Our Neighbor Scream In The Middle Of The Night And He Himself Called Called Cops On Us About Noise Complaint.

So me and my husband live in the building for past 4 years and did not have a single complaint for any reason. On Friday a new neighbor moved in to the apartment next door. We met in the lobby briefly (did not talk - keep in mind we live on the 7th floor). From Saturday night to Sunday Morning at 4 AM in the morning we suddenly heard yelling and accusation next door. We did not do anything. Then From Sunday night to Monday morning, we heard another yelling and screaming around the same time 3-4 AM from the same apartment. Then around 5:20 AM police showed up at out door mentioning that they receive noise complaint notice anonymously on our apartment.
Next day maintenance guy for the building showed up informing us that that the same neighbor reported us to the management and management contacted this maintenance guy to talk to us first and then if this will not work out, management will send us a email.
Things to notice, something what i was considering could affect this situation. My husband's nationality is Trinidad and I am from Russia and neighbor is white (but we are all from USA). It get this concern because when maintenance guy was informing us, he did say the guy from other apartment felt threatened and called police guys because he did not what we might do or if we were dangerous. And last things to consider, we have a slight unpaid rent balance, we currently negotiated with management to pay it in full. Also we do not have any proof that guy was making noise and not us, we were sleeping at that time, because my husband has 2 jobs and has to wake up at 7 am in the morning.
What should we do in this situation, how to prove that we were falsely accused? I do not want to leave this situation as it is, because I am concern that if we did not defend ourself people will think that it was us.
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