Required transmit power for broadcast systems with Tomlinson-Harashima-precoding

Tomlinson-Harashima-precoding can be used as dirty-paper-coding method for transmissions over a broadcast channel. From single user systems it is known that this symbol wise precoding method suffers, amongst others, from a power loss. However, for broadcast scenarios it is also possible to observe a power gain. This paper investigates the required transmit power for Tomlinson-Harashima-precoding in broadcast systems. Additionally, upper and lower bounds on the required power are derived.