RCS targets may mask the presence of smallertargets. As noted in Figure 2-24, sidelobes are suppressed by applying an amplitudeweighting to the complex samples collected at a range gate. When selecting an amplitudetaper, the associated reduction in resolution and loss in SNR should be taken intoaccount [36].2.5.5 Straddle Loss and Range AmbiguitiesThe range profile generated by an SF waveform may exhibit undesired artifacts as a resultof ambiguities and straddle loss. The following sections examine these issues and theimpact of waveform parameter selection on performance.2.5.5.1 Straddle LossStraddle loss is introduced at two points in the processing chain: (1) when sampling thepulse’s match filtered response; and (2) within the DFT. The loss associated with the DFTwas discussed in Section 2.5.4.2. The loss associated with sampling is examined in thissection. When sampling the return from a pulse, the resultant straddle loss is a functionof the range gate spacing and the single-pulse bandwidth or range resolution. Severalexamples are provided to illustrate the loss.In a radar system, range gates are often spaced by the transmit pulse’s range resolution.A similar spacing may be applied to a stepped frequency waveform where the range gates