I’m not familiar with SUCR-TA-IPA.

]]>As per my understanding, Y_ j^p (which I will call Y for convenience) is an M_ j by tau_p received matrix. From what I could understand, the rows of this matrix correspond to different antennae in the base station, while the columns correspond to different instants in time. We have tau_p different instances, corresponding to tau_p different pilot symbols. Now, are we assuming here that all multipath components arrive at the same time in the base station? This is what I am lead to believe according to eq. 2.21.

From what I could understand, all UEs are synchronized. Now, they will be spread out in the cell, with different UEs being in different positions in the cell. If they begin transmission at the same time, their signals will be received at different times at the BS. So, the tau_p samples of UE1 will be arriving at a different time as compared to the tau_p samples of UE2 and so on. So even if we assume we have no multipath, I don’t understand how we only have tau_p columns for Y. Wouldn’t the ‘spread’ caused due to different UE positions (relative to the Base station) cause signals to arrive at different times?

Are we assuming that the UE signals arrive at the same time at the Base Station in addition to there being a single path? I am a bit confused as to how the UEs could be synchronized to make their signals arrive at the same time at the base station.

Sorry for the long post. Hope you can clarify! Thank you once again for the informative blog and the book!

]]>See Section 3 in Massive MIMO Networks for details: https://massivemimobook.com

]]>So if we use orthogonal pilot sequences, what methods would we use to remove these pilots? This is what I mean:

We have four users, each having orthogonal pilot sequences, who transmit at the same time to the BS. Now the BS receives a superposition of the four (faded) pilots, plus some amount of noise. What would be the usual process to estimate the four users’s channels? If we attempt to estimate each channel individually, I think we will still have to deal with all the “interference” from the pilots in spite of orthogonality. Do we use some kind of joint estimation technique? Any sources you could point me to would be great!

Thank you for the informative article!

]]>In particular, the paper “Massive MIMO has unlimited capacity” shows that utilization of spatial correlation information is key to solving the pilot contamination problem. This raises the question: How can we acquire such spatial correlation information in real systems with many antennas? Some first attempts to do that have been outline in the recent overview paper “Towards Massive MIMO 2.0: Understanding spatial correlation, interference suppression, and pilot contamination” (https://arxiv.org/abs/1904.03406)

]]>sequences for all users in all cells, Due to the limitation of

the channel coherence interval.

Could you explain why coherence interval has a limitation? ]]>

No. The entire system bandwidth, B0, is used. Effectively multiple consecutive coherence intervals are used simultaneously. But each coherence interval can be treated independently in the analysis. See figures 2.4 and 2.6.

]]>a) The largest throughput gains from Massive MIMO comes from using it for spatial multiplexing. (http://ma-mimo.ellintech.se/2018/03/23/a-basic-way-to-quantify-the-massive-mimo-gain/)

b) The channel hardening property is a consequence of spatial diversity. (http://ma-mimo.ellintech.se/2017/01/25/channel-hardening-makes-fading-channels-behave-as-deterministic/)

]]>I don’t think we need to worry much about the computational complexity, but first find the type of processing that performs the best and then find an efficient implementation of it.

]]>Can pilot contamination be neglected, with orthogonal sequences allocated (feasible since there are only tens of active users)?

Or does it still need to be considered as an inter-user interference? ]]>

1. Inter-cell interference

2. Noise in the channel

Does it also mean there is no way to know which pilot signal arrives first at the BS?

Just thinking about it.

]]>Is it possible for each pilot signal to have a unique signature…..

]]>You can find examples of how to compute the coherence time and coherence bandwidth in Fundamentals of Wireless Communications, which is freely available here: https://web.stanford.edu/~dntse/wireless_book.html

You can also find a detailed explanation in the book “Fundamentals of Massive MIMO” and a short description in the book “Massive MIMO Networks”.

]]>http://www.diva-portal.org/smash/get/diva2:1049059/FULLTEXT02.pdf

Its dimensionality is the product of the coherence time and the coherence bandwidth. You can check out Chapter 2 in “Fundamentals “Fundamentals of Massive MIMO” or “Massive MIMO Networks” for details on how to compute these parameters in different scenarios. I think Fundamentals of Wireless Communications also contain discussions about this.

The covariance matrix of a random channel h is E{(h-E{h})(h-E{h})^H}, where E{} stands for expectation.

]]>The number of antennas does not affect the required number of pilots, if we use TDD and channel reciprocity.

]]>I would only like to inquire what is specific for Massive MIMO systems? Pilot contamination can occur in any cellular system. So, is the only difference the limited number of orthogonal pilot signal due to the massive antenna array?

Thank you ]]>

The potential benefit of having random pilots is that you can “share” the pilot contamination between the users, so that everyone get an equal share on average. However, since cell-edge users are more sensitive to pilot contamination than cell-center users, you might want to coordinate the pilot allocation across cells instead of randomize it. In that sense, random pilots is the baseline scheme that any “smart” scheme should be able to beat.

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