Distributed Cophasing With Autonomous Constellation Selection

In this paper, we consider a distributed cophasing (DCP) technique in which multiple sensor nodes (SNs) communicating their observations to a fusion center (FC) need to transmit different classes of data requiring different levels of error protection. To achieve this, we propose a variant of the DCP technique with autonomous constellation selection at the different SNs. In the first stage of the two-stage time division duplexed cophasing scheme, the SNs obtain estimates of the channels to the FC using pilot symbols transmitted by the latter. Following this, the SNs simultaneously transmit their data symbols prerotated according to the estimated channel phases to combine coherently at the FC. The symbols transmitted by different SNs are drawn from possibly different constellations selected based on the estimated instantaneous channel gains. We show that this scheme is equivalent to transmitting symbols from hierarchical constellations. Based on the properties of hierarchical constellations, we develop recursive expressions for the BER of the proposed system. Following this, we use the properties of the effective channel coefficients to show that it is possible to recover the transmitted data bits from the signal received at the FC blindly, without requiring explicit pilot symbols to be sent by the power-starved SNs. We develop three blind channel estimation and data detection schemes for the presented system model. Using Monte Carlo simulations, we show that the proposed blind channel estimation algorithm achieves a probability of error performance close to that with genie aided perfect channel state information (CSI) at the FC, while using only a moderate number of unknown data symbols for channel estimation.