Prof. Erik. G. Larsson gave a 2.5 hour tutorial on the fundamentals of Massive MIMO, which is highly recommended for anyone learning this topic. You can then follow up by reading his book with the same topic.
When you have viewed Erik’s introduction, you can learn more about the state-of-the-art signal processing schemes for Massive MIMO from another talk at the summer school. Dr. Emil Björnson gave a 3 hour tutorial on this topic:
The received signal power is proportional to the number of antennas in Massive MIMO systems. This property is known as the array gain and it can basically be utilized in two different ways.
One option is to let the signal power become times larger than in a single-antenna reference scenario. The increase in SNR will then lead to higher data rates for the users. The gain can be anything from bit/s/Hz to almost negligible, depending on how interference-limited the system is. Another option is to utilize the array gain to reduce the transmit power, to maintain the same SNR as in the reference scenario. The corresponding power saving can be very helpful to improve the energy efficiency of the system.
In the uplink, with single-antenna user terminals, we can choose between these options. However, in the downlink, we might not have a choice. There are strict regulations on the permitted level of out-of-band radiation in practical systems. Since Massive MIMO uses downlink precoding, the transmitted signals from the base station have a stronger directivity than in the single-antenna reference scenario. The signal components that leak into the bands adjacent to the intended frequency band will then also be more directive.
For example, consider a line-of-sight scenario where the precoding creates an angular beam towards the intended user (as illustrated in the figure below). The out-of-band radiation will then get a similar angular directivity and lead to larger interference to systems operating in adjacent bands, if their receivers are close to the user (as the victim in the figure below). To counteract this effect, our only choice might be to reduce the downlink transmit power to keep the worst-case out-of-band radiation constant.
Another alternative is that the regulations are made more flexible with respect to precoded transmissions. The probability that a receiver in an adjacent band is hit by an interfering out-of-band beam, such that the interference becomes times larger than in the reference scenario, reduces with an increasing number of antennas since the beams are narrower. Hence, if one can allow for beamformed out-of-band interference if it occurs with sufficiently low probability, the array gain in Massive MIMO can still be utilized to increase the SNRs. A third option will then be to (partially) reduce the transmit power to also allow for relaxed linearity requirements of the hardware.
I am borrowing the title from a column written by my advisor two decades ago, in the array signal processing gold rush era.
Asymptotic analysis is a popular tool within statistical signal processing (infinite SNR or number of samples), information theory (infinitely long blocks) and more recently, [massive] MIMO wireless communications (infinitely many antennas).
Some caution is strongly advisable with respect to the latter. In fact, there are compelling reasons to avoid asymptotics in the number of antennas altogether:
First, elegant, rigorous and intuitively comprehensible capacity bound formulas are available in closed form.
The proofs of these expressions use basic random matrix theory, but no asymptotics at all.
Second, the notion of “asymptotic limit” or “asymptotic behavior” helps propagate the myth that Massive MIMO somehow relies on asymptotics or “infinite” numbers (or even exorbitantly large numbers) of antennas.
Third, many approximate performance results for Massive MIMO (particularly “deterministic equivalents”) based on asymptotic analysis are complicated, require numerical evaluation, and offer little intuitive insight. (And, the verification of their accuracy is a formidable task.)
Finally, and perhaps most importantly, careless use of asymptotic arguments may yield erroneous conclusions. For example in the effective SINRs in multi-cell Massive MIMO, the coherent interference scales with M (number of antennas) – which yields the commonly held misconception that coherent interference is the main impairment caused by pilot contamination. But in fact, in many relevant circumstances it is not (see case studies here): the main impairment for “reasonable” values of M is the reduction in coherent beamforming gain due to reduced estimation quality, which in turn is independent of M.
In addition, the number of antennas beyond which the far-field assumption is violated is actually smaller than what one might first think (problem 3.14).
IEEE ComSoc provides new online material every month and in August the focus is on Massive MIMO.
First, four carefully selected articles are offered free of charge, see the screenshot below and click here for details.
More precisely, IEEE offers free access to the published versions of these articles, while the accepted versions were already openly available: Paper 1, Paper 2, Paper 3, and Paper 4.
Second, a live webinar entitled “5G Massive MIMO: Achieving Spectrum Efficiency” is organized by IEEE ComSoc on August 24. The speaker is Professor Liesbet Van der Perre from KU Leuven. She was the scientific leader of the MAMMOET project, which is famous for demonstrating that Massive MIMO works in practice. You can expect a unique mix of theoretical concepts and practical implementation insights from this webinar.
Many researchers have analyzed pilot contamination over the six years that have passed since Marzetta uncovered its importance in Massive MIMO systems. We now have a quite good understanding of how to mitigate pilot contamination. There is a plethora of different approaches, whereof many have complementary benefits. If pilot contamination is not mitigated, it will both reduce the array gain and create coherent interference. Some approaches mitigate the pilot interference in the channel estimation phase, while some approaches combat the coherent interference caused by pilot contamination. In this post, I will try to categorize the approaches and point to some key references.
