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• 1.
Princeton University, NJ 08544 USA.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Princeton University, NJ 08544 USA.
Wireless Information and Power Transfer in Multiway Massive MIMO Relay Networks2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 6, p. 3837-3855Article in journal (Refereed)

Simultaneous wireless information and power transfer techniques for multiway massive multiple-input multiple-output (MIMO) relay networks are investigated. By using two practically viable relay receiver designs, namely 1) the power splitting receiver and 2) the time switching receiver, asymptotic signal-to-interference-plus-noise ratio (SINR) expressions are derived for an unlimited number of antennas at the relay. These asymptotic SINRs are then used to derive asymptotic symmetric sum rate expressions in closed form. Notably, these asymptotic SINRs and sum rates become independent of radio frequency-to-direct current (RF-to-DC) conversion efficiency in the limit of infinitely many relay antennas. Moreover, tight average sum rate approximations are derived in closed form for finitely many relay antennas. The fundamental tradeoff between the harvested energy and the sum rate is quantified for both relay receiver structures. Notably, the detrimental impact of imperfect channel state information (CSI) on the MIMO detector/precoder is investigated, and thereby, the performance degradation caused by pilot contamination, which is the residual interference due to nonorthogonal pilot sequence usage in adjacent/cochannel systems, is quantified. The presence of cochannel interference (CCI) can be exploited to be beneficial for energy harvesting at the relay, and consequently, the asymptotic harvested energy is an increasing function of the number of cochannel interferers. Notably, in the genie-aided perfect CSI case, the detrimental impact of CCI for signal decoding can be cancelled completely whenever the number of relay antennas grows without bound. Nevertheless, the pilot contamination severely degrades the sum rate performance even for infinitely many relay antennas.

• 2.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Comments on "Multiple Antenna Spectrum Sensing in Cognitive Radios"2011In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 10, no 5, p. 1678-1680Article in journal (Refereed)

We point out an error in a derivation in the recent paper [1], and provide a correct and much shorter calculation of the result in question. In passing, we also connect the results in [1] to the literature on array signal processing and on principal component analysis, and show that the main findings of [1] follow as special cases of standard results in these fields.

• 3.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Aalborg University, Denmark. Aalborg University, Denmark. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Aalborg University, Denmark.
A Random Access Protocol for Pilot Allocation in Crowded Massive MIMO Systems2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 4, p. 2220-2234Article in journal (Refereed)

The massive multiple-input multiple-output (MIMO) technology has great potential to manage the rapid growth of wireless data traffic. Massive MIMO achieves tremendous spectral efficiency by spatial multiplexing many tens of user equipments (UEs). These gains are only achieved in practice if many more UEs can connect efficiently to the network than today. As the number of UEs increases, while each UE intermittently accesses the network, the random access functionality becomes essential to share the limited number of pilots among the UEs. In this paper, we revisit the random access problem in the Massive MIMO context and develop a reengineered protocol, termed strongest-user collision resolution (SUCRe). An accessing UE asks for a dedicated pilot by sending an uncoordinated random access pilot, with a risk that other UEs send the same pilot. The favorable propagation of massive MIMO channels is utilized to enable distributed collision detection at each UE, thereby determining the strength of the contenders signals and deciding to repeat the pilot if the UE judges that its signal at the receiver is the strongest. The SUCRe protocol resolves the vast majority of all pilot collisions in crowded urban scenarios and continues to admit UEs efficiently in overloaded networks.

• 4.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Paris Saclay, France. Univ Pisa, Italy.
Massive MIMO Has Unlimited Capacity2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 1, p. 574-590Article in journal (Refereed)

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.

• 5.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. CentraleSupelec, France; Huawei, France.
Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 2, p. 1293-1308Article in journal (Refereed)

Massive MIMO is a promising technique for increasing 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.

• 6.
KTH Royal Institute Technology, Sweden; Supelec, France.
Chalmers, Sweden; Queens University of Belfast, North Ireland. CentraleSupelec, France.
Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 8, p. 4353-4368Article in journal (Refereed)

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas N  . Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N  while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as N − −  √   , instead of linearly, by careful circuit-aware system design

• 7.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Univ Pisa, Italy.
Making Cell-Free Massive MIMO Competitive With MMSE Processing and Centralized Implementation2020In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 19, no 1, p. 77-90Article in journal (Refereed)

Cell-free Massive MIMO is considered as a promising technology for satisfying the increasing number of users and high rate expectations in beyond-5G networks. The key idea is to let many distributed access points (APs) communicate with all users in the network, possibly by using joint coherent signal processing. The aim of this paper is to provide the first comprehensive analysis of this technology under different degrees of cooperation among the APs. Particularly, the uplink spectral efficiencies of four different cell-free implementations are analyzed, with spatially correlated fading and arbitrary linear processing. It turns out that it is possible to outperform conventional Cellular Massive MIMO and small cell networks by a wide margin, but only using global or local minimum mean-square error (MMSE) combining. This is in sharp contrast to the existing literature, which advocates for maximum-ratio combining. Also, we show that a centralized implementation with optimal MMSE processing not only maximizes the SE but largely reduces the fronthaul signaling compared to the standard distributed approach. This makes it the preferred way to operate Cell-free Massive MIMO networks. Non-linear decoding is also investigated and shown to bring negligible improvements.

