Category Archives: Technical insights

5G, Beyond 5G, Commentary, Technical insights

Two Roles of Deep Learning in Massive MIMO

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The hype around machine learning, particularly deep learning, has spread over the world. It is not only affecting engineers but also philosophers and government agencies, which try to predict what implications machine learning will have on our society.

When the initial excitement has subsided, I think machine learning will be an important tool that many engineers will find useful, alongside more classical tools such as optimization theory and Fourier analysis. I have spent the last two years thinking about what role deep learning can have in the field of communications. This field is rather different from other areas where deep learning has been successful: We deal with man-made systems that have designed based on rigorous theory to operate close to the fundamental performance limits, for example, the Shannon capacity. Hence, at first sight, there seems to be little room for improvement.

I have nevertheless identified two main applications of supervised deep learning in the physical layer of communication systems: 1) algorithmic approximation and 2) function inversion.

You can read about them in my recent survey paper “Two Applications of Deep Learning in the Physical Layer of Communication Systems” or watch the following video:

In the video, I’m exemplifying the applications through two recent papers where we applied deep learning to improve Massive MIMO systems. Here are links to those papers:

Trinh Van Chien, Emil Björnson, Erik G. Larsson, “Sum Spectral Efficiency Maximization in Massive MIMO Systems: Benefits from Deep Learning,” IEEE International Conference on Communications (ICC), 2019.

Özlem Tugfe Demir, Emil Björnson, “Channel Estimation in Massive MIMO under Hardware Non-Linearities: Bayesian Methods versus Deep Learning,” IEEE Open Journal of the Communications Society, 2020.

Beyond 5G, Commentary, Education, Technical insights

Intelligent Reflecting Surfaces: On Use Cases and Path Loss Model

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Emerging intelligent reflecting surface (IRS) technology, also known under the names “reconfigurable intelligent surface” and “software-controlled metasurface”, is sometimes marketed as an enabling technology for 6G. How do they work, what are their use cases and how much will they improve wireless access performance at large?

The physical principle of an IRS is that the surface is composed of N atoms, each of which acts as an “intelligent” scatterer: a small antenna that receives and re-radiates without amplification, but with a controllable phase-shift. Typically, an atom is implemented as a small patch antenna terminated with an adjustable impedance. Assuming the phase shifts are properly adjusted, the N scattered wavefronts can be made to add up constructively at the receiver. If coupling between the atoms is neglected, the analysis of an IRS essentially entails (i) finding the Green’s function of the source (a sum of spherical waves if close, or a plane wave if far away), (ii) computing the impinging field at each atom, (iii) integrating this field over the surface of each atom to find a current density, (iv) computing the radiated field from each atom using physical-optics approximation, and (v) applying the superposition principle to find the field at the receiver. If the atoms are electrically small, one can approximate the re-radiated field by pretending the atoms are point sources and then the received “signal” is basically a superposition of phase-shifted (as e^{jkr}), amplitude-scaled (as 1/r) source signals.

A point worth re-iterating is that an atom is a scatterer, not a “mirror”. A more subtle point is that the entire IRS as such, consisting of a collection of scatterers, is itself also a scatterer, not a mirror. “Mirrors” exist only in textbooks, when a plane wave is impinging onto an infinitely large conducting plate (none of which exist in practice). Irrespective of how the IRS is constructed, if it is viewed from far enough away, its radiated field will have a beamwidth that is inversely proportional to its size measured in wavelengths.

Two different operating regimes of IRSs can be distinguished:

1. Both transmitter and receiver are in the far-field of the surface. Then the waves seen at the surface can be approximated as planar; the phase differential from the surface center to its edge is less than a few degrees, say. In this case the phase shifts applied to each atom should be linear in the surface coordinate. The foreseen use case would be to improve coverage, or provide an extra path to improve the rank of a point-to-point MIMO channel. Unfortunately in this case the transmitter-IRS-path loss scales very unfavorably, as (N/(r_1r_2))^2 where N is the number of meta-atoms in the surface, and the reason is that again, the IRS itself acts as a (large) scatterer, not a “mirror”. Therefore the IRS has to be quite large before it becomes competitive with a standard single-antenna decode-and-forward relay, a simple, well understood technology that can be implemented using already widely available components, at small power consumption and with a small form factor. (In addition, full-duplex technology is emerging and may eventually be combined with relaying, or even massive MIMO relaying.)

