Principles of Modern Radar - Volume 2 1891121537

2.2 Stretch Processing 27The data bus and signal processor’s requirements are driven by the data rate and thenumber of samples collected per pulse. The minimum number of samples is equal to thewaveform’s time–bandwidth product. For pulse compression waveforms, time–bandwidthproducts range from 2 to 1,000,000 or even greater. For an LFM waveform with a 10 μsecpulse width and a 1 GHz bandwidth, the minimum number of samples to process per pulseis 10,000. The data bus and signal processor must be sized to transfer and process largequantities of data in real time, which may be a challenge. Stretch processing reduces boththe data rate and number of samples to process while maintaining the range resolutionafforded by the transmit bandwidth.2.2.3 Technique OverviewCaputi [2] developed the stretch processing technique, which converts a received LFMpulse into a tone whose frequency is fixed and is proportional to the target’s time delay.A filter with a passband less than the waveform’s bandwidth is used to limit the range offrequencies passed to the ADC. Limiting the processing bandwidth constrains the rangeof observable time delays or, equivalently, the size of the range window. In general, theconstraint or limitation placed on the range window is acceptable when there is knowledgeof the distance to the target or area to be imaged. For example, a missile defense radar mayemploy stretch processing to image a target that is already under track. In a SAR system,the size and location of the area to be imaged is known. The samples at the output of theADC are processed using a discrete Fourier transform (DFT) that compresses the returnsin range. The range resolution at the output of the DFT is inversely proportional to thetransmit bandwidth and is not limited by the reduced ADC sampling rate.2.2.4 ImplementationStretch processing is uniquely associated with an LFM waveform and is implemented inboth pulsed and frequency modulated continuous wave (FMCW) radar systems. In thischapter, the focus is placed on pulsed systems. A modern implementation consists of thefollowing:1. The transmission of a wideband, linear frequency modulated waveform2. A mixing operation on receive that converts the received waveform into a set of toneswith frequencies proportional to the relative time delay between scatterers3. A filter following the mixer to limit the highest frequency passed to the ADC4. An ADC sampling at a rate proportional to the filter bandwidth5. A DFT to compress the received waveformEach step is examined in the following sections.2.2.4.1 Transmit WaveformConsider an LFM waveform, centered at an IF, f 1 ,(x (t) = cos 2π f 1 t + π β (t − τ ) ) 2+ θ 1τ 20 ≤ t ≤ τ (2.1)where β is the bandwidth over which the waveform is swept, τ is the pulse length, andθ 1 is the phase of the oscillator used to generate f 1 . Approaches for synthesizing an