arXiv subjects

Erik G. Larsson

Publications and source records attributed to Erik G. Larsson.

At least 235 records · Page 13Linked to original sources

arXiv2016

How Much Do Downlink Pilots Improve Cell-Free Massive MIMO?

In this paper, we analyze the benefits of including downlink pilots in a cell-free massive MIMO system. We derive an approximate per-user achievable downlink rate for conjugate beamforming processing, which takes into account both uplink and downlink channel estimation errors, and power control. A performance comparison is carried out, in terms of per-user net throughput, considering cell-free massive MIMO operation with and without downlink training, for different network densities. We take also into account the performance improvement provided by max-min fairness power control in the downlink. Numerical results show that, exploiting downlink pilots, the performance can be considerably improved in low density networks over the conventional scheme where the users rely on statistical channel knowledge only. In high density networks, performance improvements are moderate.

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arXiv2016

Multi-Cell Massive MIMO Performance with Double Scattering Channels

This paper investigates the spectral efficiency (SE) of multi-cell Massive Multi-Input Multi-Output (MIMO) using different channel models. Prior works have derived closed-form SE bounds and approximations for Gaussian distributed channels, while we consider the double scattering model-a prime example of a non-Gaussian channel for which it is intractable to obtain closed form SE expressions. The channels are estimated using limited resources, which gives rise to pilot contamination, and the estimates are used for linear detection and to compute the SE numerically. Analytical and numerical examples are used to describe the key behaviors of the double scattering models, which differ from conventional Massive MIMO models. Finally, we provide multi-cell simulation results that compare the double scattering model with uncorrelated Rayleigh fading and explain under what conditions we can expect to achieve similar SEs.

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arXiv2016

Joint Power Allocation and User Association Optimization for Massive MIMO Systems

This paper investigates the joint power allocation and user association problem in multi-cell Massive MIMO (multiple-input multiple-output) downlink (DL) systems. The target is to minimize the total transmit power consumption when each user is served by an optimized subset of the base stations (BSs), using non-coherent joint transmission. We first derive a lower bound on the ergodic spectral efficiency (SE), which is applicable for any channel distribution and precoding scheme. Closed-form expressions are obtained for Rayleigh fading channels with either maximum ratio transmission (MRT) or zero forcing (ZF) precoding. From these bounds, we further formulate the DL power minimization problems with fixed SE constraints for the users. These problems are proved to be solvable as linear programs, giving the optimal power allocation and BS-user association with low complexity. Furthermore, we formulate a max-min fairness problem which maximizes the worst SE among the users, and we show that it can be solved as a quasi-linear program. Simulations manifest that the proposed methods provide good SE for the users using less transmit power than in small-scale systems and the optimal user association can effectively balance the load between BSs when needed. Even though our framework allows the joint transmission from multiple BSs, there is an overwhelming probability that only one BS is associated with each user at the optimal solution.

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arXiv2016

Downlink Power Control for Massive MIMO Cellular Systems with Optimal User Association

This paper aims to minimize the total transmit power consumption for Massive MIMO (multiple-input multiple-output) downlink cellular systems when each user is served by the optimized subset of the base stations (BSs). We derive a lower bound on the ergodic spectral efficiency (SE) for Rayleigh fading channels and maximum ratio transmission (MRT) when the BSs cooperate using non-coherent joint transmission. We solve the joint user association and downlink transmit power minimization problem optimally under fixed SE constraints. Furthermore, we solve a max-min fairness problem with user specific weights that maximizes the worst SE among the users. The optimal BS-user association rule is derived, which is different from maximum signal-to-noise-ratio (max-SNR) association. Simulation results manifest that the proposed methods can provide good SE for the users using less transmit power than in small-scale systems and that the optimal user association can effectively balance the load between BSs when needed.

