# LTE PSS Channel Estimation for coarse SSS Equalization

In LTE the Primary Synchronisation Signal (PSS) can be detected by taking a correlation with the known 3 zadoff chu sequences (roots: 25,29,34). Once the peak has been detected the receiver knows which sequence has been sent. The sequence is placed at the middle 63 subcarriers (DC with 0 in the middle). Assuming $$x_{u}$$ is the detected zadoff chu sequence with the root $$u \in \{ 25,29,34\}$$ (length of 63), the channel response can be calculated by: $$h_{x_u}(f_i) = \frac{x^*_{u}(f_i) \cdot r_{x_{u}}(f_i)}{|x_{u}(f_i)|^2} = \frac{x^*_{u}(f_i) \cdot x_u(f_i) \cdot h_{x_u}(f_i)}{|x_{u}(f_i)|^2}$$ Where $$r_{x_u}(f_i)$$ is the received symbol at the $$f_i$$th subcarrier with the zadoff chu sequence $$x_u(f_i)$$ including the channel response $$h_{x_u}(f_i)$$: $$r_{x_u}(f_i) = x_u(f_i) \cdot h_{x_u}(f_i)$$

With this it is possible to calculate a channel response for the middle 63 Subcarriers on every OFDM symbol which carries a PSS. Every 5 ms it is sent an OFDM Symbol which carries a PSS. So by using the block based channel estimation it might be possible to interpolate these PSS channel responses over time to get a $$h_{x_u}(f,t)$$.

The Secondary Synchronisation Signal (SSS) is placed at the previous OFDM symbol of the PSS.

So the SSS could be equalized using the PSS channel estimation.

1. Does anybody know if interpolating the PSS channel responses is a good way to obtain an estimation for the SSS?

2. In case no, does anybody has any idea how to get a good estimation for the SSS using the PSS channel responses?

The following picture visualises the block based channel estimation. Here the marked OFDM symbols are the PSS and the goal is to estimate the channel for each previous symbol.

Every 5 ms it is sent an OFDM Symbol which carries a PSS. So by using the block based channel estimation it might be possible to interpolate these PSS channel responses over time to get a $$h_{x_u}(f,t)$$.