2. At least one of the transmitter and the receiver is in the surface near-field. Here the plane-wave approximation is no longer valid. The IRS can then either be sub-optimally configured to act as a “mirror”, in which case the phase shifts vary linearly as function of the surface coordinate. Alternatively, it can be configured to act as a “lens”, with optimized phase-shifts, which is typically better. As shown for example in this paper, in the near-field case the path loss scales more favorably than in the far-field case. The use cases for the near-field case are less obvious, but one can think of perhaps indoor environments with users close to the walls and every wall covered by an IRS. Another potential use case that I learned about recently is to use the IRS as a MIMO transmitter: a single-antenna transmitter near an IRS can be jointly configured to act as a MIMO beamforming array.

So how useful will IRS technology be in 6G? The question seems open. Indoor coverage in niche scenarios, but isn’t this an already solved problem? Outdoor coverage improvement, but then (cell-free) massive MIMO seems to be a much better option? Building MIMO transmitters from a single-antenna seems exciting, but is it better than using conventional RF? Perhaps it is for the Terahertz bands, where implementation of coherent MIMO may prove truly challenging, that IRS technology will be most beneficial.

A final point is that nothing requires the atoms in an IRS to be located adjacently to one another, or even to form a surface! But they are probably easier to coordinate if they are in more or less the same place.

Beyond 5G, Commentary, Technical insights

Dynamic Cooperation Clusters

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By deploying many distributed antennas instead of a few multi-antenna base stations, a more uniform communication performance can be achieved over a coverage area. The peak rates might go down but there is a much higher chance of getting a decent rate with 95% probability. This is the main motivation behind Cell-free Massive MIMO, which is the new name for Network MIMO with a large number of antennas (many more than the number of users). The key difference from conventional ultra-dense networks is that the distributed antennas are cooperating to transmit phase-coherently in the downlink and process the received uplink signals coherently. One promising way to deploy these systems is by using radio stripes.

The first papers on Cell-free Massive MIMO assumed that all antennas have access to the downlink data of all users and take part in the uplink signal detection of all users. This is both impractical and unnecessary in a large network, where each user is only physically close to a subset of the antennas. Hence, it makes practical sense that only those antennas that can reach the user with a signal power that is non-negligible compared to the thermal noise should transmit to that user and participate in the detection of its uplink data. 

I designed a framework for this 10 years ago, which I called “dynamic cooperation clusters” (DCC) and it can be readily applied to Cell-free Massive MIMO. The main idea was that every user selects which antennas should serve it in a user-centric manner, which means that any antenna subset can be selected. This stands in contrast to the conventional network-centric approach (which dominated the 4G CoMP literature) where only certain predefined disjoint groups of antennas are allowed to cooperate.

Although the DCC framework is a perfect fit for Cell-free Massive MIMO, the performance analysis that we did 10 years ago was admittedly simplified compared to what is possible with the latest methodology. We considered TDD systems that utilize reciprocity but assumed slowly fading channels that can be estimated without error, thereby avoiding pilot contamination and the computation of ergodic rates. To provide a bridge to the past, we wrote the paper “Scalable Cell-Free Massive MIMO Systems” which revisits the DCC framework in the context of Cell-free Massive MIMO, using the latest analytical methods from the Massive MIMO literature. 

Most importantly, the new paper provides an intuitive way to select the user-centric cooperation clusters based on the uplink pilot transmissions. When a user connects to the network, we suggest that the antenna with the best channel condition is given the responsibility to guarantee the user service. The user is assigned to the pilot that is least affected by pilot contamination in that particular region. Moreover, all antennas serve as many users as there are pilots; at most one user per pilot to limit the negative effect of pilot contamination. Under these assumptions, we show that the users get nearly the same rates as if all the antennas serve all users, but with greatly reduced complexity and fronthaul requirements. In conclusion, scalable and well-performing implementations of Cell-free Massive MIMO are possible!

The following video explains the main ideas:

Beyond 5G, Education, Technical insights

Cell-free Massive MIMO and Radio Stripes

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I have recorded a popular science video that explains how a cell-free network architecture can provide major performance improvements over 5G cellular networks, and why radio stripes is a promising way to implement it:

If you want more technical details, I recommend our recent survey paper “Ubiquitous Cell-Free Massive MIMO Communications“. One of the authors, Dr. Hien Quoc Ngo at Queen’s University Belfast, has created a blog about Cell-free Massive MIMO. In particular, it contains a list of papers on the topic and links to the programming code of some of them.

