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I am getting confused about the received signal expression in case of SIMO wireless channel.

SIMO system=> Here we will have one antenna at Tx and multiple ($N$) antenna at Rx.

Therefore received signal will be $$\bar{y}(n) = \bar{h}s(n)+\bar{w}(n) \tag{1}$$

where bar indicates a vector, $s(n)$ is transmitted signal, $\bar{w}(n)$ is AWGN vector of dimension $N \times 1$, $\bar{h}$ is channel vector of dimension $N \times 1$.

I am confident in writing equation (1). But confusion starts because in many research papers, they take transpose of $\bar{h}$ i.e., $\bar{h}^T$ and hence the received signal expression becomes

$$\bar{y}(n) = \bar{h}^Ts(n)+\bar{w}(n) \tag{2}$$

My query is which of the equation among (1) and (2) is correct way of writing the expression for received signal.

I would really appreciate any help in overcoming this confusion.

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  • $\begingroup$ Can you give an example of the use of (2) in a paper that's accessible to us? $\endgroup$
    – Peter K.
    Jun 1, 2022 at 15:48
  • $\begingroup$ Thank you so much sir for your answer..... arxiv.org/pdf/2112.01336.pdf In this paper there is a base station (BS) with one antenna and intelligent reflecting surface (IRS) with $K$ elements. Therefore, the channel from BS to IRS is SIMO and they have mentioned conjugate transpose of it.... $\endgroup$
    – paru
    Jun 1, 2022 at 15:55
  • $\begingroup$ Thanks for the link. I can't see anywhere where the signal model as in your (2) is used. I can see $h_{sn} + \mathbf{h}^H_{rn} \Theta_R \mathbf{h}_{sr}$ in equation (1) of the linked paper, but that's not the same as your equation (2). Which equation in the paper do you mean? $\endgroup$
    – Peter K.
    Jun 1, 2022 at 17:19
  • $\begingroup$ On page number 4 , above equation 2..... It starts with word "Denoting" $\endgroup$
    – paru
    Jun 1, 2022 at 17:29
  • $\begingroup$ That's just so they don't have to write $\mathbf{h}_{sr} = \left [ \begin{array}{c} h^1_{sr}\\ \vdots\\ h^K_{sr} \end{array} \right ]$. That is, they can write it as a row vector rather than a column vector. The row vector takes up less space on the page. The vectur $\mathbf{h}_{sr}$ is still a column vector. $\endgroup$
    – Peter K.
    Jun 1, 2022 at 17:31

1 Answer 1

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I can't see anywhere where the signal model as in your (2) is used. I can see β„Žπ‘ π‘›+π‘π»π‘Ÿπ‘›Ξ˜π‘…π‘π‘ π‘Ÿ in equation (1) of the linked paper, but that's not the same as your equation (2).

The notation before the paper's equation (2) is just so they don't have to write $$\mathbf{h}_{sr} = \left [ \begin{array}{c} h^1_{sr}\\ \vdots\\ h^K_{sr} \end{array} \right ].$$ That is, they can write it as a row vector rather than a column vector. The row vector takes up less space on the page. The vectur $\mathbf{h}_{sr}$ is still a column vector.

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