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arXiv2016

Direct Localization for Massive MIMO

Large-scale MIMO systems are well known for their advantages in communications, but they also have the potential for providing very accurate localization thanks to their high angular resolution. A difficult problem arising indoors and outdoors is localizing users over multipath channels. Localization based on angle of arrival (AOA) generally involves a two-step procedure, where signals are first processed to obtain a user's AOA at different base stations, followed by triangulation to determine the user's position. In the presence of multipath, the performance of these methods is greatly degraded due to the inability to correctly detect and/or estimate the AOA of the line-of-sight (LOS) paths. To counter the limitations of this two-step procedure which is inherently sub-optimal, we propose a direct localization approach in which the position of a user is localized by jointly processing the observations obtained at distributed massive MIMO base stations. Our approach is based on a novel compressed sensing framework that exploits channel properties to distinguish LOS from non-LOS signal paths, and leads to improved performance results compared to previous existing methods.

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arXiv2016

Random Access for Massive MIMO Systems with Intra-Cell Pilot Contamination

Massive MIMO systems, where the base stations are equipped with hundreds of antenna elements, are an attractive way to attain unprecedented spectral efficiency in future wireless networks. In the "classical" massive MIMO setting, the terminals are assumed fully loaded and a main impairment to the performance comes from the inter-cell pilot contamination, i.e., interference from terminals in neighboring cells using the same pilots as in the home cell. However, when the terminals are active intermittently, it is viable to avoid inter-cell contamination by pre-allocation of pilots, while same-cell terminals use random access to select the allocated pilot sequences. This leads to the problem of intra-cell pilot contamination. We propose a framework for random access in massive MIMO networks and derive new uplink sum rate expressions that take intra-cell pilot collisions, intermittent terminal activity, and interference into account. We use these expressions to optimize the terminal activation probability and pilot length.

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arXiv2016

Joint Beamforming and Broadcasting in Massive MIMO

The downlink of a massive MIMO system is considered for the case in which the base station must concurrently serve two categories of terminals: one group to which imperfect instantaneous channel state information (CSI) is available, and one group to which no CSI is available. Motivating applications include broadcasting of public channels and control information in wireless networks. A new technique is developed and analyzed: joint beamforming and broadcasting (JBB), by which the base station beamforms to the group of terminals to which CSI is available, and broadcasts to the other group of terminals, to which no CSI is available. The broadcast information does not interfere with the beamforming as it is placed in the nullspace of the channel matrix collectively seen by the terminals targeted by the beamforming. JBB is compared to orthogonal access (OA), by which the base station partitions the time-frequency resources into two disjunct parts, one for each group of terminals. It is shown that JBB can substantially outperform OA in terms of required total radiated power for given rate targets.

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arXiv2016

Random Access Protocol for Massive MIMO: Strongest-User Collision Resolution (SUCR)

Wireless networks with many antennas at the base stations and multiplexing of many users, known as Massive MIMO systems, are key to handle the rapid growth of data traffic. As the number of users increases, the random access in contemporary networks will be flooded by user collisions. In this paper, we propose a reengineered random access protocol, coined strongest-user collision resolution (SUCR). It exploits the channel hardening feature of Massive MIMO channels to enable each user to detect collisions, determine how strong the contenders' channels are, and only keep transmitting if it has the strongest channel gain. The proposed SUCR protocol can quickly and distributively resolve the vast majority of all pilot collisions.

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arXiv2016

On the Feasibility of Wireless Energy Transfer Using Massive Antenna Arrays

We illustrate potential benefits of using massive antenna arrays for wireless energy transfer (WET). Specifically, we analyze probability of outage in WET over fading channels when a base station (BS) with multiple antennas beamforms energy to a wireless sensor node (WSN). Our analytical results show that by using massive antenna arrays, the range of WET can be increased for a given target outage probability. We prove that by using multiple-antenna arrays at the BS, a lower downlink energy is required to get the same outage performance, resulting into savings of radiated energy. We show that for energy levels used in WET, the outage performance with least-squares or minimum mean-square error channel estimates is same as that obtained based on perfect channel estimates. We observe that a strong line-of-sight component between the BS and WSN lowers outage probability. Furthermore, by deploying more antennas at the BS, a larger energy can be transferred reliably to the WSN at a given target outage performance for the sensor to be able to perform its main tasks. In our numerical examples, the RF power received at the input of the sensor is assumed to be on the order of a mW, such that the rectenna operates at an efficiency in the order of 50 %.