Beyond 5G, Commentary, Technical insights

Centralized Versus Distributed Processing in Cell-Free Massive MIMO

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A figure from my first paper on Network MIMO, which is nowadays called Cell-Free Massive MIMO.

The new Cell-Free Massive MIMO concept has its roots in the classical Network MIMO concept, and has also been given many other names over the years (e.g., coordinated multipoint). When I started my research on the topic in 2009, the standard assumption was that a set of base stations were jointly transmitting to a set of users by sharing both the data signals and their respective channel state information (CSI). In my first journal paper, we showed that one can get away with only sharing the data signals between the base stations because each one only needs local CSI (between itself and the users) to beamform to the users. The price to pay is that the base stations cannot cancel each others’ interference, so each one should preferably have multiple antennas so it can control how much interference it causes. This was my first well-cited paper but, to be honest, I am still not sure how significant results are.

On the one hand, it is very convenient to only utilize local CSI at every base station, because it can be estimated from uplink pilots in a TDD system, which was a key motivation behind our 2010 paper. The time-critical precoding computation can then be initiated immediately after the pilots have been received, instead of waiting for the CSI to be shared between the base stations. This property was later utilized in the first Cell-Free Massive MIMO papers [Ngo, Nayebi] to alleviate the need for sharing CSI.

On the other hand, CSI is usually a small fraction of the signaling between a base station and the rest of the system in Network MIMO. The majority of the signaling consists of the data signals; for example, if a coherence block with 200 channel uses consists of 20 pilot symbols and 180 data symbols, then there is 180/20 = 9 times more data than CSI. Interestingly, our recent paper “Making Cell-Free Massive MIMO Competitive With MMSE Processing and Centralized Implementation” shows that if Cell-Free Massive MIMO is implemented by sending all CSI to an edge-cloud processor that takes care of all the signal processing, both the communication performance and the signaling load can be greatly improved as compared to the fully distributed approach (which was considered in my 2010 paper and then became the standard assumption in the Cell-Free Massive MIMO literature).

The bottom line is that it is hard to make a distributed network implementation competitive compared to a centralized one. Unless we can find a really clever implementation, there is a risk that we lose too much in communication performance and also raise the fronthaul capacity requirements.

5G, Technical insights

Is the Pathloss Larger at mmWave Frequencies?

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The range of mmWave communication signals is often said to be lower than for signals in the conventional sub-6 GHz bands. This is usually also the case but the reason for it might not be the one that you think. I will explain what I mean in this blog post.

If one takes a look at the classical free-space pathloss formula, the received power P_r is

(1)   \begin{equation*}P_r = P_t \left( \frac{\lambda}{4\pi d} \right)^2,\end{equation*}

where the transmit power is denoted by P_t, the wavelength is \lambda, and the propagation distance is d. This formula shows that the received power is proportional to the wavelength and, thus, will be smaller when we increase the carrier frequency; that is, the received power is lower at 60 GHz (\lambda=5 mm) than at 3 GHz (\lambda=10 cm). But there is an important catch: the dependence on \lambda is due to the underlying assumption of having a receive antenna with the effective area

(2)   \begin{equation*}A = \frac{\lambda^2}{4\pi}.\end{equation*}

Hence, if we consider a receive antenna with arbitrary effective area A, we can instead write the received signal in (1) as

(3)   \begin{equation*}P_r = P_t \frac{A}{4\pi d^2},\end{equation*}

which is frequency-independent as long as we keep the antenna area A fixed as we change the carrier frequency. Since the area of a fixed-gain antenna actually is proportional to \lambda^2, as exemplified in (2), in practice we will need to use arrays of multiple antennas in mmWave bands to achieve the same total antenna area A as in lower bands. This is what is normally done in mmWave communications for cellular networks, while a single high-gain antenna with large area can be used for fixed links (e.g., backhaul between base stations or between a satellite and ground station). As explained in Section 7.5 of Massive MIMO Networks, one can actually play with the antenna areas at both the transmitter and receiver to keep the same pathloss in the mmWave bands, while actually reducing the total antenna area!

So why is the signal range shorter in mmWave bands?

The main reasons for the shorter range are:

  • Larger propagation losses in non-line-of-sight scenarios, for example, due to less scattering (fewer propagation paths) and larger penetration losses.
  • The use more bandwidth, which leads to lower SNR.

