# Why is the received signal=information+RF signal+noise,not just information+noise?

Here is its system model

In this model,it said the received signal in each DR is

$$y_k=\mathbf h_k^H \mathbf w_k s_k^D+\sum\limits_{i=1,i \neq k}^{K}\mathbf h_k^H \mathbf w_i s_i^D+\sum\limits_{j=1}^{J}\mathbf h_k^H \mathbf v_j s_j^E+n_k$$, Notice that due to the energy symbol $$s^E_j$$ is randomly generated, which carries no information but only satisﬁes the RF regulations;$$s_k^D$$ is data symbol for DR k .

Honestly,i don't understand about $$s^E_j$$,i mean i know the received signal of DR1,

$$y_{DR1}=$$(signal from RRH1) + (signal from RRH2 and RRH3,etc)+(noise),that is

$$y_k=\mathbf h_k^H \mathbf w_k s_k^D+\sum\limits_{i=1,i \neq k}^{K}\mathbf h_k^H \mathbf w_i s_i^D+n_k$$

but i don't know where does $$\sum\limits_{j=1}^{J}\mathbf h_k^H \mathbf v_j s_j^E$$ come from

I have a thinking before,the signal RRH transmit is information+RF signal,that is $$s_k^D+s_j^E$$,but in the other paper,they will only mention the $$s_k^D$$,like this paper: https://arxiv.org/pdf/1805.08898.pdf ,it just said $$y_k=\mathbf h_k^H \sum\limits_{j=1}^K \mathbf f_j s_j+n_{a_k}$$,so does anyone know about what the $$s_j^E$$ is?

Well, it seems the authors assume a setup where there are separate data receivers (DR) and energy receivers (ER) ("To achieve a balanced user experience for separately located datareceivers (DRs) and energy receivers (ERs) in the network, joint transmit beamforming vectors are optimized [...]"). In that setup, $$s_k^E$$ would be symbols that are used for sending energy to the ERs whereas $$s_k^D$$ are data symbols for the DRs.
Therefore, if you are a DR and want to receive data, you care about two types of interferences: data symbols for other DRs and energy symbols for the ERs. Note that you didn't copy equation (1) exactly: the second term should be $$s_i^D$$ (data symbol interference). Then you have the third term with interference of energy symbols for the ERs and the fourth term for the noise.