# What is the time unit of the converted Channel Impulse Response?

I don't have a lot of background on wireless communication but as far as I understand, applying IFFT on Channel Frequency Response (CFR) would transform the data into time domain Channel Impulse Response (CIR), in which it shows the delay spread of the different multiple paths.

The CSI measuring tool I'm using measures 30 subcarriers resulting in 30 complex number CFRs per a single CSI trace. So when I apply 30-point IFFT on the CFR, the output is a CIR with 30 time-domain values.

My question is,

• What is the time unit of the converted CIR?
• How much seconds are they (the 30 impulse responses) apart?
• Also, are the impulses like the echoes of the transmitted signal?
• The number of multi-path is not determined. So I assume that an impulse response does not represent a single path, since the number of impulse response is fixed to 30. Then how should I understand the CIR value with respect to the multi-paths?
• You need to know the sampling frequency; that tells you the time between samples of the impulse response. The impulses are indeed the "echoes" caused by the channel. – MBaz Jul 26 '17 at 1:59
• Thank you @MBaz for your answer! To clarify my understanding, each impulses would be 1(sample)/sampling_rate(Hz) seconds apart right? – danielle Jul 26 '17 at 7:55
• Do you also know where I can obtain the sampling frequency? It's not specified in the 802.11n standards. It seems like the sampling rate is an adjustable value, but I have no clue on how I can find or set the value. – danielle Jul 26 '17 at 8:12
• 1) That is right. 2) If you're looking at 802.11n then the sampling rate is specified by the carrier frequency separation (spacing), as AlexTP explains below. – MBaz Jul 26 '17 at 13:17

Because you don't have background in wireless communications, I will try to answer as simply as possible.

What is the time unit of the converted CIR?

Just time unit. It can be second, ms, us, etc. They are convertible, aren't they?

How much seconds are they (the 30 impulse responses) apart?

In the case that CSI-pilots are equally seperated, impulses are $1/(N_p \times \Delta p)$ second apart, where $N_p$ is the number of CSI-pilots, e.g. $N_p = 30$ in your example, and $\Delta p$ is CSI-pilot spacing in Hz.

Also, are the impulses like the echoes of the transmitted signal?

Impulse reponse is the output if we use a Dirac pulse as input. It represents the effect of scaled-delayed echoes of the TX signal.

The number of multi-path is not determined. So I assume that an impulse response does not represent a single path, since the number of impulse response is fixed to 30. Then how should I understand the CIR value with respect to the multi-paths?

The generated CIR is the interpolated version of the multipath response. For example, in the figure below, the CIR samples are green and physical paths are in other colors.

Note that if you accept CIR by using iDFT like that, you are implying that your multipath response is invariant during the acquisition time of your 30 CSI-pilots.

Some other resources if you want to learn more or to find the answers by yourself if I have missed something. :)

Multipath fading channel visualization in MATLAB

Statistical Characteristics of Multipath Channels

• Thank you so much @AlexTP!! Your figure is really helpful. Clarifies a lot of the unclear understandings!! – danielle Jul 27 '17 at 1:32