# How the length of cyclic prefix is determined with the help of sss?

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How the length of cyclic prefix is determined with the help of sss?
posted Sep 16, 2014

+1 vote

Length of CP is determined by PCI scans (PSS and SSS). When the UE gets the PSS and it goes for the SSS, it gets to know the symbol length because PSS and SSS are placed together. Once, the UE gets the symbol length, it knows which type of CP is used i.e. Normal CP or extended CP as later one has larger symbol length.

In short, decoding of SSS helps to decide to use normal CP or extended CP.

answer Sep 16, 2014
+1 vote

I agree with the previous post 100%, but I thought I'd add a little bit for some more clarity.

To understand how this really happens, you need to understand the method that is used to detect PSS and SSS in the first place. The PSS and SSS are essentially created by packing 62 resource elements each in the last and second to last OFDM symbols in slot 0.

There are 3 different PSS and 168 (I think) SSS signals. The way the resource elements are "packed", i.e. the complex numbers to use are described in 36.211. What's germane to this discussion is that each of the packing methods for the PSS and SSS signals will result in a different signal in the time domain. The time domain signal is generated by the inverse FFT of the RE in a particular OFDM symbol.

Because of the unique time domain structure of each of the signals (and some other properties that I don't really have the time to get into) a technique called "correlation" can be used to detect the presence. Take a look at the wikipedia article on correlation here: Wikipedia Correlation.

The key part of correlation that gets to the heart of your question is the so-called correlation peak. The important picture from the wiki is seen here ...
Correlation Images

On the right hand side of the picture images of "autocorrelation" are shown. The important feature to extract is the pointy shape on top of the autocorrelation function referred to as the correlation "peak". So in order to detect a particular signal, one should postulate a particular signal by creating a time domain replica and correlating that against what it received. The presence of the correlation peak at high amplitude indicates a positive detection. Moreover, the peak of the signal indicates the best alignment between your received and replicated signals.

Once you understand that, then it's very easy to understand that the difference between the PSS correlation peak and the SSS correlation peak is directly related to the cyclic prefix length. Qualitatively, since there are 7 symbols per slot in normal CP and 6 in extended CP, the PSS and SSS peaks will be closer together in normal CP, and further apart in extended CP.

So in short....
1. Postulate a PSS and verify through correlation
2. Postulate SSS and verify through correlation
The difference in time between the peaks gives you the answer you're after.

I hope that helps

Jeff

answer Sep 16, 2014
How is the difference between the PSS correlation peak and the SSS correlation peak is directly related to the cyclic prefix length??
My apologies for not being clear on the matter.

The nature of correlation is that the peak will occur when the signals are best aligned in time.  As part of the correlation result, you will know where the peak occurs in time relative to your sampled data stream.

The key insight is that the correlation peaks will appear in the same time indices relative to the start of the OFDM symbols.  Therefore the distance between correlation peaks (which is measured in units of time) is the same as the duration of an OFDM symbol.

For Normal CP this is 1/14 of 1 ms.  For Extended CP this is 1/12 of 1 ms.  If you prefer to count samples, rather than measure time, you need to incorporate the sampling rate.  So for example, assuming a 10 MHz LTE bandwidth, the minimum recommended sampling rate is 15.36 x 10^6 samples per second.  So for normal CP this represents about 1097 samples, and for extended CP this represents 1280 samples.  This is clearly a wide enough margin to allow for some error in the measurement of the correlation peak.

I hope that helps.

Jeff
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