• 8.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. KTH Royal Institute Technology, Sweden; Supelec, France.
University of Pisa, Italy; CentraleSupelec, France. Bell Labs, Germany. CentraleSupelec, France.
Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 6, p. 3059-3075Article in journal (Refereed)

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.

• 9.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Massive MIMO for Communications With Drone Swarms2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 3, p. 1604-1629Article in journal (Refereed)

We illustrate the potential of Massive MIMO for communication with unmanned aerial vehicles (UAVs). We consider a scenario, where multiple single-antenna UAVs simultaneously communicate with a ground station (GS) equipped with a large number of antennas. Specifically, we discuss the achievable uplink (UAV to GS) capacity performance in the case of line-of-sight conditions. We develop a realistic geometric model, which incorporates an arbitrary orientation, of the GS and UAV antenna elements to characterize the polarization mismatch loss, which occurs due to the movement and orientation of the UAVs. A closed-form expression for a lower bound on the ergodic rate for a maximum-ratio combining receiver with estimated channel state information is derived. The optimal antenna spacing that maximizes the ergodic rate achieved by an UAV is also determined for uniform linear and rectangular arrays. It is shown that when the UAVs are spherically uniformly distributed around the GS, the ergodic rate per UAV is maximized for an antenna spacing equal to an integer multiple of one-half wavelength.

• 10.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. University of Paris Sud, France.
Daegu Gyeongbuk Institute Science and Technology, South Korea. Singapore University of Technology and Design, Singapore. Huawei Technology France SASU, France.
Cooperative Caching and Transmission Design in Cluster-Centric Small Cell Networks2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 5, p. 3401-3415Article in journal (Refereed)

Wireless content caching in small cell networks (SCNs) has recently been considered as an efficient way to reduce the data traffic and the energy consumption of the backhaul in emerging heterogeneous cellular networks. In this paper, we consider a cluster-centric SCN with combined design of cooperative caching and transmission policy. Small base stations (SBSs) are grouped into disjoint clusters, in which in-cluster cache space is utilized as an entity. We propose a combined caching scheme, where part of the cache space in each cluster is reserved for caching the most popular content in every SBS, while the remaining is used for cooperatively caching different partitions of the less popular content in different SBSs, as a means to increase local content diversity. Depending on the availability and placement of the requested content, coordinated multi-point technique with either joint transmission or parallel transmission is used to deliver content to the served user. Using Poisson point process for the SBS location distribution and a hexagonal grid model for the clusters, we provide analytical results on the successful content delivery probability of both transmission schemes for a user located at the cluster center. Our analysis shows an inherent tradeoff between transmission diversity and content diversity in our cooperation design. We also study the optimal cache space assignment for two objective functions: maximization of the cache service performance and the energy efficiency. Simulation results show that the proposed scheme achieves performance gain by leveraging cache-level and signal-level cooperation and adapting to the network environment and user quality-of-service requirements.

• 11.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Huawei Technol Co Ltd, France. Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Throughput With Delay Constraints in a Shared Access Network With Priorities2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 9, p. 5885-5899Article in journal (Refereed)

In this paper, we analyze a shared access network with a fixed primary node and randomly distributed secondary nodes whose spatial distribution follows a poisson point process. The secondary nodes use a random access protocol allowing them to access the channel with probabilities that depend on the queue size of the primary node. Assuming a system with multipacket reception receivers, having bursty packet arrivals at the primary and saturated traffic at the secondary nodes, our protocol can be tuned to alleviate congestion at the primary. We analyze the throughput of the secondary network and the primary average delay, as well as the impact of the secondary node access probability and transmit power. We formulate an optimization problem to maximize the throughput of the secondary network under delay constraints for the primary node; in the case of no congestion control, the optimal access probability can be provided in closed form. Our numerical results illustrate the effect of network operating parameters on the performance of the proposed priority-based shared access protocol.

