Do Cooperative Radios Collide?

When cooperative terminals transmit concurrently, the receiver experiences additional distortion by the presence of radios carrier offsets and time delays. With the inevitable inaccuracy in estimating the channel at the receiving end, is it realistic to assume that relays transmissions do not collide? To address this question, we provide an analytical framework to model the effect of channel estimation methods that treat the channel as deterministic and unknown, and derive the average symbol error rate (SER) of a maximum likelihood sequence decoder (MLSD) and of a linear minimum mean squared error (LMMSE) equalizer using such estimates. We select the appropriate architecture by mapping two different channel estimation techniques onto the proposed analytical framework, and derive their diversity gain. First we analyze the well known linear least square channel estimation (LLSE), then, we show how to cast a compressed channel sensing (CCS) method onto our analytical model, by a novel approximation of the estimator noise and modeling mismatch. We observe that the latter is the key bottleneck in LLSE whereas the CCS appears sufficiently flexible to deliver the promised gains. This conclusion shows that collisions models are overly pessimistic, but it also underscores the need for an advanced receiver synchronization design.