Principles of Modern Radar - Volume 2 1891121537

10.2 Space-Time Signal Representation 467400300Power Spectral Density FIGURE 10-50Power spectraldensity of threespace-time signals.−10Doppler Frequency (Hz)2001000−100−200−20−30−40−50dB−300−400−90 −70 −50 −30 −10 10 30 50 70 90Angle (Degrees)−60−70point scatterer with spatial frequency f sp and normalized Doppler frequency ˜f d is x s−t =a s−t s s−t ( f sp , ˜f d ). Analogous to the one-dimensional spatial or temporal cases, a s−t is acomplex voltage proportional to the square root of the target radar cross section, ands s−t ( f sp , ˜f d ) is the NM × 1 space-time steering vector. We conveniently describe thespace-time steering vector as the Kronecker product of the temporal and spatial steeringvectors:s s−t ( f sp , ˜f d ) = s t ( ˜f d ) ⊗ s s ( f sp )[T= 1 · ss T ( f sp) e j2π ˜f d· ss T ( f sp) e j2π(2 ˜f d) · ss T ( f sp) ···e j2π(N−1) ˜f d· ss sp)] T ( f .Figure 10-5 shows the two-dimensional power spectral density (PSD) of three unity amplitudespace-time signals: the first signal corresponds to –200 Hz Doppler frequency and20 ◦ DOA, the second to a Doppler of 200 Hz and DOA of –20 ◦ , and the third originatingfrom array broadside with 0 Hz Doppler frequency. We use a 12-channel array (M = 12)receiving N = 32 pulses for this simulation. Observe that each space-time signal appearsas a two-dimensional sinc function.The multichannel, pulse-Doppler radar collects M spatial samples, N temporal samples,and L unambiguous range samples. The data cube of Figure 10-6, correspondingto a single CPI, organizes these samples. Preprocessing steps convert the RF signals atthe multiple receiver channels to complex baseband space-time and range samples. TheADC clock rate is at least as high as the waveform bandwidth for complex sampling; theprocessor match filters the data in the range dimension and performs digital decimation (ifnecessary) to yield one complex, demodulated sample per range bin. The range dimensionis known as fast time and the pulse dimension is called slow time since the sample rate isat the PRI and is much less than the ADC clock rate. The k-th space and slow-time slice(10.34)