• 12.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Performance Analysis of NOMA in Training-Based Multiuser MIMO Systems2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 1, p. 372-385Article in journal (Refereed)

This paper considers the use of non-orthogonal-multiple-access (NOMA) in multiuser MIMO systems in practical scenarios where channel state information (CSI) is acquired through pilot signaling. A new NOMA scheme that uses shared pilots is proposed. Achievable rate analysis is carried out for different pilot signaling schemes, including both uplink and downlink pilots. The achievable rate performance of the proposed NOMA scheme with shared pilot within each group is compared with the traditional orthogonal access scheme with orthogonal pilots. Our proposed scheme is a generalization of the orthogonal scheme, and can be reduced to the orthogonal scheme when appropriate power allocation parameters are chosen. Numerical results show that when downlink CSI is available at the users, our proposed NOMA scheme outperforms orthogonal schemes. However with more groups of users present in the cell, it is preferable to use multi-user beamforming instead of NOMA.

• 13.
IIT Guwahati, India.
Indian Inst Sci, India. Univ Peradeniya, Sri Lanka. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Performance Analysis of FDD Massive MIMO Systems Under Channel Aging2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 2, p. 1094-1108Article in journal (Refereed)

• 14.
Telecommun Technol Ctr Catalonia CTTC CERCA, Spain. Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Telecommun Technol Ctr Catalonia CTTC CERCA, Spain.
Matching Theory for Over-the-Top Service Provision in 5G Networks2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 8, p. 5452-5464Article in journal (Refereed)

Modern over-the-top (OTT) applications can be accessed via Internet connections over cellular networks, possibly shared and managed by multiple mobile network operators (MNOs). The OTT service providers (OSPs) need to interact with MNOs, requesting resources for serving users of different categories and with different quality-of-service requirements. For this purpose, OSPs need OTT application flow prioritization in resource allocation, while the network resource scheduling should respect network neutrality that forbids OSP prioritization. OSPs also need to request resources periodically, according to their performance goals, i.e., grade-of-service (GoS) level (blocking probability), causing delay in flows accommodation due to: 1) the time required for information exchange between OSPs and MNOs, affected by network congestion, and 2) the time required for flows to receive resources, affected by the number of concurrently active flows. Acknowledging the lack of OSP-oriented resource management approaches, we: 1) introduce a novel matching theoretic flow prioritization (MTFP) algorithm that respects network neutrality and 2) design analytical models that enable the thorough investigation of the GoS and delay performance in various scenarios. Our results (analytical and simulation) show that MTFP improves both metrics compared to the best effort approach, whereas its performance is affected by the number of flows and the resource allocation frequency.

• 15.
Aalborg University, Denmark.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Aalborg University, Denmark. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Aalborg University, Denmark.
Random Pilot and Data Access in Massive MIMO for Machine-Type Communications2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 12, p. 7703-7717Article in journal (Refereed)

A massive MIMO system, represented by a base station with hundreds of antennas, is capable of spatially multiplexing many devices and thus naturally suited to serve dense crowds of wireless devices in emerging applications, such as machine-type communications. Crowd scenarios pose new challenges in the pilot-based acquisition of channel state information and call for pilot access protocols that match the intermittent pattern of device activity. A joint pilot assignment and data transmission protocol based on random access is proposed in this paper for the uplink of a massive MIMO system. The protocol relies on the averaging across multiple transmission slots of the pilot collision events that result from the random access process. We derive new uplink sum rate expressions that take pilot collisions, intermittent device activity, and interference into account. Simplified bounds are obtained and used to optimize the device activation probability and pilot length. A performance analysis indicates how performance scales as a function of the number of antennas and the transmission slot duration.

• 16.
Department of Mathematics, University of Patras, Greece.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Stable Throughput and Delay Analysis of a Random Access Network With Queue-Aware Transmission2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 5, p. 3170-3184Article in journal (Refereed)

In this work we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities and a queue-aware transmission control. In this setting, the nodes can adapt their transmission probabilities and their transmission parameters based on the status of the other nodes. Each user has external bursty arrivals that are stored in their infinite capacity queues. We focus on the fundamental problem of characterizing the stable throughput region, as well as of investigating the queueing delay. For the two- and the three-user cases we obtain the exact stability region, whereas in the former case we also provide the conditions under which the stability region is a convex set. We perform a detailed mathematical analysis to study the queueing delay in the two-user case by formulating two boundary value problems, the solution of which provide the generating function of the joint stationary probability distribution of the queue size at user nodes. Furthermore, for the two-user symmetric case with MPR we obtain a lower and an upper bound for the average delay without the need of solving a boundary value problem. In addition, we provide a closed form expression for the gap between the lower and the upper bound. The bounds as it is seen in the numerical results appear to be tight. Explicit expressions for the average delay are obtained for the symmetrical model with capture effect. We also provide a closed form expression for the optimal transmission probability that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results.

