Space-time adaptive processing (STAP) is a signal processing technique most commonly used in radar systems. It involves adaptive array processing algorithms to aid in target detection. Radar signal processing benefits from STAP in areas where interference is a problem (i.e. ground clutter, jamming, etc.). Through careful application of STAP, it is possible to achieve order-of-magnitude sensitivity improvements in target detection. STAP involves a two-dimensional filtering technique using a phased-array antenna with multiple spatial channels. Coupling multiple spatial channels with pulse-Doppler waveforms lends to the name "space-time." Applying the statistics of the interference environment, an adaptive STAP weight vector is formed. This weight vector is applied to the coherent samples received by the radar.
History The theory of STAP was first published by Lawrence E. Brennan and Irving S. Reed in the early 1970s. At the time of publication, both Brennan and Reed were at Technology Service Corporation (TSC). While it was formally introduced in 1973, it has theoretical roots dating back to 1959.
Motivation and applications For ground-based radar, cluttered returns tend to be at DC, making them easily discriminated by Moving Target Indication (MTI). Thus, a notch filter at the zero-Doppler bin can be used. Airborne platforms with ownship motion experience relative ground clutter motion dependent on the angle, resulting in angle-Doppler coupling at the input. In this case, 1D filtering is not sufficient, since clutter can overlap the desired target's Doppler from multiple directions. The resulting interference is typically called a "clutter ridge," since it forms a line in the angle-Doppler domain. Narrowband jamming signals are also a source of interference, and exhibit significant spatial correlation. Thus receiver noise and interference must be considered, and detection processors must attempt to maximize the signal-to-interference and noise ratio (SINR). While primarily developed for radar, STAP techniques have applications for communications systems.
Basic theory
STAP is essentially filtering in the space-time domain. This means that we are filtering over multiple dimensions, and multi-dimensional signal processing techniques must be employed. The goal is to find the optimal space-time weights in N M {\displaystyle NM} -dimensional space, where N {\displaystyle N} is the number of antenna elements (our spatial degrees of freedom) and M {\displaystyle M} is the number of pulse-repetition interval (PRI) taps (our time degrees of freedom), to maximize the signal-to-interference and noise ratio (SINR). Thus, the goal is to suppress noise, clutter, jammers, etc., while keeping the desired radar return. It can be thought of as a 2-D finite-impulse response (FIR) filter, with a standard 1-D FIR filter for each channel (steered spatial channels from an electronically steered array or individual elements), and the taps of these 1-D FIR filters corresponding to multiple returns (spaced at PRI time). Having degrees of freedom in both the spatial domain and time domain is crucial, as clutter can be correlated in time and space, while jammers tend to be correlated spatially (along a specific bearing). A simple, trivial example of STAP is shown in the first figure, for N = M = 10 {\displaystyle N=M=10} . This is an idealized example of a steering pattern, where the response of the array has been steered to the ideal target response, s {\displaystyle s} . Unfortunately, in practice, this is oversimplified, as the interference to be overcome by steering the nulls shown is not deterministic, but statistical in nature. This is what requires STAP to be an adaptive technique. Note that even in this idealized example, in general, we must steer over the 2-D angle-Doppler plane at discrete points to detect potential targets (moving the location of the 2-D sinc main lobe shown in the figure), and do so for each of the range bins in our system. The basic functional diagram is shown to the right. For each antenna, a down conversion and analog-to-digital conversion step is typically completed. Then, a 1-D FIR filter with PRI length delay elements is used for each steered antenna channel. The lexicographically ordered weights W 1 {\displaystyle W_{1}} to W N M {\displaystyle W_{NM}} are the degrees of freedom to be solved in the STAP problem. That is, STAP aims to find the optimal weights for the antenna array. It can be shown, that for a given M N × M N {\displaystyle MN\times MN} interference covariance matrix, R {\displaystyle \mathbf {R} } , the optimal weights maximizing the SINR are calculated as
W = κ R − 1 s {\displaystyle \mathbf {W} =\kappa \mathbf {R} ^{-1}s}
where κ {\displaystyle \kappa } is a scalar that does not affect the SINR. The optimal detector input is given by:
y = W x {\displaystyle y=\mathbf {W} x}
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