Edit: The atmospheric, molecular, and rain attenuation losses are larger in some mmWave bands, but it is primarily a concern for macro cells with ranges measured in kilometers (see Figures 2-3 in this paper).

Commentary, Technical insights

How to Normalize a Precoding Matrix?

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The transmitted signal \mathbf{x} from an M-antenna base station can consist of multiple information signals that are transmitted using different precoding (e.g., different spatial directivity). When there are K unit-power data signals s_1,\ldots,s_K intended for K different users, the transmitted signal can be expressed as

(1)   \begin{equation*}\mathbf{x} = \sum_{i=1}^{K} \mathbf{w}_i s_i,\end{equation*}

where \mathbf{w}_1,\ldots,\mathbf{w}_K are the M-dimensional precoding vectors assigned to the different users. The direction of the vector \mathbf{w}_i determines the spatial directivity of the signal s_i, while the squared norm \|\mathbf{w}_i\|^2 determines the associated transmit power. Massive MIMO usually means that M\gg K.

When selecting the precoding vectors, we need to make sure that we are not using too much transmit power. If the maximum power is P and we define the M \times K precoding matrix

(2)   \begin{equation*} \mathbf{W} = [\mathbf{w}_1 \, \, \ldots \,\, \mathbf{w}_K],\end{equation*}

then we need to make sure that the squared Frobenius norm of \mathbf{W} equals the maximum transmit power:

(3)   \begin{equation*} \| \mathbf{W} \|_F^2 = P.\end{equation*}

In the Massive MIMO literature, there are two popular methods to achieve that: matrix normalization and vector normalization. The papers [Ref1], [Ref2] consider both methods, while other papers only consider one of the methods. The main idea is to start from an arbitrarily selected precoding matrix \mathbf{F} = [\mathbf{f}_1 \, \, \ldots \,\, \mathbf{f}_K] and then adapt it to satisfy the power constraint in (3).

Matrix normalization: In this case, we take the matrix \mathbf{F} and scales all the entries with the same number, which is selected to satisfy (3). More precisely, we select

(4)   \begin{equation*}\mathbf{W} = \frac{\sqrt{P}}{\|\mathbf{F} \|_F} \mathbf{F}.\end{equation*}

Vector normalization: In this case, we first normalize each column in \mathbf{F} to have unit norm and then scale them all with \sqrt{P/K} to satisfy (3). More precisely, we select

(5)   \begin{equation*}\mathbf{W} = \sqrt{\frac{P}{K}} \left[ \frac{\mathbf{f}_1}{\| \mathbf{f}_1\|} \, \, \ldots \,\, \frac{\mathbf{f}_K}{\| \mathbf{f}_K\|} \right].\end{equation*}

Which of the two normalizations should be used?

This is a question that I receive now and then, so I wrote this blog post to answer it once and for all. My answer: none of them!

The problem with matrix normalization is that the method that was used to select \mathbf{F} will determine how the transmit power is allocated between the different signals/users. Hence, we are not in control of the power allocation and we cannot fairly compare different precoding schemes. For example, maximum-ratio (MR) allocates more power to users with strong channels than users with weak channels, while zero-forcing (ZF) does the opposite. Hence, if one tries to compare MR and ZF under matrix normalization, the different power allocations will strongly influence the results.

This issue is resolved by vector normalization. However, the problem with vector normalization is that all users are assigned the same amount of power, which is undesirable if some users have strong channels and others have weak channels. One should always make a conscious decision when it comes to power allocation between users.

What we should do instead is to select the precoding matrix as

(6)   \begin{equation*}\mathbf{W} = \left[ \sqrt{p_1} \frac{\mathbf{f}_1}{\| \mathbf{f}_1\|} \, \, \ldots \,\, \sqrt{p_K} \frac{\mathbf{f}_K}{\| \mathbf{f}_K\|} \right],\end{equation*}

where p_1,\ldots,p_K are variables representing the power assigned to each of the users. These should be carefully selected to maximize some performance goals of the network, such as the sum rate, proportional fairness, or max-min fairness. In any case, the power allocation must be selected to satisfy the constraint

(7)   \begin{equation*} \| \mathbf{W} \|_F^2 = \sum_{i=1}^{K} p_i = P.\end{equation*}

There are plenty of optimization algorithms that can be used for this purpose. You can find further details, examples, and references in Section 7.1 of my book Massive MIMO networks.