• 17.
Lund Univ, Sweden.
Lund Univ, Sweden. Lund Univ, Sweden. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Lund Univ, Sweden.
Massive MIMO Performance-TDD Versus FDD: What Do Measurements Say?2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 4, p. 2247-2261Article in journal (Refereed)

Downlink beamforming in Massive multiple-input and multiple-output (MIMO) either relies on uplink pilot measurements-exploiting reciprocity and time-division duplexing operation, or on the use of a predetermined grid of beams with user equipments reporting their preferred beams, mostly in frequency-division duplexing operation. Massive MIMO in its originally conceived form uses the first strategy, with uplink pilots, whereas there is currently significant commercial interest in the second, grid-of-beams. It has been analytically shown that with isotropic scattering (independent Rayleigh fading) the first approach outperforms the second. Nevertheless, there remains controversy regarding their relative performance in practical channels. In this contribution, the performances of these two strategies are compared using measured channel data at 2.6 GHz.

• 18.
S China University of Technology, Peoples R China.
University of Maryland, MD 20742 USA. Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. University of Maryland, MD 20742 USA.
Improving the Cognitive Access Efficiency by Non-Uniform Bandwidth Allocation2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 11, p. 6435-6447Article in journal (Refereed)

In cognitive communication, dynamic sensing and opportunistic access enable secondary users to recognize and utilize the white spaces of the licensed bandwidth. Most present efforts focus on designing smarter channel sensing and access algorithms for secondary users, with the aim of optimizing the overall throughput and bandwidth utilization efficiency, under the condition of not interfering with primary users communication. However, as the transmissions of the primary users are inherently random and unpredictable, sensing and sharing spectrum with the primary users inevitably make the cognitive process of the secondary users complex and ineffective. In this paper, a non-uniform bandwidth allocation scheme is proposed that regularizes the primary users bandwidth occupancy pattern. The regularization is not designed to reshape the primary userss traffic, but to improve the sensing efficiency and throughput of the secondary users by optimizing the spectrum allocation. After the description of the new allocation scheme, we demonstrate its performance by theoretic analysis. Then we verify the validity of the non-uniform scheme with numerical simulations under non-fading and fading situations respectively. Through comparisons with the conventional uniform bandwidth allocation scheme, the non-uniform one shows higher sensing efficiency and better spectrum utilization due to lower sensing cost and reduced bandwidth loss.

• 19.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Queen’s University Belfast, UK. Ericsson Research, Ericsson AB, Linköping, Sweden. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Downlink Training in Cell-Free Massive MIMO: A Blessing in Disguise2019In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 18, no 11, p. 5153-5169Article in journal (Refereed)

• 20.
Chalmers University of Technology,Gothenburg, Sweden.
KTH Royal Institute of Technology, Sweden; Supelec, France. Chalmers University of Technology,Gothenburg, Sweden. Chalmers University of Technology,Gothenburg, Sweden,. CentraleSupelec, France.
Joint Precoding and Load Balancing Optimization for Energy-Efficient Heterogeneous Networks2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 10, p. 5810-5822Article in journal (Refereed)

This paper considers a downlink heterogeneous network, where different types of multiantenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality-of-service constraints at the users. This problem is nonconvex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the nonconvex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multicell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.

• 21.
University of Luxembourg, Luxembourg .
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Hong Kong University of Science and Technology, Peoples R China . Lund University, Sweden .
Optimal Two-Dimensional Lattices for Precoding of Linear Channels2013In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 12, no 5, p. 2104-2113Article in journal (Refereed)

Consider the communication system model y = HFx+n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any non-singular M x 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D-4.

• 22.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. University of Maryland, MD 20742 USA. Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Max-Min Power Control in Wireless Networks With Successive Interference Cancelation2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 11, p. 6269-6282Article in journal (Refereed)

We consider a wireless network comprising a number of cochannel (hence mutually interfering) links. We study the power control problem of maximizing the rate that all links can simultaneously support under a novel setup, where receivers have interference cancelation (IC) capabilities. The problem of allocating the transmitting power is intertwined with determining the links on which receivers can perform IC and the order of cancelations. We provide and prove the theoretical results of the problem complexity and structural properties. For the problem solution, we propose a mixed-integer linear programming framework that enables jointly determining the optimal power and the IC patterns using off-the-shelf algorithms. This allows for the accurate assessment of the potential of IC for power control. Extensive numerical results are presented for performance evaluation, demonstrating the benefit of deploying IC in power control.

