Category Archives: 5G

Channel Sparsity in Massive MIMO

Channel estimation is critical in Massive MIMO. One can use the basic least-squares (LS) channel estimator to learn the multi-antenna channel from pilot signals, but if one has prior information about the channel’s properties, that can be used to improve the estimation quality. For example, if one knows the average channel gain, the linear minimum mean-squared error (LMMSE) estimator can be used, as in most of the literature on Massive MIMO.

There are many attempts to exploit further channel properties, in particularly channel sparsity is commonly assumed in the academic literature. I have recently received several questions about this topic, so I will take the opportunity to give a detailed answer. In particular, this blog post discusses temporal and spatial sparsity.

Temporal sparsity

This means that the channel’s impulse response contains one or several pulses with zeros in between. These pulses could represent different paths, in a multipath environment, which are characterized by non-overlapping time delays. This does not happen in a rich scattering environment with many diffuse scatterers having overlapping delays, but it could happen in mmWave bands where there are only a few reflected paths.

If one knows that the channel has temporal sparsity, one can utilize such knowledge in the estimator to determine when the pulses arrive and what properties (e.g., phase and amplitude) each one has. However, several hardware-related conditions need to be satisfied. Firstly, the sampling rate must be sufficiently high so that the pulses can be temporally resolved without being smeared together by aliasing. Secondly, the receiver filter has an impulse response that spreads signals out over time, and this must not remove the sparsity.

Spatial sparsity

This means that the multipath channel between the transmitter and receiver only involves paths in a limited subset of all angular directions. If these directions are known a priori, it can be utilized in the channel estimation to only estimate the properties (e.g., phase and amplitude) in those directions. One way to determine the existence of spatial sparsity is by computing a spatial correlation matrix of the channel and analyze its eigenvalues. Each eigenvalue represents the average squared amplitude in one set of angular directions, thus spatial sparsity would lead to some of the eigenvalues being zero.

Just as for temporal sparsity, it is not necessary that spatial sparsity can be utilized even if it physically exists. The antenna array must be sufficiently large (in terms of aperture and number of antennas) to differentiate between directions with signals and directions without signals. If the angular distance between the channel paths is smaller than the beamwidth of the array, it will smear out the paths over many angles. The following example shows that Massive MIMO is not a guarantee for utilizing spatial sparsity.

The figure below considers a 64-antenna scenario where the received signal contains only three paths, having azimuth angles -20°, +30° and +40° and a common elevation angle of 0°. If the 64 antennas are vertically stacked (denoted 1 x 64), the signal gain seems to be the same from all azimuth directions, so the sparsity cannot be observed at all. If the 64 antennas are horizontally stacked (denoted 64 x 1), the signal gain has distinct peaks at the angles of the three paths, but there are also ripples that could have hidden other paths. A more common 64-antenna configuration is a 8 x 8 planar array, for which only two peaks are visible. The paths 30° and 40° are lumped together due to the limited resolution of the array.

Figure: The received signal gain that is observed from different azimuth angles, using different array geometries. The true signal only contains three paths, which are coming from the azimuth angles -20°, +30° and +40°.

In addition to have a sufficiently high spatial resolution, a phase-calibrated array might be needed to make use of sparsity, since random phase differences between the antennas could destroy the structure.

Do we need sparsity?

There is no doubt that temporal and spatial sparsity exist, but not every channel will have it. Moreover, the transceiver hardware will destroy the sparsity unless a series of conditions are satisfied. That is why one should not build a wireless technology that requires channel sparsity because then it might not function properly for many of the users. Sparsity is rather something to utilize to improve the channel estimation in certain special cases.

TDD-reciprocity based Massive MIMO, as proposed by Marzetta and further considered in my book Massive MIMO networks, does not require channel sparsity. However, sparsity can be utilized as an add-on when available. In contrast, there are many FDD-based frameworks that require channel sparsity to function properly.

Reproduce the results: The code that was used to produce the plot can be downloaded from my GitHub.

Massive MIMO Enables Fixed Wireless Access

The largest performance gains from Massive MIMO are achieved when the technology is used for spatial multiplexing of many users. These gains can only be harnessed when there actually are many users that ask for data services simultaneously. I sometimes hear the following negative comments about Massive MIMO:

  1. The data traffic is so bursty that there seldom are more than one or two users that ask for data simultaneously.
  2. When there are multiple users, the uplink SNR is often too poor to get the high quality channel state information that is needed to truly benefit from spatial multiplexing.

These points might indeed be true in current cellular networks, but I believe the situation will change in the future. In particular, the new fixed wireless access services require that the network can simultaneously deliver high-rate services to many customers. The business case for these service rely strongly on Massive MIMO and spatial multiplexing, so that one base station site can guarantee a certain data rate to as many customers as possible (just as fiber and cable connections can). The fixed installation of the customer equipment means that channel state information is much easier to acquire (due to better channel conditions, higher transmit power, and absence of mobility). The following video from Ericsson touches upon some of these aspects:

Scalable Cell-Free Massive MIMO

Cell-free massive MIMO is likely one of the technologies that will form the backbone of any xG with x>5. What distinguishes cell-free massive MIMO from distributed MIMO, network MIMO or cooperative multi-point (CoMP)? The short answer is that cell-free massive MIMO works, it can deliver uniformly good service throughout the coverage area, and it requires no prior knowledge of short-term CSI (just like regular cellular massive MIMO). A longer answer is here. The price to pay for this superiority, no shock, is the lack of scalability: for canonical cell-free massive MIMO there is a practical limit on how large the system can be, and this scalability concerns both the power control, the signal processing, and the organization of the backhaul.

