ZF means when u have mutiple users and ur transmission is intended for one particular user and zero transmission (ideally) for others. But in practice there is interference for other users when u considering BC.
ZF is just a detector, which has the property that it inverts the channel (which introduces cross-talking) and consequently from each user's perspective, there is on interference from others, namely forcing interference to zeros.
Turn to MIMO BC, I knew A.Goldsmith from Stanford has series of paper on this topic.
the word zero forcing in communiction particularly digital communication means that u have an equilizer that takes an input signal comming from a distant place contaminated with noise and distortion and ir u process this signal without passing it through this equilizer ur system is not go no work , one of the many reasons is that the signal strength is deteriorated....so when we pass a digital signal through a zero forcing equilier it detects the zero crossing of the incomming signal and in this way get and information about the phase , frequency of the incomming signal...and if there is a regenerative repeater also after as is in digital communication it would use the information provided by zero forcing equilizer and generate new pulses