• 23.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Performance of In-Band Transmission of System Information in Massive MIMO Systems2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 3, p. 1700-1712Article in journal (Refereed)

We consider transmission of system information in massive multiple-input multiple-output (MIMO). This information needs to be reliably delivered to inactive users in the cell without any channel state information at the base station. Downlink transmission entails the use of downlink pilots and a special type of precoding that aims to reduce the dimension of the downlink channel and the pilot overhead, which would otherwise scale with the number of base station antennas. We consider a scenario in which the base station transmits over a small number of coherence intervals, providing little time/frequency diversity. The system information is transmitted with orthogonal space-time block codes to increase reliability and performance is measured using outage rates. Several different codes are compared, both for spatially correlated and uncorrelated channels and for varying amounts of time/frequency diversity. We show that a massive MIMO base station can outperform a single-antenna base station in all considered scenarios.

• 24.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
On the Feasibility of Wireless Energy Transfer Using Massive Antenna Arrays2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 5, p. 3466-3480Article in journal (Refereed)

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 in 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 the 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%.

• 25.
ASTAR, Singapore.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. ASTAR, Singapore.
Power and Load Coupling in Cellular Networks for Energy Optimization2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 1, p. 509-519Article in journal (Refereed)

We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio (SINR) coupling model. Both cell load and transmission power, where cell load measures the average level of resource usage in the cell, interact via the coupling model. The coupling is implicitly characterized with load and power as the variables of interest using two equivalent equations, namely, non-linear load coupling equation (NLCE) and non-linear power coupling equation (NPCE), respectively. By analyzing the NLCE and NPCE, we prove that operating at full load is optimal in minimizing sum energy, and provide an iterative power adjustment algorithm to obtain the corresponding optimal power solution with guaranteed convergence, where in each iteration a standard bisection search is employed. To obtain the algorithmic result, we use the properties of the so-called standard interference function; the proof is nonstandard because the NPCE cannot even be expressed as a closed-form expression with power as the implicit variable of interest. We present numerical results illustrating the theoretical findings for a real-life and large-scale cellular network, showing the advantage of our solution compared to the conventional solution of deploying uniform power for base stations.

• 26.
ASTAR, Singapore .
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. ASTAR, Singapore .
Data Offloading in Load Coupled Networks: A Utility Maximization Framework2014In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 13, no 4, p. 1921-1931Article in journal (Refereed)

We provide a general framework for the problem of data offloading in a heterogeneous wireless network, where some demand of cellular users is served by a complementary network. The complementary network is either a small-cell network that shares the same resources as the cellular network, or a WiFi network that uses orthogonal resources. For a given demand served in a cellular network, the load, or the level of resource usage, of each cell depends in a non-linear manner on the load of other cells due to the mutual coupling of interference seen by one another. With load coupling, we optimize the demand to be served in the cellular or the complementary networks, so as to maximize a utility function. We consider three representative utility functions that balance, to varying degrees, the revenue from serving the users vs the user fairness. We establish conditions for which the optimization problem has a feasible solution and is convex, and hence tractable to numerical computations. Finally, we propose a strategy with theoretical justification to constrain the load to some maximum value, as required for practical implementation. Numerical studies are conducted for both under-loaded and over-loaded networks.

• 27.
Indian Institute Technology, India; Indian Institute Technology, India.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Improving the Performance of the Zero-Forcing Multiuser MISO Downlink Precoder Through User Grouping2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 2, p. 811-826Article in journal (Refereed)

We consider the multiple input single output (MISO) Gaussian broadcast channel with N-t antennas at the base station (BS) and N-u single-antenna users in the downlink. We propose a novel user grouping precoder which improves the sum rate performance of the zero-forcing (ZF) precoder specially when the channel is ill-conditioned. The proposed precoder partitions all the users into small groups of equal size. Downlink beamforming is then done in such a way that, at each users receiver, the interference from the signal intended for users not in its group is nulled out. Intragroup interference still remains, and is cancelled through successive interference presubtraction at the BS using dirty paper coding (DPC). The proposed user grouping method is different from user selection, since it is a method for precoding of information to the selected (scheduled) users, and not for selecting which users are to be scheduled. The proposed precoder is a generalization of two special cases, one where each group has only one user (ZF precoder) and another where all users are in a single group (ZF-DP precoder). A larger group size helps improve the sum rate performance but at the cost of greater complexity. The proposed generalization, therefore, allows for tradeoff between performance and complexity.

• 28.
Royal Institute of Technology (KTH).
Royal Institute of Technology (KTH). Royal Institute of Technology (KTH). Royal Institute of Technology (KTH).
Combining Long-Term and Low-Rate Short-Term Channel State Information over Correlated MIMO Channels2008In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 7, no 7, p. 2409-2414Article in journal (Refereed)

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is combined with a unitary transformation based on the long-term channel statistics. The heavily quantized feedback link is directly optimized to maximize the expected achievable rate under different power constraints, using vector quantization and convex optimization techniques on a sample channel distribution. Robustness against errors in the feedback link is also pursued with tools in channel optimized vector quantization. Simulations indicate the benefits of the proposed scheme.

