In randomized cooperative transmission, relay nodes transmit a random linear combination of a space-time code (STC), to realize MISO gains at the end receiver without prior coordination of relays. Unlike selective cooperative combining schemes, the channel estimation and tracking becomes inherently much more challenging, due the fact that each radio has its own local oscillator, clock, propagation and processing delay, and multiple of them will be normally cooperating at unison. In this paper we show that the new class of channel estimators, that are based on compressed sensing models, can retain much of the diversity gain that the codes are theoretically designed to harvest when the channel is ideally known. This is in contrast with standard schemes for linear equalization, which fail to compensate for the channel distortion in the presence of realistic amounts of asynchrony and channel dispersion. The contribution of this paper is a semi-analytical performance evaluation that leads to the insightful comparison of the receiver architectures.