Jakob Hoydis

Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?

We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.

Green Small-Cell Networks

The exponentially increasing demand for wireless data services requires a massive network densification that is neither economically nor ecologically viable with the current cellular system architectures. A promising solution to this problem is the concept of small-cell networks (SCNs), which is founded by the idea of a very dense deployment of self-organizing, low-cost, low-power, base stations (BSs). Although SCNs have the potential to significantly increase the capacity of cellular networks while reducing their energy consumption, they pose many new challenges to the optimal system design. We show in this article how a large system analysis based on random matrix theory (RMT) can provide tight and tractable approximations of key performance measures of SCNs.

Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits

The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?

Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

Massive MIMO: How many antennas do we need?

We consider a multicell MIMO uplink channel where each base station (BS) is equipped with a large number of antennas N. The BSs are assumed to estimate their channels based on pilot sequences sent by the user terminals (UTs). Recent work has shown that, as N → ∞, (i) the simplest form of user detection, i.e., the matched filter (MF), becomes optimal, (ii) the transmit power per UT can be made arbitrarily small, (iii) the system performance is limited by pilot contamination. The aim of this paper is to assess to which extent the above conclusions hold true for large, but finite N. In particular, we derive how many antennas per UT are needed to achieve η % of the ultimate performance. We then study how much can be gained through more sophisticated minimum-mean-square-error (MMSE) detection and how many more antennas are needed with the MF to achieve the same performance. Our analysis relies on novel results from random matrix theory which allow us to derive tight approximations of achievable rates with a class of linear receivers.

Channel measurements for large antenna arrays

Equipping base stations (BSs) with very large antenna arrays is a promising way to increase the spectral and energy efficiency of mobile communication systems without the need for new cell sites. However, the prominently theoretical works on this topic are based on several crucial assumptions about the wireless channel which have not been sufficiently validated by measurements. In this paper, we report on an outdoor measurement campaign with a scalable virtual antenna array consisting of up to 112 elements. The large amount of acquired data allows us to study several important aspects of large-scale MIMO systems. For example, we partially confirm the theoretical results based on uncorrelated channels which predict that the channels at different positions become more and more orthogonal as the number of antennas grows. However, for the measured channels, the marginal gain of an additional antenna quickly diminishes. Nevertheless, our results indicate that most of the theoretical benefits of large-scale MIMO could be realized also over the measured channels.

Making smart use of excess antennas: Massive MIMO, small cells, and TDD

In this paper, we present a vision beyond the conventional Long Term Evolution Fourth Generation (LTE-4G) evolution path and suggest that time division duplexing (TDD) could be a key enabler for a new heterogeneous network architecture with the potential to provide ubiquitous coverage and unprecedented spectral area efficiencies. This architecture is based on a cochannel deployment of macro base stations (BSs) with very large antenna arrays and a secondary tier of small cells (SCs) with a few antennas each. Both tiers employ a TDD protocol in a synchronized fashion. The resulting channel reciprocity enables not only the estimation of large-dimensional channels at the BSs, but also an implicit coordination between both tiers without the need to exchange user data or channel state information (CSI) over the backhaul. In particular, during the uplink (UL), the BSs and SCs can locally estimate the dominant interference sub-space. This knowledge can be leveraged for downlink (DL) precoding to reduce intra- and inter-tier interference. In other words, the BSs and SCs “sacrifice” some of their degrees of freedom for interference rejection. Our simulation results demonstrate that the proposed architecture and precoding scheme can achieve a very attractive rate region compared to several baseline scenarios. For example, with 100 antennas at each BS and four antennas at each SC, we observe an aggregate area throughput of 7.63 Gb/s/km2 (DL) and 8.93 Gb/s/km2 (UL) on a 20 MHz band shared by about 100 mobile devices.

Massive MIMO and small cells: How to densify heterogeneous networks

We propose a time division duplex (TDD) based network architecture where a macrocell tier with a “massive” multiple-input multiple-output (MIMO) base station (BS) is overlaid with a dense tier of small cells (SCs). In this context, the TDD protocol and the resulting channel reciprocity have two compelling advantages. First, a large number of BS antennas can be deployed without incurring a prohibitive overhead for channel training. Second, the BS can estimate the interference covariance matrix from the SC tier which can be leveraged for downlink precoding. In particular, the BS designs its precoding vectors to transmit independent data streams to its users while being orthogonal to the subspace spanned by the strongest interference directions; thereby minimizing the sum interference imposed on the SCs. In other words, the BS “sacrifices” some of its antennas for interference cancellation while the TDD protocol allows for an implicit coordination across both tiers. Simulation results suggest that, given a sufficiently large number of BS antennas, the proposed scheme can significantly improve the sum-rate of the SC tier at the price of a small macro performance loss.

An Introduction to Deep Learning for the Physical Layer

We present and discuss several novel applications of deep learning for the physical layer. By interpreting a communications system as an autoencoder, we develop a fundamental new way to think about communications system design as an end-to-end reconstruction task that seeks to jointly optimize transmitter and receiver components in a single process. We show how this idea can be extended to networks of multiple transmitters and receivers and present the concept of radio transformer networks as a means to incorporate expert domain knowledge in the machine learning model. Lastly, we demonstrate the application of convolutional neural networks on raw IQ samples for modulation classification which achieves competitive accuracy with respect to traditional schemes relying on expert features. This paper is concluded with a discussion of open challenges and areas for future investigation.

Asymptotic analysis of distributed multi-cell beamforming

We consider the problem of multi-cell downlink beamforming with N cells and K terminals per cell. Cooperation among base stations (BSs) has been found to increase the system throughput in a multi-cell set up by mitigating inter-cell interference. Most of the previous works assume that the BSs can exchange the instantaneous channel state information (CSI) of all their user terminals (UTs) via high speed backhaul links. However, this approach quickly becomes impractical as N and K grow large. In this work, we formulate a distributed beamforming algorithm in a multi-cell scenario under the assumption that the system dimensions are large. The design objective is the minimize the total transmit power across all BSs subject to satisfying the user SINR constraints while implementing the beamformers in a distributed manner. In our algorithm, the BSs would only need to exchange the channel statistics rather than the instantaneous CSI. We make use of tools from random matrix theory to formulate the distributed algorithm. The simulation results illustrate that our algorithm closely satisfies the target SINR constraints when the number of UTs per cell grows large, while implementing the beamforming vectors in a distributed manner.