Technical report | Optimal Detection in the K-Distributed Clutter Environment -- Non-Coherent Radar Detector Processing
Non-coherent detection of Gaussian targets (Swerling II targets) in the K-distributed clutter environment is investigated. The optimal detector is derived based on the Neyman-Pearson principle. It is shown to be the well-known square-law detector. Amplitude detector, log detector, and the like are not optimal, and result in some detection loss. Temporally correlated clutter provides a target gain, and improves detection. The higher the temporal correlation, the higher the target gain. Spatially correlated non-Gaussian clutter can also provide a CFAR gain. The autoregressive technique is used to optimally estimate the texture of the clutter. That in turn significanly improves the detection compared to the traditional cell-averaging processing.
In the maritime environment, radar detectors unavoidably need to deal with undesired signals, primarily sea clutter (echoes from the sea surface). How to detect target signals, especially relatively weak ones, against the clutter is challenging.
Optimal detectors, based on the Neyman-Pearson principle, that maximise the probability of detection for a given false-alarm rate are the most interesting detectors to the radar community. Their derivation depends on the statistical models of both the clutter and the target. In a recent paper, 'Optimal coherent radar detection in a K-distributed environment' we have discussed the problem of optimal coherent detection. This report focuses on the non-coherent detection of Gaussian targets (Swerling II targets) in the compound K-distributed clutter environment.
This report makes the following three contributions.
First the optimal detector for multi-look non-coherent detection of Gaussian targets in the compound K-distributed clutter is derived. The optimal detector derived is shown to be the well-known square-law detector. This is because the clutter undergoes a Gaussian random process during the multi-look processing period (i.e., the multi-pulse processing period), as the slowly-varying component of the compound clutter remains unchanged during the period, according to the assumption. Although the derived optimal detector is not new, the derivation itself has a guiding meaning. As the detector has been rigorously derived for the first time using the Neyman-Pearson principle, it means that no other detectors exist which would perform better for the given conditions. Other detectors, such as the multi-look amplitude detector, the multi-look log detector, and the like are not optimal and inherently result in some detection loss.
Secondly we have shown that for temporally correlated clutter, the use of a multi-look whitening process provides a target gain and improves the detection. The higher the correlation, the larger the target gain. The target gain comes from the difference between the spectrum of the correlated clutter and the spectrum of uncorrelated target signals (a non-uniform spectrum against a uniform spectrum), providing a second characteristic (in addition to the intensity) for discriminating the target from the clutter. On the other hand, if both the clutter and the target signals are individually uncorrelated (the cross-correlation between the two is always zero), each of them has a
uniform spectrum, and there is only one characteristic (intensity) that can be employed in the detection. Therefore the event of the uncorrelated Gaussian targets embedded in the uncorrelated compound clutter represents the worst scenario in terms of detection. If the correlation of the target signals is the same as the correlation of the clutter, a treatment of de-correlation leads to the same processing for the uncorrelated target in the uncorrelated clutter.
Lastly, spatially correlated non-Gaussian clutter may be able to provide some constant false-alarm rate (CFAR) gains. The CFAR gain is dependent on the estimate of the local mean. For this analysis we have examined the use of the linear autoregressive technique and derived the optimal weights for estimating the local mean of clutter. The autoregressive estimation is optimal under the linear assumption and better than the traditional cell-averaging estimation. The optimal estimation (under the linear assumption) of the clutter texture has in turn resulted in a further significant detection improvement (a few dB) for highly spatially correlated K-distributed clutter compared to the traditional cell-averaging estimation.
This work was carried out in support of the ADF’s Air 7000 Project.
Dong, Y. (2012), "Optimal coherent radar detection in a K-distributed clutter environment",
IET Radar, Sonar and Navig., 6(5), 283-292.