Lets say we have 4x4 MIMO system. With 4 single antenna transmitters are transmitter over same time and frequency resources, the receiver has to be equipped with atleast 4 antennas or more. If we have 4 antennas at the receiver, is our MMSE or ZF able to remove the inter user interference? Or we will still have some residual interference even at high SNR regime.
Thanks
With perfect CSI, ZF cancels out all interference. But it is pretty hard to obtain sufficiently good CSI in practice. This is why researchers on MU-MIMO are now looking at systems with more BS antennas than user terminals. In that case, the residual interference that you cannot suppress due to imperfect CSI will not hurt so much.
This is the main principle and idea behind the massive MIMO concept.
A final note: ZF is very nice for mathematical analysis, but should never be used. MMSE processing is always better (or equal) to ZF and will have roughly the same computational complexity.
Hi,
As you mention, this looks like SIMO. If you use cooperative then it could be 4x4 MU-MIMO. Interference can be removed as noise is white Gaussian (uncorrelated). Contact me if you require detail derivation.
Hi,
I think ZFBF and MMSE are sub-optimal solutions for cancelling inter-user interference and the optimal solution is based on dirty paper coding (DPC) but it is not practical in implementation.
@selim ... DPC is good for downlink interference cancellation. However, for uplink the interference cancellation is rather straightforward. My question is typical for uplink scenarios where number of users with single antenna are transmitting using same time-frequency resource. What i have noticed so far in my simulations, MMSE and ZF are unable to mitigate completely the interference in case of full rank MIMO (4x4) i.e. 4 users with single antenna and 4 receive antenna at BS. I observed error floor at high SNR region. Any comments on this.
Hi,
It should be possible to remove interference even with ZF, and when the noise power approaches zero the error probability should do the same.
Did you consider some non-ideality, like imperfect channel estimation, frequency misalignment, or something else?
Thank you Giulio,
Since i am focusing on receiver performance, i am assuming ideal scenario where we have perfect channel estimation. The thing is, in case of 2x4 MU-MIMO case, we have performance without error floor. For 4x4 MU-MIMO, the error decays slowly and stays at 1e-5. I have seen references in which authors are claiming the MMSE can not remove interference completely. May be this is true in 4x4 MIMO case.
if we consider the limiting casefor N0=0 (absence of noise), we get
a) MMSE = ZF
b) r = Hs
Hence, you can get the desired signal by multiplying the received one by the inverse of the channel (ZF equalizer). Maybe some error in the code?
Hi Giulio,
Thanks. I have double checked my code (Simulink Flowgraph) but not being able to find any error. May be the channel estimation block in which i am employing interpolation as pilots symbols of one user should not be mixed with pilot symbols of other user. What do you think about this pilot orthogonality?
Hi Talha,
Well, I'm sure that pilots must be orthogonal for a correct estimate. This merely means that pilots have to be placed in different positions.
Unfortunately, I don't use Simulink, so I have not awareness of the functioning, but I think that if channel estimation is somehow "active", some kind of error in the CSI may be unavoidable.
Hi Talha Faizur Rahman ,
ZF is capable of significantly cancelling the interference, but causing improvement of noise power. Meanwhile, MMSE takes into account jointly of interference and noise power. It means that MMSE cannot completely cancel the interference, but suppress the enhancement of noise power.
If you can promise the accuracy of channel estimation, you could choose non-linear ZF-SIC or MMSE-SIC detectors. they not only significantly mitigate the inter-user interference but also suppress the enhancement of noise power, so as to obtain the better performance.
With perfect CSI, ZF cancels out all interference. But it is pretty hard to obtain sufficiently good CSI in practice. This is why researchers on MU-MIMO are now looking at systems with more BS antennas than user terminals. In that case, the residual interference that you cannot suppress due to imperfect CSI will not hurt so much.
This is the main principle and idea behind the massive MIMO concept.
A final note: ZF is very nice for mathematical analysis, but should never be used. MMSE processing is always better (or equal) to ZF and will have roughly the same computational complexity.
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