Usage of the word 'Each'

Question

I saw the following sentence in a journal paper.

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

I'm sure it means that each of them is equipped with one antenna.
However, I can't understand how the word 'each' is placed there in the sentence above.
I've learned that 'each' acts as a determiner or a pronoun depending on the sentence.
Hence, as far as I am concerned, it should be written as

Each of the base stations, users, and relays is equipped with one antenna.

or

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

However, I've seen the structure of the first sentence several times.
Accordingly, I felt there is a sentence structure or grammar that I don't know.
Please explain how 'each' can be placed between be verb and past participle.

Shoe · Accepted Answer

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.

Greybeard · Answer

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.

BillJ · Answer

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

Usage of the word 'Each'

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