# MIMO multipath delay [duplicate]

How is multi-path delay dealt with in MIMO systems? Most of the theory I have read on MIMO doesn't address multipath delay and assumes the multipath interference is limited to secondary antenna transmitting or receiving(so the MIMO channel is a matrix).

Is multipath delay equalization addressed after the multipath matrix model has been inverted? How does it work?

• In practical implementations, you first try your very best to convert your channel to be flat, so that you don't have to care about multipath, THEN apply MIMO processing. I.e., OFDM first to convert your wideband channel to many smaller channels that don't "see" the multiple paths, then OFDM. I tried to explain that in this answer: – Marcus Müller Feb 22 '20 at 9:19
• (by the way, I'd love to see more mathematical foundation and applications for actual multipath MIMO for wireless comms, i.e. where you don't first divide the channel using CP-OFDM or filterbank multicarrier systems, but really, I'm not aware of a single MIMO system that doesn't assume single-path channels and goes through lengths to ensure them. The optimization problem of dividing a multipath-MIMO channel into orthogonal subchannels just seems to be too computationally complex for practical applications.) – Marcus Müller Feb 22 '20 at 10:31
• (and to answer your last question: it simply doesn't work. You can't represent a multipath MIMO channel as $N_{TX}\times N_{RX}$ matrix; you'd need something higher-dimensional than a matrix. and then most of the decomposition math we use falls flat or becomes very hard.) – Marcus Müller Feb 22 '20 at 12:24
• Thanks, that makes sense. So if you have a MIMO OFDM system how does it work? How does the process of estimating the channel matrix happen? I have seen deviation of ofdm synchronization but it always assumed SISO. – FourierFlux Feb 22 '20 at 16:05
• yes, exactly that. – Marcus Müller Feb 22 '20 at 22:47