Undetectable wireless transmissions are fundamental to avoid eavesdroppers. To address this issue, wireless steganography hides covert information inside primary information by slightly modifying the transmitted waveform such that primary information will still be decodable, while covert information will be seen as noise by agnostic receivers. Since the addition of covert information inevitably decreases the SNR of the primary transmission, key challenges in wireless steganography are: i) to assess the impact of the covert channel on the primary channel as a function of different channel conditions; and ii) to make sure that the covert channel is undetectable. Existing approaches are protocol-specific, also we notice that existing wireless technologies rely on phase-keying modulations that in most cases do not use the channel up to its Shannon capacity. Therefore, the residual capacity can be leveraged to implement a wireless system based on a pseudo-noise asymmetric shift keying (PN-ASK) modulation, where covert symbols are mapped by shifting the amplitude of primary symbols. This way, covert information will be undetectable, since a receiver expecting phase-modulated symbols will see their shift in amplitude as an effect of channel/path loss degradation. We first investigate the SER of PN-ASK as a function of the channel; then, we find the optimal PN-ASK parameters that optimize primary and covert throughput under different channel condition. We evaluate the throughput performance and undetectability of PN-ASK through extensive simulations and on an experimental testbed based on USRP N210 software-defined radios. We show that PN-ASK improves the throughput by more than 8x with respect to prior art. Finally, we demonstrate through experiments that PN-ASK is able to transmit covert data on top of IEEE 802.11g frames, which are correctly decoded by an off-the-shelf laptop WiFi.