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arXiv2015

Kernel Methods for Accurate UWB-Based Ranging with Reduced Complexity

Accurate and robust positioning in multipath environments can enable many applications, such as search-and-rescue and asset tracking. For this problem, ultra-wideband (UWB) technology can provide the most accurate range estimates, which are required for range-based positioning. However, UWB still faces a problem with non-line-of-sight (NLOS) measurements, in which the range estimates based on time-of-arrival (TOA) will typically be positively biased. There are many techniques that address this problem, mainly based on NLOS identification and NLOS error mitigation algorithms. However, these techniques do not exploit all available information in the UWB channel impulse response. Kernel-based machine learning methods, such as Gaussian Process Regression (GPR), are able to make use of all information, but they may be too complex in their original form. In this paper, we propose novel ranging methods based on kernel principal component analysis (kPCA), in which the selected channel parameters are projected onto a nonlinear orthogonal high-dimensional space, and a subset of these projections is then used as an input for ranging. We evaluate the proposed methods using real UWB measurements obtained in a basement tunnel, and found that one of the proposed methods is able to outperform state-of-the-art, even if little training samples are available.

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arXiv2015

ML Detection in Phase Noise Impaired SIMO Channels with Uplink Training

The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e. the case when the channel is deterministic and known (constant channel) and the case when the channel is stochastic and unknown (fading channel). Further, two different operations with respect to the phase noise sources are considered, namely, the case of identical phase noise sources and the case of independent phase noise sources over the antennas. In all scenarios the optimal detector is derived for a very general parametrization of the phase noise distribution. Further, a high signal-to-noise-ratio (SNR) analysis is performed to show that symbol-error-rate (SER) floors appear in all cases. The SER floor in the case of identical phase noise sources (for both constant and fading channels) is independent of the number of antenna elements. In contrast, the SER floor in the case of independent phase noise sources is reduced when increasing the number of antenna elements (for both constant and fading channels). Finally, the system model is extended to multiple data channel uses and it is shown that the conclusions are valid for these setups, as well.

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arXiv2015

Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?

Massive MIMO is a promising technique to increase the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas, $M$, than scheduled users, $K$, because the users' channels are likely to be near-orthogonal when $M/K > 10$. However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users, $K^\star$, depends on $M$ and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of $K^\star$ in the large-$M$ regime is derived in closed form, while simulations are used to show what happens at finite $M$, in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal $M/K$ is less than 10 in many cases of practical relevance. Interestingly, $K^\star$ depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same $K$.

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arXiv2015

Out-of-Band Radiation Measure for MIMO Arrays with Beamformed Transmission

The spatial characteristics of the out-of-band radiation that a multiuser MIMO system emits in the environment, due to its power amplifiers (modeled by a polynomial model) are nonlinear, is studied by deriving an analytical expression for the continuous-time cross-correlation of the transmit signals. At a random spatial point, the same power is received at any frequency on average with a MIMO base station as with a SISO base station when the two radiate the same amount of power. For a specific channel realization however, the received power depends on the channel. We show that the power received out-of-band only deviates little from the average in a MIMO system with multiple users and that the deviation can be significant with only one user. Using an ergodicity argument, we conclude that out-of-band radiation is less of a problem in massive MIMO, where total radiated power is lower compared to SISO systems and that requirements on spectral regrowth can be relaxed in MIMO systems without causing more total out-of-band radiation.

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arXiv2015

Waveforms for the Massive MIMO Downlink: Amplifier Efficiency, Distortion and Performance

In massive MIMO, most precoders result in downlink signals that suffer from high PAR, independently of modulation order and whether single-carrier or OFDM transmission is used. The high PAR lowers the power efficiency of the base station amplifiers. To increase power efficiency, low-PAR precoders have been proposed. In this article, we compare different transmission schemes for massive MIMO in terms of the power consumed by the amplifiers. It is found that (i) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and (ii) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station.