At ICC this year we presented this approach towards scalable cell-free massive MIMO. A key insight is that power control is extremely vital for performance, and a scalable cell-free massive MIMO solution requires a scalable power control policy. No surprise, some performance must be sacrificed relative to canonical cell-free massive MIMO. Coincidentally, another paper in the same session (WC-26) also devised a power control policy with similar qualities!

Take-away point? There are only three things that matter for the design of cell-free massive MIMO signal processing algorithms and power control policies: scalability, scalability and scalability…

A case against Massive MIMO?

I had an interesting conversation with a respected colleague who expressed some significant reservations against massive MIMO. Let’s dissect the arguments. 


The first argument against massive MIMO was that most traffic is indoors, and that deployment of large arrays indoors is impractical and that outdoor-to-indoor coverage through massive MIMO is undesirable (or technically infeasible). I think the obvious counterargument here is that before anything else, the main selling argument for massive MIMO is not indoor service provision but outdoor macrocell coverage: the ability of TDD/reciprocity based beamforming to handle high mobility, and efficiently suppress interference thus provide cell-edge coverage. (The notion of a “cell-edge” user should be broadly interpreted: anyone having poor nominal signal-to-interference-and-noise ratio, before the MIMO processing kicks in.) But nothing prevents massive MIMO from being installed indoors, if capacity requirements are so high that conventional small cell or WiFi technology cannot handle the load. Antennas could be integrated into walls, ceilings, window panes, furniture or even pieces of art. For construction of new buildings, prefabricated building blocks are often used and antennas could be integrated into these already at their production. Nothing prevents the integration of thousands of antennas into natural objects in a large room.

Outdoor-to-indoor coverage doesn’t work? Importantly, current systems provide outdoor-to-indoor coverage already, and there is no reason Massive MIMO would not do the same (to the contrary, adding base station antennas is always beneficial for performance!). But yet the ideal deployment scenario of massive MIMO is probably not outdoor-to-indoor so this seems like a valid point, partly. The arguments against the outdoor-to-indoor are that modern energy-saving windows have a coating that takes out 20 dB, at least, of the link budget. In addition, small angular spreads when all signals have to pass through windows (maybe except for in wooden buildings) may reduce the rank of the channel so much that not much multiplexing to indoor users is possible. This is mostly speculation and not sure whether experiments are available to confirm, or refute it.

Let’s move on to the second argument. Here the theme is that as systems use larger and larger bandwidths, but can’t increase radiated power, the maximum transmission distance shrinks (because the SNR is inversely proportional to the bandwidth). Hence, the cells have to get smaller and smaller, and eventually, there will be so few users per cell that the aggressive spatial multiplexing on which massive MIMO relies becomes useless – as there is only a single user to multiplex. This argument may be partly valid at least given the traffic situation in current networks. But we do not know what future requirements will be. New applications may change the demand for traffic entirely: augmented or virtual reality, large-scale communication with drones and robots, or other use cases that we cannot even envision today.

It is also not too obvious that with massive MIMO, the larger bandwidths are really required. Spatial multiplexing to 20 terminals improves the bandwidth efficiency 20 times compared to conventional technology. So instead of 20 times more bandwidth, one may use 20 times more antennas. Significant multiplexing gains are not only proven theoretically but have been demonstrated in commercial field trials. It is argued sometimes that traffic is bursty so that these multiplexing gains cannot materialize in practice, but this is partly a misconception and partly a consequence of defect higher-layer designs (most importantly TCP/IP) and vested interests in these flawed designs. For example, for the services that constitute most of the raw bits, especially video streaming, there is no good reason to use TCP/IP at all. Hopefully, once the enormous potential of massive MIMO physical layer technology becomes more widely known and understood, the market forces will push a re-design of higher-layer and application protocols so that they can maximally benefit from the massive MIMO physical layer.  Does this entail a complete re-design of the Internet? No, probably not, but buffers have to be installed and parts of the link layer should be revamped to maximally use the “wires in the air”, ideally suited for aggressive multiplexing of circuit-switched data, that massive MIMO offers.

When Will Hybrid Beamforming Disappear?

There has been a lot of fuss about hybrid analog-digital beamforming in the development of 5G. Strangely, it is not because of this technology’s merits but rather due to general disbelief in the telecom industry’s ability to build fully digital transceivers in frequency bands above 6 GHz. I find this rather odd; we are living in a society that becomes increasingly digitalized, with everything changing from being analog to digital. Why would the wireless technology suddenly move in the opposite direction?

