In some pseudo-orthogonal waveform embodiments, a radar system transmits pseudo-orthogonal waveforms and performs multiple correlations on a combined single receiver channel signal. In some quadratic polyphase waveform embodiments, a radar system may simultaneously transmit frequency separated versions of a single quadratic polyphase waveform on a plurality of transmit antennas, combine the return signal from each antenna into a combined time-domain signal, and perform a Fourier transformation on the combined time-domain signal to locate a target. The radar system may identify a target, such as sniper's bullet, incoming projectile, rocket-propelled grenade (RPG) or a mortar shell. In some embodiments, the system may estimate the target's trajectory to intercept the target. In some embodiments, the system may estimate the target's trajectory and may further extrapolate the target's trajectory to locate the target's source, such as the sniper.