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arXiv2015

Three Practical Aspects of Massive MIMO: Intermittent User Activity, Pilot Synchronism, and Asymmetric Deployment

This paper considers three aspects of Massive MIMO (multiple-input multiple-output) communication networks that have received little attention in previous works, but are important to understand when designing and implementing this promising wireless technology. First, we analyze how bursty data traffic behaviors affect the system. Using a probabilistic model for intermittent user activity, we show that the spectral efficiency (SE) scales gracefully with reduced user activity. Then, we make an analytic comparison between synchronous and asynchronous pilot signaling, and prove that the choice between these has no impact on the SE. Finally, we provide an analytical and numerical study of the SE achieved with random network deployment.

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arXiv2015

Uplink Pilot and Data Power Control for Single Cell Massive MIMO Systems with MRC

This paper considers the jointly optimal pilot and data power allocation in single cell uplink massive MIMO systems. A closed form solution for the optimal length of the training interval is derived. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per co- herence interval the power control is formulated as optimization problems for two different objective functions: the minimum SE among the users and the sum SE. The optimal power control policy is found for the case of maximizing the minimum SE by converting it to a geometric program (GP). Since maximizing the sum SE is an NP-hard problem, an efficient algorithm is developed for finding KKT (local maximum) points. Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to heuristic power control policies.

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arXiv2015

A Multi-cell MMSE Detector for Massive MIMO Systems and New Large System Analysis

In this paper, a new multi-cell MMSE detector is proposed for massive MIMO systems. Let $K$ and $B$ denote the number of users in each cell and the number of available pilot sequences in the network, respectively, with $B = βK$, where $β\ge 1 $ is called the pilot reuse factor. The novelty of the multi-cell MMSE detector is that it utilizes all $B$ channel directions that can be estimated locally at a base station, so that intra-cell interference, parts of the inter-cell interference and the noise can all be actively suppressed, while conventional detectors only use the $K$ intra-cell channels. Furthermore, in the large-system limit, a deterministic equivalent expression of the uplink SINR for the proposed multi-cell MMSE is derived. The expression is easy to compute and accounts for power control for the pilot and payload, imperfect channel estimation and arbitrary pilot allocation. Numerical results show that significant sum spectral efficiency gains can be obtained by the multi-cell MMSE over the conventional single-cell MMSE and the recent multi-cell ZF, and the gains become more significant as $β$ and/or $K$ increases. Furthermore, the deterministic equivalent is shown to be very accurate even for relatively small system dimensions.

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arXiv2015

A Multi-cell MMSE Precoder for Massive MIMO Systems and New Large System Analysis

In this paper, a new multi-cell MMSE precoder is proposed for massive MIMO systems. We consider a multi-cell network where each cell has $K$ users and $B$ orthogonal pilot sequences are available, with $B = βK$ and $β\ge 1$ being the pilot reuse factor over the network. In comparison with conventional single-cell precoding which only uses the $K$ intra-cell channel estimates, the proposed multi-cell MMSE precoder utilizes all $B$ channel directions that can be estimated locally at a base station, so that the transmission is designed spatially to suppress both parts of the inter-cell and intra-cell interference. To evaluate the performance, a large-scale approximation of the downlink SINR for the proposed multi-cell MMSE precoder is derived and the approximation is tight in the large-system limit. Power control for the pilot and payload, imperfect channel estimation and arbitrary pilot allocation are accounted for in our precoder. Numerical results show that the proposed multi-cell MMSE precoder achieves a significant sum spectral efficiency gain over the classical single-cell MMSE precoder and the gain increases as $K$ or $β$ grows. Compared with the recent M-ZF precoder, whose performance degrades drastically for a large $K$, our M-MMSE can always guarantee a high and stable performance. Moreover, the large-scale approximation is easy to compute and shown to be accurate even for small system dimensions.

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