When Marzetta published his seminal Massive MIMO paper in 2010, the idea of having an array with a hundred or more fully digital antennas was considered science fiction, or at least prohibitively costly and power consuming. Today, we know that Massive MIMO is actually a pre-5G technology, with 64-antenna systems already deployed in LTE systems operating below 6 GHz. These antenna panels are very commercially competitive; 95% of the base stations that Huawei are currently selling have at least 32 antennas. The fast technological development demonstrates that the initial skepticism against Massive MIMO was based on misconceptions rather than fundamental facts.

In the same way, there is nothing fundamental that prevents the development of fully digital transceivers in mmWave bands, but it is only a matter of time before such transceivers are developed and will dominate the market. With digital beamforming, we can get rid of the complicated beam-searching and beam-tracking algorithms that have been developed over the past five years and achieve a simpler and more reliable system operation, particularly, using TDD operation and reciprocity-based beamforming.

Figure 1: Photo of the experimental equipment with 24 digital transceivers that was used by NEC. It uses 300 MHz of bandwidth in the 28 GHz band.

I didn’t jump onto the hybrid beamforming research train since it already had many passengers and I thought that this research topic would become irrelevant after 5-10 years. But I was wrong – it now seems that the digital solutions will be released much earlier than I thought. At the 2018 European Microwave Conference, NEC Cooperation presented an experimental verification of an active antenna system (AAS) for the 28 GHz band with 24 fully digital transceiver chains. The design is modular and consists of 24 horizontally stacked antennas, which means that the same design could be used for even larger arrays.

Tomoya Kaneko, Chief Advanced Technologist for RF Technologies Development at NEC, told me that they target to release a fully digital AAS in just a few years. So maybe hybrid analog-digital beamforming will be replaced by digital beamforming already in the beginning of the 5G mmWave deployments?

Figure 2: Illustration of what is found inside the AAS box in Figure 1. There are 12 horizontal cards, with two antennas and transceivers each. The dimensions are 308 mm x 199 mm.

That said, I think that the hybrid beamforming algorithms will have new roles to play in the future. The first generations of new communication systems might reach faster to the market by using a hybrid analog-digital architecture, which require hybrid beamforming, than waiting for the fully digital implementation to be finalized. This could, for example, be the case for holographic beamforming or MIMO systems operating in the sub-THz bands. There will also remain to exist non-mobile point-to-point communication systems with line-of-sight channels (e.g., satellite communications) where analog solutions are quite enough to achieve all the necessary performance gains that MIMO can provide.

The Role of Massive MIMO in 5G Deployments

The support for mmWave spectrum is a key feature of 5G, but mmWave communication is also known to be inherently unreliable due to the blockage and penetration losses, as can be demonstrated in this simple way:

This is why the sub-6 GHz bands will continue to be the backbone of the future 5G networks, just as in previous cellular generations, while mmWave bands will define the best-case performance. A clear example of this is the 5G deployment strategy of the US operator Sprint, which I heard about in a keynote by John Saw, CTO at Sprint, at the Brooklyn 5G Summit. (Here is a video of the keynote.)

Sprint will use spectrum in the 600 MHz band to achieve wide-spread 5G coverage. This low frequency will enable spatial multiplexing of many users if Massive MIMO is used, but the data rates per user will be rather limited since only a few tens of MHz of bandwidth is available. Nevertheless, this band will define the guaranteed service level of the 5G network.

In addition, Sprint has 120 MHz of TDD spectrum in the 2.5 GHz band and are deploying 64-antenna Massive MIMO base stations in many major cities; there will be more than 1000 sites in 2019. These can both be used to simultaneously do spatial multiplexing of many users and to improve the per-user data rates thanks to the beamforming gains. John Saw pointed out that the word “massive” in Massive MIMO sounds scary, but the actual arrays are neat and compact in the 2.5 GHz band. He also explained that this frequency band supports high mobility, which is very challenging at mmWave frequencies. The mobility support is demonstrated in the following video:

The initial tests of Sprint’s Massive MIMO systems pretty much confirm the theoretical predictions. In Plano, Texas, a 3.4x gain in downlink sum rates and 8.9x gain in uplink sum rates were observed when comparing 64-antenna and 8-antenna panels. These gains come from a combination of spatial multiplexing and beamforming; this is particularly evident in the uplink where the rates increased faster than the number of antennas. Recent measurements at the Reston Town Center, Virginia, showed similar gains: between 4x and 20x improvements at different locations (see the image below).

Tom Marzetta, the originator of Massive MIMO, attended the keynote and gave me the following comment: “It is gratifying to hear the CTO of Sprint confirm, through actual commercial deployments, what the advocates of Massive MIMO have said for so long.”

Screenshot from the presentation at the Brooklyn 5G Summit, showing measured data rates before and after Massive MIMO was turned on.

Interestingly, Sprint noticed that their customers immediately used more data when Massive MIMO was turned on, and there were more simultaneous users in the network. This demonstrates the fact that whenever you create a more capable cellular network, the users will be encouraged to use more data and new use cases will gradually appear. This is why we need to continue looking for ways to improve the spectral efficiency beyond 5G and Massive MIMO.