Methods and apparatus for multiple-antenna communication of wireless signals with embedded pilot signals

Embodiments of methods and apparatus for wirelessly communicating signals include one or more transmitters configured to generate a plurality of wireless signal for transmission. Each of the wireless signals includes a plurality of pilot signals represented in a plurality of unevenly spaced, in-band subcarriers. Pilot signals of each wireless signal are positioned at subcarriers that are orthogonal in frequency with subcarriers at which pilot signals of all other wireless signals are positioned. According to an embodiment, subcarrier indices each the plurality of pilot signals are determined using a third order or higher order polynomial parameterization of pilot subcarriers in conjunction with a convex optimization algorithm to produce pilot signals having near-optimal channel estimate mean square error (MSE) performance. The wireless signals are simultaneously radiated over a wireless communication channel using a plurality of co-located or distributed antennas.