We consider the downlink of an Ultra-Wideband (UWB) sensor network, i.e. communication from a central unit to many sensor nodes. The key to achieve low-complexity, low-power and low-cost sensor nodes are non-coherent receivers. Conventionally, their detection performance strongly suffers from inter-symbol interference due to multipath, which substantially limits the data rate or requires expensive receiver post-processing. To overcome this problem, we propose a novel precoding scheme to transmit to several nodes simultaneously. This way the sum data rate can be increased, while low complexity of sensor nodes is maintained. Specifically, we consider nodes with generalized energy detection receivers and transmission of pulse position modulated data. First, precoding optimization is derived from a Signal-to-Interference-plus-Noise Ratio (SINR) expression for this setup based on full channel state information. To achieve the best sensor network coverage, the minimum SINR of all nodes is maximized. In a second step, optimization is extended to statistical channel knowledge, which depends on the position of the nodes. Performance evaluation based on an extensive measurement campaign shows that multiple nodes can efficiently be served simultaneously. Only marginal increase in transmit power is necessary compared to time-multiplexing.