# Non-Coherent Joint Transmission in Poisson Cellular Networks Under Pilot Contamination

## TL;DR

This paper analyzes the impact of pilot contamination on non-coherent joint transmission in Poisson cellular networks, providing a simple SNR model that guides system optimization and reveals phase transition phenomena in cooperation strategies.

## Contribution

It introduces an easy-to-compute SNR expression considering pilot contamination, enabling efficient optimization of cooperation and training parameters in cellular networks.

## Key findings

- Multipoint transmissions can outperform non-cooperative operation under certain conditions.
- A phase transition phenomenon determines the optimal number of cooperating access points.
- Minimal training overhead is identified for maintaining target SNR levels.

## Abstract

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.