# MIMO system model

We consider a wireless communication system, where there is only Line Of Sight path between the MIMO transmitter and the MIMO receiver. MIMO antennas are used here to increase the directivity of the transmitter and receiver and create a pencil beam (assuming that good alignment can be achieved). The MIMO is used as an array antenna to increase the gain. Is there a simple way of representing the MIMO channel without a matrix form since in our case we don't have diversity and we are not exploiting the multipath components? Or do we have always to represent MIMO channel as a matrix H?

We consider a wireless communication system, where there is only Line Of Sight path between the MIMO transmitter and the MIMO receiver.

Good news: having line of sight is a good situation, often.

Bad news: you don't get any diversity in that case, so your MIMO system, in the best case, is as good as a SISO system with a directive antenna (as you noticed).

Is there a simple way of representing the MIMO channel without a matrix form since in our case we don't have diversity and we are not exploiting the multipath components?

Exactly!

It's just a complex channel coefficient, then. (but that means you consider your N antennas as just one antenna with a fixed combiner – which again is a matrix.

Is there a simple way of representing the MIMO channel without a matrix form since in our case we don't have diversity and we are not exploiting the multipath components? Or do we have always to represent MIMO channel as a matrix H?

Yes and no.

Yes

Each of the T transmit antennas has a path to each receive antenna. So by definition, you have TxR equations. You can represent them individually as TxR equations. Or you can represent them in compact matrix form as [R] = [channel]*[T], where [channel] is a TxR matrix. Your choice. Of course as you have line of sight, the channel matrix will have a rank of around one.

No

If you have 'beamformed' your T transmit antennae properly, then you need only T-1 equations to describe the beam, with another one, bringing you up to T total, for the gain. Similarly with the receive side. Although you can't exploit any spatial capacity gain, your SNR has improved, so you can increase the distance over which you can operate, or the environmental or co-channel noise you can tolerate.