What's the difference between SISO and SIMO in using matched Filters

Suppose we are transmitting a signal $$x$$ in $$OFDM$$ with $$N$$ subcarriers, After performing Parallel/Serial conversion and then N-points FFT, we suppose to have signal $$s = IFFT^Hx$$, Then adding the Cyclic prefix $$P$$ will create the transmitted signal $$M$$ such that: $$M = s + P$$. Before transmitting that signal, let's use Passband with matched filter (Or rrcpulse filter) whose sampling frequency is $$Fs$$ and period $$Ts = 1/Fs$$, and carrier frequency $$Fc$$.

In SISO (Singl input singl output) system, it's clear that we should use matched filters with same parameters of that matched Filter which was used in transmitter side.

My question, suppose that we are using SIMO (Singl input Multi output) system, four copies of signal should be recieved with total length 4-times the transmitted signal. My question, In that case, Should we use same matched Filter parameters for the received signal of SIMO system? How should we deal with received SIMO signal? Or I think the period Ts should equal to $$Ts/4$$ ?? What's paramters should be changed?..

thank you

• You very much do not apply a matched filter to an OFDM signal – that damages the orthogonality unnecessarily. I'm not quite sure what to make of this question – because, again, pulse shaping filters and OFDM do not mix well and are not used together. Can you explain which system does use a matched filter with OFDM, and more importantly, why? I think the answer to your question lies in why you would do that. Without knowing why you do matched filtering here, your question is too broad to answer, imho. – Marcus Müller Oct 9 '18 at 23:00
• hmmm ..let's consider, for example, that rrcpulse filter is used as matched filter in both transmitter and receiver sides. Well, OFDM is used very widely including with double-selective channel and in multi-path environments and so on. basically, OFDM itself might not need rrcpulse filter if we are using it with ideal LTI system. but in systems where we have Doppler spread, multi-path effects, OR frequency or/and time selective effects, rrcpulse filter is usually used to avoid ISI. By the way, OFDM is used in SISO system, so we can't say that it's not used in SIMO system ! – Fatima_Ali Oct 10 '18 at 2:09
• ne more thing, regarding "pulse shaping filters and OFDM do not mix well and are not used together" .. who said that ?! assuming you are using OFDM through passband system, so you will need to used pulse shaping filters in such environments which were mentioned in my above comments.. Although it's not common, but I think, GENERALLY, we should understand exceptions better than rules. – Fatima_Ali Oct 10 '18 at 2:45
• but in systems where we have Doppler spread, multi-path effects, OR frequency or/and time selective effects, rrcpulse filter is usually used to avoid ISI. No, as I said twice now: Not in OFDM system, because RRC makes the problem worse, not better. OFDM is designed to solve exactly the problems you think RRC solves here, and you damage OFDM when you use RRC. So you do not use RRC. – Marcus Müller Oct 10 '18 at 14:31
• It's pretty dramatic how long you've been arguing for RRC over OFDM without bringing a single mathematical argument why that works. Remember, Matched Filtering is optimal for the AWGN channel. You wouldn't use OFDM for the AWGN channel, that'd just be a waste of energy and bandwidth. Especially in highly frequency-selective channels, matched filtering itself doesn't maximize SNR. – Marcus Müller Oct 11 '18 at 11:02

I don't know why we can't use RRC filter with OFDM ?!! Yes, of course, we do can. The only disadvantage for that is the complexity. however the gain will be in spectral efficiency improvement and bandwidth efficiency because of avoiding the needs of guard interval which is used in the regular OFDM. In Engineering, we should always ask, why and why not? why should we use it and why can't we use it?

So, Firstly, it's important to know that ISI in context of OFDM is different about ISI in the other types of modulations. As known, the ISI happens when the symbol, in time domain, has a tail to the time of next symbol, but that's not the same case for OFDM. In term of OFDM, that issue can be solves in two steps, because of the orthogonality, (and remember the use of FFT and iFFT), and second we insert the guard interval like CP which create circular convolution to eliminate the ISI. Be careful, in multi-path channels and large delay spread, that ISI will be exist in OFDM !! so we should present new solutions to deal with. "That exactly what the example reference,you provided above, tries to deal with that issue too".

But the question you will ask now, Why regular OFDM doesn't use RRC filter? In reality, As I mentioned above, Regular OFDM is using Rectangular filter instead of RRC filter for minimal complexity, but the cost of that low complexity is a.) inserting CP which reduce the bandwidth efficiency b.) spectral efficiency reduction by sidelobes.

These two issues in regular OFDM, CP insertion and low spectral efficiency, can be solved by using RRC-OFDM, this RRC-OFDM doesn't use CP and the spectral efficiency is improved very well there. That technique was first presented in 2001, and then patented as US7065150 in 2006.

Coming back to the question, Should we use one matched filter in received SIMO signal or Multi filters. That depends on the simulation you are doing. you can use only one, but be careful how implement it. Or try to filter each copy of signal separately and then collect them back again and continue your work.

thnx

• Thank you for that detailed answer. Exactly, we use RRC OFDM in multi-path environment. I'll try to use your idea of using filter and let you know. thanks again. – Fatima_Ali Oct 12 '18 at 4:12
• Hey, that patent just expired due to motorola failing to pay the fees! – Marcus Müller Oct 30 '18 at 9:30