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We extend a scatter/target detection framework for the Uniform Linear Array (ULA) with non-negligible spatial delay across its aperture length. We present a simple yet effective Discrete Fourier Transform (DFT) based approach for detecting sparsely distributed targets. We investigate and develop the system model for observing controlled leakage at the low subcarrier-antenna index and exploit this fact to avoid path overlapping. In order to detect the number of targets correctly, we develop a peak finding-based (unlike clustering-based) target detection algorithm by identifying the peaks present in the noisy DFT spectrum. Furthermore, we demonstrate the utility of percentile-based threshold for sparse wireless scenarios. We show the criterion of selecting among various percentile thresholds under different noise levels through evaluations of appropriate numerical metrics in simulations.