Systems based on secondary surveillance radar (SSR) downlink signals, both with directional and with omni-directional antennae (such as in multilateration), are operational today and more and more installations are being planned. In this frame, high-density traffic leads to the reception of a mixture of several overlapping SSR replies. By nature, SSR sources are sparse, i.e. with amplitude equal to zero with significantly high probability. While in the literature several algorithms performing sources separation with an m-element antenna have been proposed, none has satisfactorily employed the full potential of sparsity for SSR signals. Most sparsity algorithms can separate only real-valued sources, although we present in this study two algorithms to separate the complex-valued SSR sources. Recorded signals in a live environment are used to demonstrate the effectiveness of the proposed techniques.