• 29.
Zhejiang Univ, Peoples R China; Xidian Univ, Peoples R China.
Zhejiang Univ, Peoples R China; Xidian Univ, Peoples R China. Queens Univ Belfast, North Ireland. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Zhejiang Univ, Peoples R China.
Multipair Two-Way Half-Duplex DF Relaying With Massive Arrays and Imperfect CSI2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 5, p. 3269-3283Article in journal (Refereed)

This paper considers a two-way half-duplex decode-and-forward relaying system, where multiple pairs of single-antenna users exchange information via a multiple-antenna relay. Assuming that the channel knowledge is nonideal and the relay employs maximum ratio processing, we derive a large-scale approximation of the sum spectral efficiency (SE) that is tight when the number of relay antennas M becomes very large. Furthermore, we study how the transmit power scales with M to maintain a desired SE. In particular, three special power-scaling cases are discussed and the corresponding asymptotic SE is deduced with clear insights. Our elegant power-scaling laws reveal a tradeoff between the transmit powers of the user/relay and pilot symbol. Finally, we formulate a power allocation problem in terms of maximizing the sum SE and obtain a local optimum by solving a sequence of geometric programming problems.

• 30.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Royal Institute of Technology (KTH).
Cognitive Radio in a Frequency-Planned Environment: Some Basic Limits2008In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 7, no 12, p. 4800-4806Article in journal (Refereed)

The objective of this work is to assess some fundamental limits for opportunistic spectrum reuse via cognitive radio in a frequency-planned environment. We present a first-order analysis of the signal-to-noise-and-interference situation in a wireless cellular network, and analyze the impact of cognitive users starting to transmit. Two main conclusions emerge from our study. First, obtaining any substantial benefits from opportunistic spatial spectrum reuse in a frequency-planned network without causing substantial interference is going to be very challenging. Second, the cognitive users need to be more sensitive, by orders of magnitude, than the receivers in the primary system, especially if there is significant shadow fading. This latter problem can be alleviated by having cognitive users cooperate, but only if they are separated far apart so that they experience independent shadowing.

• 31.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Princeton University, NJ 08544 USA.
Joint Beamforming and Broadcasting in Massive MIMO2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 4, p. 3058-3070Article in journal (Refereed)

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.

• 32.
Department of Electrical and Computer Engineering, George Washington University, USA.
Department of Electrical and Computer Engineering, University of Florida, USA.
Nonuniform unitary space-time codes for layered source coding2004In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 3, no 3, p. 958-965Article in journal (Refereed)

We discuss new space-time codes tailored to point-to-multipoint, or broadcast, communications using layered source coding. Our codes can be encoded (and decoded) differentially, and they are based entirely on phase-shift keying. We discuss design criteria for the codes, and the design of optimal and suboptimal receiver structures. We also discuss the relation between our codes and a differentially encoded Alamouti code. Finally, we illustrate how our codes can be used to improve the throughput of a broadcasting network.

• 33.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. ASTAR, Singapore . ASTAR, Singapore .
A Unified Graph Labeling Algorithm for Consecutive-Block Channel Allocation in SC-FDMA2013In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 12, no 11, p. 5767-5779Article in journal (Refereed)

Optimal channel allocation is a key performance engineering aspect in single-carrier frequency-division multiple access (SC-FDMA). In SC-FDMA with localized channel assignment, the channels of each user must form a consecutive block. Subject to this constraint, various performance objectives, such as maximum utility, minimum power, and minimum number of channels, have been studied. We present a unified graph labeling algorithm for these problems, based on the structural insight that SC-FDMA channel allocation can be modeled as finding an optimal path in an acyclic graph. By this insight, our algorithm applies the concept of labeling and label domination that represent non-trivial extensions of finding a shortest or longest path. The key parameter in trading performance versus computation is the number of labels kept per node. Increasing the number ultimately enables global optimality. The algorithms approach is further justified by its global optimality guarantee with strong polynomial-time complexity for two specific scenarios, where the input is user-invariant and channel-invariant, respectively. For the general case, we provide numerical results demonstrating the algorithms ability of attaining near-optimal solutions.

