# Multi-input Single-output communication system

In case of communication in MISO system, if we have a system of 4 x 1, which means 4 transmitter with 1 receiver. Will the received signal be a vector of dimension 4 x 1 ? Or it will be 1 x 1 since the transmitter are sending to the same receiver?

Thank you

• The receiver only receives 1 signal, but the channel matrix is 4x1. – user253751 Jul 16 at 16:33
• What that means? could you explain it mathematically? Do you mean the received signal is a vector of dimension $4$x$1$ ? – New_student Jul 16 at 16:34
• No, I mean the receiver only receives 1 signal, and the channel matrix is 4x1. – user253751 Jul 16 at 16:35

Multi-input single-output (MISO) is describing the inputs and outputs of the system. In communication, this is the channel, so if you have a single-output it means that the received vector is $$1 \times 1$$.

The general model for a MISO system is:

$$\begin{split} y &= \mathbf{h^Tx}+\text{noise} \\ &= (h_1x_1+h_2x_2+...+h_Nx_N)+\text{noise} \end{split}$$

The single output in a MISO system is a combination of the multiple inputs plus the noise.

• So, in that case, MISO is useless, it's very similar to SISO. is that right ? – New_student Jul 16 at 16:33
• It is similar I guess in the case that there is a single output. The difference is that in a MISO system, the output is a combination of the multiple inputs. – Engineer Jul 16 at 17:07
• @New_student MISO is not useless. It offers an opportunity to perform precoding (en.wikipedia.org/wiki/Precoding) which you didn't have with a SISO system. – Engineer Jul 16 at 17:16

Stop thinking about the maths and just think about the reality. You have 1 receiver. That means there is a signal coming from the receiver into the processor. There is only one signal. You can't measure it twice and get two different signals.

You may be thinking of the channel matrix, which has dimension 1x4 (not 4x1, sorry). That's because the channel matrix measures the channel from each transmitter to each transceiver. So it measures the way the signal propagates (1) between transmitter 1 and receiver 1, (2) between transmitter 2 and receiver 1, (3) between transmitter 3 and receiver 1, and (4) between transmitter 4 and receiver 1. That is a 1x4 matrix (or vector).