  The compressed sensing (CS) model can represent the signal recovery process
of a large number of radar systems. The detection problem of such radar systems
has been studied in many pieces of literature through the technology of
debiased least absolute shrinkage and selection operator (LASSO). While naive
LASSO treats all the entries equally, there are many applications in which
prior information varies depending on each entry. Weighted LASSO, in which the
weights of the regularization terms are tuned depending on the entry-dependent
prior, is proven to be more effective with the prior information by many
researchers. In the present paper, existing results obtained by methods of
statistical mechanics are utilized to derive the debiased weighted LASSO
estimator for randomly constructed row-orthogonal measurement matrices. Based
on this estimator, we construct a detector, termed the debiased weighted LASSO
detector (DWLD), for CS radar systems and prove its advantages. The threshold
of this detector can be calculated by false alarm rate, which yields better
detection performance than the naive weighted LASSO detector (NWLD) under the
Neyman-Pearson principle. The improvement of the detection performance brought
by tuning weights is demonstrated by numerical experiments. With the same false
alarm rate, the detection probability of DWLD is obviously higher than those of
NWLD and the debiased (non-weighted) LASSO detector (DLD).
