# Can the j be equal to k in the first formula ?In MISO system

In this system model,the received signal available for RF EH at each RX_k is given by

However,its SINR formula is given by

We can find that author said the j can't be equal to k,but their range are the same in the second formula .However,in the first formula,i am not sure that is the j equal to the j in the second formula? I mean,now i know j which is in the second formula can't be the same as k,but how about j in the first formula?can it be equal to k ?

Well,i think j can be equal to k in the first formula,however,i found that if i write the code in "j can be equal to k" this situation,i can't get the optimal value every time,sometimes,the optimal value will be "Inf".however,if i write the code in "j can't be equal to k" this situation,i can get the optimal value every time,it is strange,so i need someone to tell me can j be equal to k in the first formula? Paper link: https://arxiv.org/pdf/1805.08898.pdf

• The first formula is the aggregate received signal, and it includes all received signals from all users/antennas (i.e., $k$ is included). In the second formula, it's the SINR of user/antenna $k$ which is defined as the signal power of user/antenna $k$ over the interference power from all other users and the noise power. That's why $k$ is not included in the denominator but it's included in nominator. – BlackMath Mar 26 at 9:47
• Thanks for your information,with your information,i have confidence to convince me i am right – Shine Sun Mar 27 at 0:07