• 34.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. University of Maryland, MD 20740 USA. ASTAR, Singapore. ASTAR, Singapore.
Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless Networks2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 11, p. 6150-6163Article in journal (Refereed)

Optimizing activation and deactivation of base station transmissions provides an instrument for improving energy efficiency in cellular networks. In this paper, we study the problem of performing cell clustering and setting the activation time of each cluster, with the objective of minimizing the sum energy, subject to a time constraint of serving the users traffic demand. Our optimization framework accounts for inter-cell interference, and, thus, the users achievable rates depend on cluster formation. We provide mathematical formulations and analysis, and prove the problems NP hardness. For problem solution, we first apply an optimization method that successively augments the set of variables under consideration, with the capability of approaching global optimum. Then, we derive a second solution algorithm to deal with the trade-off between optimality and the combinatorial nature of cluster formation. Numerical results demonstrate that our solutions achieve more than 40% energy saving over existing schemes, and that the solutions we obtain are within a few percent of deviation from global optimum.

• 35.
Tsinghua University, Peoples R China.
Tsinghua University, Peoples R China. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Tsinghua University, Peoples R China.
Capacity Analysis for Spatially Non-Wide Sense Stationary Uplink Massive MIMO Systems2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 12, p. 7044-7056Article in journal (Refereed)

Channel measurements show that significant spatially non-wide-sense-stationary characteristics rise in massive MIMO channels. Notable parameter variations are experienced along the base station array, such as the average received energy at each antenna, and the directions of arrival of signals impinging on different parts of the array. In this paper, a new channel model is proposed to describe this spatial non-stationarity in massive MIMO channels by incorporating the concepts of partially visible clusters and wholly visible clusters. Furthermore, a closed-form expression of an upper bound on the ergodic sum capacity is derived for the new model, and the influence of the spatial non-stationarity on the sum capacity is analyzed. Analysis shows that for non-identically-and-independent-distributed (i.i.d.) Rayleigh fading channels, the non-stationarity benefits the sum capacity by bringing a more even spread of channel eigenvalues. Specifically, more partially visible clusters, smaller cluster visibility regions, and a larger antenna array can all help to yield a well-conditioned channel, and benefit the sum capacity. This shows the advantage of using a large antenna array in a non-i.i.d. channel: the sum capacity benefits not only from a higher array gain, but also from a more spatially non-stationary channel. Numerical results demonstrate our analysis and the tightness of the upper bound.

• 36.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Dresden University of Technology.
Parameterization of the MISO IFC Rate Region: The Case of Partial Channel State Information2010In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 9, no 2, p. 500-504Article in journal (Refereed)

We study the achievable rate region of the multiple-input  single-output (MISO) interference channel (IFC), under the  assumption that all receivers treat the interference as additive  Gaussian noise. We assume the case of two users, and that the  channel state information (CSI) is only partially known at the  transmitters. Our main result is a characterization of  Pareto-optimal transmit strategies, for channel matrices that  satisfy a certain technical condition. Numerical examples are  provided to illustrate the theoretical results.

• 37.
Department of Electrical Engineering and the Bharti School of Telecommunication, IIT Delhi, New Delhi, India.
Department of Electrical Engineering and the Bharti School of Telecommunication, IIT Delhi, New Delhi, India. IBM India Research Laboratory, Bangalore, India.
Dilemma at RF Energy Harvesting Relay: Downlink Energy Relaying or Uplink Information Transfer?2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 8, p. 4939-4955Article in journal (Refereed)

The performance of RF powered communication networks is bottlenecked by the short downlink energy transfer range and the doubly near-far problem faced in uplink information transfer to hybrid access point (HAP). These problems can be resolved by cooperation of an RF energy harvesting node R present between HAP and RF energy harvesting information source S. However, there lies a dilemma at R on whether to transfer its harvested energy to S or to act as an information relay for transferring its data to HAP in a two-hop fashion. This paper resolves this dilemma at R by providing insights into its optimal positions suited for either energy relaying (ER) or information relaying (IR). It also investigates the possibilities of integrated ER and IR along with the regions where neither ER nor IR will be useful. In this regard, while considering Rician fading channels and practical nonlinear RF energy harvesting model, the expression for mean harvested dc power at S via energy transfer from HAP and ER from R is first derived. The closed-form outage probability expression is also derived for decode-and-forward relaying with maximal-ratio-combining at HAP over Rician channels. Using these expressions, insights into optimal relaying mode is obtained along with global-optimal utilization of harvested energy at R for ER and IR to maximize the delay-limited RF-powered throughput. Numerical results validate the analysis and provide insights into the optimal relaying mode.

