Lecture 7: Multiuser MIMO With Optimal Linear Detection

[@bobbaberson3654]

I was wondering what is the physical meaning of a_i (@21:46). Can we call it the receiver beam steering vector? The term filter is rather vague to me since we use filters in many places in RF processing chain.

[@WirelessFuture]

There are many different names that are used for this vector in the literature. I think this video uses the filter terminology from the book “Fundamentals of Massive MIMO”, since it is a “spatial filter”, but a better name is probably “receive beamforming vector” or “receive combining vector”. The physical meaning is that we are combining the received signals from multiple antennas in such a way that the signal components are in phase (reinforce each other), while the noise is not and the interference can be partially suppressed.

[@ahmedalmehdhar3417]

Thank you for the nice video and for the interesting series. Can you confirm my point if it is correct, in 31:26 when we square w' we should have many g_i*g_k terms, do we assume it to be zero here? i.e. do we assume that M goes to infinity and channels become perpendicular to each other? Also in the same time stamp, you have a sqrt{ ho\eta}, I believe it should be without the root. Please correct me if I am wrong, or add it in the description for other people to notice.

[@WirelessFuture]

The cross-terms with g_i g_k are zero since they also contain q_i q_k, which has zero mean. You are right that the square root should be removed. It is a typo.

[@iceinmylean3947]

At 30:57, you say that "the randomness is in q_k and w". But shouldn't g_k also be random? After all, we are taking expectations of it right in the following line. Its probably not a problem since it seems as if g and q_k are independent and thus their product also has zero expectation. Is this correct or am I missing something?

[@WirelessFuture]

Yes, g_k is also random. We know the channel estimates, so when we condition on those ones (called Omega), only the estimation errors remain random. I didn’t mention this in the sentence that you refer to since the independence and zero mean properties of the signal and noise are sufficient to conclude that the cross terms vanishes.

[@hjg1010-x3h]

Hello Professor, thank you for always giving great lectures. I have one question about Transmit MMSE beamforming. (RZF). I didn't understand everything, but I referred to the professor's paper Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure. I am considering the alpha value of MMSE beamforming (the weight value in front of the identity matrix of the MMSE filter) in SU-MIMO. When comparing the performance of ZF and MMSE beamforming, as the Number of Transmit antenna increases, the channel capacity of ZF and MMSE matches. Is this result reasonable? (assuming the channel matrix size is 4 x #TRX) In this case, if SU-MIMO (4 layer) is used on massive mimo of 32TRX or 64TRX, is there not much difference in the performance of ZF and MMSE?

[@WirelessFuture]

Thank you for watching! MMSE beamforming is mainly meant for MU-MIMO, where the optimal solution is hard to compute. In SU-MIMO, you can use so-called SVD precoding which is capacity achieving. You are perfectly right that MMSE beamforming converges to ZF beamforming when the SNR is large. When the noise is negligible, the optimal thing is to cancel the interference and that is what ZF does. At low SNR, MMSE instead converges to MRT. The good thing with MMSE beamforming is that it can be used irrespective of what the SNR is, and it will always work well.

[@hjg1010-x3h]

@@WirelessFuture Professor, thank you for your kind response. I have one question. If the alpha value cannot be adjusted dynamically, are there any considerations for setting a single value in the entire SNR range? Simulation shows that as #TRX increases (about ~32 or 64), ZF and MMSE performance are similar in all SNR areas. Is this a reasonable result? If these results are correct, would it be reasonable to use ZF instead of MMSE when considering SU-MIMO in Massive MIMO with a large number of antennas?

[@krabbe3]

Hi Professor, it was a great lecture. Thank you! I'm always struggling with one fact and maybe you could enlighten me: Why do we use H instead of just T in so many equations in the field of mobile communications and signal processing. For example in the pilot uplink. We stack the pilot symbols of each UE into a Pilot matrix. To get the equation for Y at the BS in my understanding it is enough to just use Phi Transpose but we use Hermitian. And there are so many other cases where we use H over T for example output of adaptive filter is also weights Hermitian times input. So the question comes down to: what is the explanation for the use of H instead of T? So why the inner product in complex case needs H instead of T and why are we using the conjugate transpose pilot sequence instead of the transpose pilot sequence? I dont see the reason why we are doing this. Do you have a good explanation for this? Thank you in advance and best regards from Germany!

[@WirelessFuture]

This is a good question! The inner product is defined with a H instead of T, so that the inner product between two vectors become the squares norm. This is the “normal” thing to use when working with complex vectors and matrices. However, the physical reality doesn’t create phase-shifts of this kind so if the channel is h in on direction, it is h^T in the other direction. Many papers are nevertheless using Hermitian transposes in those situations, to make the math look prettier. Similarly, pilot sequences are often defined to contain a H instead of a T, so the math will look nicer. This is ok because we can just take the conjugate of everything and then get the practically valid equation.

[@krabbe3]

@@WirelessFuture Thank you for your answer. So in most cases people use H instead of T to make the equations and math stuff look prettier although this does not reflect the real physical behaviour of the system. Is it right to say that? Best regards!