Interference-rejecting precoding and combining
Pilot contamination makes the estimate of a desired channel correlated with the channel from pilot-sharing users in other cells. When these channel estimates are used for receive combining or transmit precoding, coherent interference typically arise. This is particularly the case if maximum ratio processing is used, because it ignores the interference. If multi-cell MMSE processing is used instead, the coherent interference is rejected in the spatial domain. In particular, recent work from Björnson et al. (see also this related paper) have shown that there is no asymptotic rate limit when using this approach, if there is just a tiny amount of spatial correlation in the channels.
Data-aided channel estimation
Another approach is to “decontaminate” the channel estimates from pilot contamination, by using the pilot sequence and the uplink data for joint channel estimation. This have the potential of both improving the estimation quality (leading to a stronger desired signal) and reducing the coherent interference. Ideally, if the data is known, data-aided channel estimation increase the length of the pilot sequences to the length of the uplink transmission block. Since the data is unknown to the receiver, semi-blind estimation techniques are needed to obtain the channel estimates. Ngo et al. and Müller et al. did early works on pilot decontamination for Massive MIMO. Recent work has proved that one can fully decontaminate the estimates, as the length of the uplink block grows large, but it remains to find the most efficient semi-blind decontamination approach for practical block lengths.
Pilot assignment and dimensioning
Which subset of users that share a pilot sequence makes a large difference, since users with large pathloss differences and different spatial channel correlation cause less contamination to each other. Recall that higher estimation quality both increases the gain of the desired signal and reduces the coherent interference. Increasing the number of orthogonal pilot sequences is a straightforward way to decrease the contamination, since each pilot can be assigned to fewer users in the network. The price to pay is a larger pilot overhead, but it seems that a reuse factor of 3 or 4 is often suitable from a sum rate perspective in cellular networks. The joint spatial division and multiplexing (JSDM) provides a basic methodology to take spatial correlation into account in the pilot reuse patterns.
A cellular network with different pilot reuse factors: Reuse 1 (left), Reuse 3 (middle), Reuse 4 (right). The cells with the same color uses the same subset of pilots.
Alternatively, pilot sequences can be superimposed on the data sequences, which gives as many orthogonal pilot sequences as the length of the uplink block and thereby reduces the pilot contamination. This approach also removes the pilot overhead, but it comes at the cost of causing interference between pilot and data transmissions. It is therefore important to assign the right fraction of power to pilots and data. A hybrid pilot solution, where some users have superimposed pilots and some have conventional pilots, may bring the best of both worlds.
If two cells use the same subset of pilots, the exact pilot-user assignment can make a large difference. Cell-center users are generally less sensitive to pilot contamination than cell-edge users, but finding the best assignment is a hard combinatorial problem. There are heuristic algorithms that can be used and also an optimization framework that can be used to evaluate such algorithms.
Multi-cell cooperation
A combination of network MIMO and macro diversity can be utilized to turn the coherent interference into desired signals. This approach is called pilot contamination precoding by Ashikhmin et al. and can be applied in both uplink and downlink. In the uplink, the base stations receive different linear combinations of the user signals. After maximum ratio combining, the coefficients in the linear combinations approach deterministic numbers as the number of antennas grow large. These numbers are only non-zero for the pilot-sharing users. Since the macro diversity naturally creates different linear combinations, the base stations can jointly solve a linear system of equations to obtain the transmitted signals. In the downlink, all signals are sent from all base stations and are precoded in such a way that the coherent interference sent from different base stations cancel out. While this is a beautiful approach for mitigating the coherent interference, it relies heavily on channel hardening, favorable propagation, and i.i.d. Rayleigh fading. It remains to be shown if the approach can provide performance gains under more practical conditions.
I hear this being claimed now and then, and it is – of course – both correct and incorrect, at the same time. For the benefit of our readers I take the opportunity to provide some free consulting on the topic.
The important fact is that ergodic capacity can be lower-bounded by a formula of the form log2(1+SINR), where SINR is an “effective SINR” (that includes, among others, the effects of the terminal’s lack of channel knowledge).
This effective SINR scales proportionally to M (number of antennas), for fixed total radiated power. Compared to a single-antenna system, reciprocity always offers M times better “beamforming gain” regardless of the system’s operating point. (In fact one of the paradoxes of Massive MIMO is that performance always increases with M, despite the fact that there are “more unknowns to estimate”!) And yes, at very low SNR, the effective SINR is proportional to SNR^2 so reciprocity-based beamforming does “break down”, however, it is still M times better than a single-antenna link (with the same total radiated power). One will also, eventually, reach a point where the capacity bound for omnidirectional transmission (e.g. using a space-time code with appropriate dimension reduction in order to host the required downlink pilots) exceeds that of reciprocity-based beamforming, however, importantly, in this regime the bounds may be loose.
These matters, along with numerous case studies involving actual link budget calculations, are of course rigorously explained in our recent textbook.
in Massive MIMO systems. This property is known as the array gain and it can basically be utilized in two different ways.
bit/s/Hz to almost negligible, depending on how interference-limited the system is. Another option is to utilize the array gain to reduce the transmit power, to maintain the same SNR as in the reference scenario. The corresponding power saving can be very helpful to improve the energy efficiency of the system.
