  This paper considers the design of tunable decision schemes capable of
rejecting with high probability mismatched signals embedded in Gaussian
interference with unknown covariance matrix. To this end, a sparse recovery
technique is exploited to enhance the resolution at which the target angle of
arrival is estimated with the objective to obtain high-selective detectors. The
outcomes of this estimation procedure are used to devise detection
architectures relying on either the twostage design paradigm or heuristic
design procedures based upon the generalized likelihood ratio test. Remarkably,
the new decision rules exhibit a bounded-constant false alarm rate property and
allow for a tradeoff between the matched detection performance and the
rejection of undesired signals by tuning a design parameter. At the analysis
stage, the performance of the newly proposed detectors is assessed also in
comparison with existing selective competitors. The results show that the new
detectors can outperform the considered counterparts in terms of rejection of
unwanted signals, while retaining reasonable detection performance of matched
signals.
