What is the time it takes to measure the SINR in LTE?

I would like to know how much time it takes the receiver to evaluate the SINR?

Scenario: Assume that a base station (eNodeB) would like to transmit to one user. Let us say that it sends a pilot signal of L bits to that user. Then the user calculates the SINR (assuming that there are a set of N other interfering base stations) and compares it to a certain threshold and then feeds back 1 bit to the base station to tell it if the SINR is above or below the threshold. How much time it takes for this process?

In general, how the standard LTE works to evaluate the SINR at the receiver?

Marcus is right. However, I think that what the OP wants to know is simply how much time it takes to estimate whatever you define as SINR and how it's done.

So first, how it's done?

That's completely up to the equipment manufacturer. I've seen several methods for estimating the SINR, with different performances and complexity requirements. Since you may use any known data pattern to perform SINR/channel estimation, both Synchronisation and Reference Signals can be used. However, if these signals are separated in frequency (and I think they are), using the same estimation method over both signals may yield different values.

How much time it takes?

Of course, it depends on the method adopted. If your estimation is based only on cell-specific Reference Signals (RS), you may have roughly one estimation every 5 ms, since there are 2 RS per LTE frame. Some methods use these two RS and extrapolate the result in order to provide 1 estimation per frame. Other methods are based in previous estimations plus some kind of prediction algorithm. And so on. But in general, I think that the time it takes to get an estimation depends more on the protocol structure (the fact that pilot signals are inserted each X ms) than hardware processing capabilities (in case your question was more linked to those issues).

So you're giving your answer yourself in the question:

In general, how the standard LTE works to evaluate the SINR at the receiver?

The point is that measures like SNR and SINR are dependent on what you consider your signal of interest, what you consider interference and what you consider noise¹.

LTE actually specifies multiple different things that describe "received signal strength", whcih you can pu in relation to unwanted effects, and all of these could be labeled as SINR (but have different values for the same transmission!). The two "S" in ("SINR") measurements you probably care about are

• RSRP, Reference Signal Received Power: Simply put, LTE uses distributed pilot symbols to figure out the channel state; just adding up the strengths of these will give you the magnitude of the impulse response over all OFDM subchannels.
• RSRQ, Reference Signal Received Quality: The reference tone powers above don't say overly much about how well-suited the channel actually is – they are really just a sum. But in an OFDM system, where all but let's say 5% of subchannels are heavily attenuated, but these 5% are extremely well power-conserving, you just won't get the same performance in a system where all channels are attenuated, but things are more evenly distributed, even if the two systems have the same RSRP; hence, RSRQ takes other things into consideration, too.

You can (weightedly) subtract these from RSSI, which is also specificially defined for LTE, to get an estimate for the "IN" part of "SINR".

Frankly, RSRQ and RSRP are probably much better suited to describe a complex multicarrier system than the simplistic SINR – so if I could, I'd just try to argue based on these, and drop the SINR terminology.

¹ This is actually the answer I most often give at my job, "SNR depends on what you consider to be signal and noise. No general formula can be given.".