الإشارة مستقرة في الشبكة اللاسلكية.

Because this is a nominal sentence in the present tense. In Arabic, the verb to be is usually not expressed in simple present-tense statements.

So:

الإشارة مستقرة
literally: the signal stable
natural English: The signal is stable

If you wanted a past-tense version, Arabic would normally use كان:

كانت الإشارة مستقرة = The signal was stable

The sentence is:

الإشارة مستقرة في الشبكة اللاسلكية

Its basic structure is:

• الإشارة = the subject / topic (the signal)
• مستقرة = the predicate (stable)
• في الشبكة اللاسلكية = a prepositional phrase (in the wireless network)

In traditional Arabic grammar, this is:

• مبتدأ: الإشارة
• خبر: مستقرة
• plus the prepositional phrase في الشبكة اللاسلكية, which adds more information about where that stability applies.

Because الإشارة is a feminine noun, and Arabic adjectives (including predicate adjectives) must agree with the noun they describe in gender.

So:

• masculine: مستقر
• feminine: مستقرة

Since الإشارة is feminine, the sentence uses مستقرة, not مستقر.

A big clue is the ة at the end of إشارة, which usually marks a feminine noun.

In Arabic, the predicate in a sentence like this is usually indefinite, even if the subject is definite.

So Arabic says:

• الإشارة مستقرة
• literally: the signal [is] stable

It normally does not say:

• الإشارة المستقرة in this sentence structure

That form would usually mean the stable signal, which is a noun phrase, not a complete sentence.

So:

• الإشارة مستقرة = The signal is stable
• الإشارة المستقرة = the stable signal

A fully vowelled version would be:

الإشارةُ مستقرةٌ في الشبكةِ اللاسلكيةِ

These endings show the grammatical case:

• الإشارةُ: nominative, because it is the subject
• مستقرةٌ: nominative, because it is the predicate
• في الشبكةِ: genitive after the preposition في
• اللاسلكيةِ: also genitive, because it agrees with الشبكة

In normal everyday writing, these short vowels are usually omitted.

Because في is a preposition meaning in (and sometimes something close to on/within, depending on context). A noun after a preposition in Arabic goes into the genitive case.

So:

• في = in
• الشبكةِ = the network (genitive after في)

That is why, in fully vowelled Arabic, you would see:

في الشبكةِ

Because اللاسلكية is an adjective describing الشبكة, and Arabic adjectives agree with the noun in:

• definiteness
• gender
• number
• case

Here:

• الشبكة = definite (the network)
• so the adjective must also be definite: اللاسلكية = the wireless

Together:

الشبكة اللاسلكية = the wireless network

If the noun were indefinite, the adjective would also be indefinite.

Because it describes الشبكة, and الشبكة is feminine.

So the adjective must match it:

• masculine: لاسلكي
• feminine: لاسلكية

That is why you get:

• شبكة لاسلكية = a wireless network
• الشبكة اللاسلكية = the wireless network

It functions here as an adjective/predicate meaning stable.

Morphologically, it comes from the verb استقرّ = to become stable, settle, be established.

Related forms:

• استقرّ = he/it became stable
• مستقرّ = stable / settled / established (masculine)
• مستقرة = stable / settled / established (feminine)

So in this sentence, مستقرة is the feminine form that matches الإشارة.

Because the underlying masculine form is مستقرّ, which ends in a shadda on ر. That means the r is doubled or strengthened in pronunciation.

So:

• مستقرّ = mustaqirr
• مستقرة = mustaqirra

This comes from the verb استقرّ, which also has that doubled r sound.

The given order is the most neutral and straightforward for a learner:

الإشارة مستقرة في الشبكة اللاسلكية

Arabic can sometimes change word order for emphasis or style, especially by moving the prepositional phrase earlier. For example, a speaker might front في الشبكة اللاسلكية to emphasize location.

But for normal learning purposes, the standard pattern is:

• subject + predicate + extra information

So this sentence is a very good basic model.

It is pronounced with a doubled l sound, because ل is a sun letter. That means the l of the article الـ assimilates into the l of the word.

So اللاسلكية is pronounced roughly like:

allā-silkiyya

not like:

al-lā-silkiyya with two clearly separate l sounds

In careful transliteration, you may still see it written in a way that reminds you the article is there, but in pronunciation the l is assimilated.