Usage of the word 'Each'

Solution 1:

The entry on each in Collins Cobuild English Usage (p204) notes in the section 'used after subject':

Each is sometimes used after the subject of the clause, For example, instead of saying 'Each of them received a new pairs of boots', you can say 'They each received a new pair of boots'.

The CCEU then goes on to state:

This type of construction is often used to indicate that an amount relates to each member of a group separately and not to the whole group.

The CCEU entry concludes by saying:

When you are talking about an amount like this, you often put each at the end of the clause.

So, an alternative to the sentence you quote is:

The base stations, users, and relays are equipped with one antenna each.

Solution 2:

Each (pronoun) acts as a distributive pronoun, i.e. almost adverbially with the meaning "individually"

OED:

Each (pron.)

B 2. Used so as to indicate distribution of a plurality of things among the members of a set.

a. Distributing a plural subject or object (e.g. the labourers will each receive a reward).

OE West Saxon Gospels: Matt. (Corpus Cambr.) xx. 9 Þa onfengon hig ælc his pening. [then each received his penny]

1945 Times 13 Feb. 4/1 The forces of the three Powers will each occupy a separate zone of Germany.

2004 S. Rothstein Predicates & Their Subj. x. 313 Four farmers have each built a fence.

Solution 3:

The base stations, users, and relays are each equipped with one antenna.

"Each" is not a pronoun, despite what some people (and most dictionaries) claim. It actually belongs to the word class (part of speech) determinative.

It is separable and not part of the subject NP but a quantificational adjunct in clause structure. The adjunct has the form of a fused-head NP.

We know that this "each" is an adjunct because when the verb is an auxiliary, it preferentially follows rather then precedes it, as it does in your example.

Note that the same applies to the determinatives "all" and "both".

Source: CGEL (Huddleston & Pullum) p428