[@WaelMuhammed]

I want to know, why we didn't consider multiple user interface in the system model?

[@WirelessFuture]

Multiuser MIMO is the multiple access scheme used in 5G, and the basic system model for this is provided in this lecture. What is it more specifically that your are looking for?

[@bobbaberson3654]

Can you please elaborate on how is \gamma_k derived in Slide 6 @11:47?

[@WirelessFuture]

It follows from the MMSE estimator of a Gaussian variable observed in Gaussian noise. The theoretical background is provided in the following video: kzbin.info/www/bejne/o5PRe5WFgbN_bKM You can look at the following slides: github.com/emilbjornson/multiple_antenna_communications/blob/main/Background5.pdf Appendix B.4 in the book Massive MIMO networks (massivemimobook.com) provides a further derivation.

[@kozhenidres314]

thank you prof , here are new bunch of new questions :) i hope you answer it as simple as possible because I'm new to these kinds of things 1. consider we have a beamforming antenna panels of 8x12x2 (192 antenna elements) why we should divide columns into subarrays ? if its because radio ports which is support upto 64 transmit/receive ports then why we can't make radios with 192 ports ? second and last question (last question only on this video don't be so happy :D) for 5G backhaul can we use wireless P2P , which vendor provide better P2P equipments able to support at least 1Gbps upto 10Km LOS ? and can we use same 5g mid band for mobile and FWA ? or if we use mid band for mobile and mmwave for FWA can we deploy them on the same macro sites ? (i mean we know that mid band can serve UE upto 1 mile and mmwave can serve upto 300m but if we use mmwave just for FWA can we serve user upto 1 mile using outdoor LOS antenna ?) thank you

[@WirelessFuture]

Hi, thank you for your questions and interest in these videos! 1. This is a cost, size, and weight issue. You could for sure build a product with 192 ports, but the vendors don’t think that the operators want to pay for this yet. Figure 4 in the following article explains how different subarray size are sufficient for different deployment scenarios: www.ericsson.com/en/reports-and-papers/white-papers/advanced-antenna-systems-for-5g-networks 2. In theory, one can use the same mid band spectrum for both mobile and FWA, but it might be preferable to use mmWave for FWA if LOS paths can be ensured. The larger bandwidth in mmWave band can be very efficient in those scenarios, while it is more problematic to utilize it efficiently in NLOS scenarios and under mobility. One can certainly deploy low-band, mid-band and high-band on the same physical site. Operators like to co-locate base stations to reduce the infrastructure requirements. As you say, one can then assign users to different base stations (located on the same site) depending on their location, so that close-by users are served using the higher bands and far-away users are served using the lower bands. This is the common practice. The drawback with this approach is that the higher bands don’t improve the performance on the cell-edge of the low-band cells. To achieve that, we will have to spread out the base stations instead.

[@Hotrod768]

Part of the MMSE estimate requires knowledge of Beta (the variance of the channel coefficient), but how do we know what this is in real life? If this is the large-scale fading in the channel, do we have to perform some sort of RSS derivation?

[@Hotrod768]

So I see in the next lecture, you perform "channel hardening" to estimate Beta, but this requires multiple (M) receive antennas to get multiple IID instances of the channel. If you only had 1 antenna (M=1), the estimate would not be very good. If you had enough coherence time samples, maybe it would work out for M=1?

[@WirelessFuture]

You are right that beta must be estimated and one can use the sample variance of the fading realization as the estimate. To get a good estimate, one needs to collect 10+ independent observations of the channel. These can be obtained in one coherence block if there are multiple antennas, or across coherence blocks if M=1. It is not enough to have many samples in a single coherence block since the channel realization is constant.

[@Hotrod768]

@@WirelessFuture Thanks for the fast reply!

[@alaaal-habashna4722]

Great lecture, thank you!

[@amahbubul85]

If we consider downlink instead of uplink, then each user needs to estimate the channel as even the receiver does not know the channel exactly. How this estimation is done? BS sends pilot signals? If this is true, then in case of Massive mimo there will be huge signalling overhead, no? Or it is still the BS who estimates the channel and sends it back to the user (considering TDD)?

[@WirelessFuture]

If the base station knows the channel, it can transmit is such a way that the downlink channel becomes predictable. Hence, in theory, it can be acquired at the user device without the need for pilots. In practice, downlink pilots are often used anyway, but only one per user is needed. Here is a blog post that elaborates on this: ma-mimo.ellintech.se/2018/11/02/when-are-downlink-pilots-needed/

[@amahbubul85]

@@WirelessFuture thanks a lot. I will check

[@huuducdo143]

Hello, maybe you have a mistake in the final expression of capacity lower bound (starting from 33.09). On the first term of B_i, the sum should cover also i as well.

[@WirelessFuture]

No, we get k≠i in the first summation because the term with k=i appears in the numerator of the SINR. This term represents the desired signal received over the known part of the channel. The reason that the second summation in B_i doesn't exclude k=i is that the receiver doesn't know the corresponding part of the channel due to channel estimation errors. You can verify the expression by adding up the terms from the previous slides.

[@huuducdo143]

@@WirelessFuture I get it. Thank you 😃