  This paper investigates the performance of downlink cellular networks with
non-coherent joint (mutlipoint) transmissions and practical channel estimation.
Under a stochastic geometry framework, the spatial average
signal-to-noise-ratio (SNR) is characterized, taking into account the effect of
channel estimation error due to pilot contamination. A simple, easy to compute
SNR expression is obtained under the assumption of randomly generated pilot
sequences and minimal prior information about the channels and positions of
access points (APs). This SNR expression allows for the efficient joint
optimization of critical system design parameters such as number of cooperating
APs and training overhead. Among others, it is shown that multipoint
transmissions are preferable to conventional (non-cooperative) cellular
operation under certain operational conditions. Furthermore, analytical
insights are obtained regarding (a) the minimum training overhead required to
achieve a given SNR degradation compared to the perfect channel estimation case
and (b) the optimal number of cooperating APs when an arbitrarily large
training overhead can be afforded. For the latter, in particular, a phase
transition phenomenon is identified, where the optimal number of cooperating
APs is either finite or infinite, depending on whether the path loss factor is
less or equal than a certain value, respectively.