• 38.
KTH Royal Institute Technology, Sweden.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. KTH Royal Institute Technology, Sweden.
Adaptive Pilot Clustering in Heterogeneous Massive MIMO Networks2016In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 15, no 8, p. 5555-5568Article in journal (Refereed)

We consider the uplink of a cellular massive multiple-input multiple-output network. Acquiring channel state information at the base stations (BSs) requires uplink pilot signaling. Since the number of orthogonal pilot sequences is limited by the channel coherence, pilot reuse across cells is necessary to achieve high spectral efficiency. However, finding efficient pilot reuse patterns is non-trivial, especially in practical asymmetric BS deployments. We approach this problem using the coalitional game theory. Each BS has a few unique pilots and can form coalitions with other BSs to gain access to more pilots. The BSs in a coalition, thus, benefit from serving more users in their cells at the expense of higher pilot contamination and interference. Given that a cells average spectral efficiency depends on the overall pilot reuse pattern, the suitable coalitional game model is in the partition form. We develop a low-complexity distributed coalition formation based on individual stability. By incorporating a BS intercommunication budget constraint, we are able to control the overhead in message exchange between the BSs and ensure the algorithms convergence to a solution of the game called individually stable coalition structure. Simulation results reveal fast algorithmic convergence and substantial performance gains over the baseline schemes with no pilot reuse, full pilot reuse, or random pilot reuse pattern.

• 39.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Department of Electrical Engineering, Pohang University of Science and Technology, Pohang, South Korea. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Wireless Networking and Communications Group, The University of Texas at Austin, Austin, TX, USA.
Uplink Performance of Wideband Massive MIMO With One-Bit ADCs2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 1, p. 87-100Article in journal (Refereed)

Analog-to-digital converters (ADCs) stand for a significant part of the total power consumption in a massive multiple-input multiple-output (MIMO) base station. One-bit ADCs are one way to reduce power consumption. This paper presents an analysis of the spectral efficiency of single-carrier and orthogonal-frequency-division-multiplexing (OFDM) transmission in massive MIMO systems that use one-bit ADCs. A closed-form achievable rate, i.e., a lower bound on capacity, is derived for a wideband system with a large number of channel taps that employ low-complexity linear channel estimation and symbol detection. Quantization results in two types of error in the symbol detection. The circularly symmetric error becomes Gaussian in massive MIMO and vanishes as the number of antennas grows. The amplitude distortion, which severely degrades the performance of OFDM, is caused by variations between symbol durations in received interference energy. As the number of channel taps grows, the amplitude distortion vanishes and OFDM has the same performance as single-carrier transmission. A main conclusion of this paper is that wideband massive MIMO systems work well with one-bit ADCs.

• 40.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Ericsson AB, Sweden. Chalmers Univ Technol, Sweden. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Spatial Characteristics of Distortion Radiated From Antenna Arrays With Transceiver Nonlinearities2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 10, p. 6663-6679Article in journal (Refereed)

The distortion from massive multiple-input multiple-output base stations with nonlinear amplifiers is studied and its radiation pattern is derived. The distortion is analyzed both in-band and out-of-band. By using an orthogonal Hermite representation of the amplified signal, the spatial cross-correlation matrix of the nonlinear distortion is obtained. It shows that, if the input signal to the amplifiers has a dominant beam, the distortion is beamformed in the same way as that beam. When there are multiple beams without any one being dominant, it is shown that the distortion is practically isotropic. The derived theory is useful to predict how the nonlinear distortion will behave, to analyze the out-of-band radiation, to do reciprocity calibration, and to schedule users in the frequency plane to minimize the effect of in-band distortion.

• 41.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Reducing Physical Layer Control Signaling Using Mobile-Assisted Scheduling2013In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 12, no 1, p. 368-379Article in journal (Refereed)

We present a scheme for reducing the part of the downlink signaling  traffic in wireless multiple access systems that contains scheduling  information.  The theoretical basis of the scheme is that the  scheduling decisions made by the base station are correlated with  the CSI reports from the mobiles.  This correlation can be exploited  by the source coding scheme that is used to compress the scheduling  maps before they are sent to the mobiles. In the proposed scheme,  this idea is implemented by letting the mobiles make tentative  scheduling decisions themselves, and then letting the base station  transmit "agreement maps" instead of raw scheduling maps to the  mobiles.  The agreement maps have lower entropy and they require  less resources to be transmitted than the original scheduling maps  do. The improvement can be substantial.  We also model the task of  finding the optimal scheduling assignments according to the proposed  scheme as a combinatorial optimization problem and present an  efficient algorithm to find the optimal solution.

• 42.
Royal Institute of Technology (KTH), Stockholm, Sweden.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Cooperative Transmission Based on Decode-and-Forward Relaying with Partial Repetition Coding2009In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 8, no 4, p. 1716-1725Article in journal (Refereed)

We propose a novel half-duplex decode-and-forward relaying scheme based on partial repetition coding at the relay. In the proposed scheme, if the relay decodes the received message successfully, it re-encodes the message using the same channel code as the one used at the source, but retransmits only a fraction of the codeword. We analyze the proposed scheme and optimize the cooperation level (i.e., the fraction of the message that the relay should transmit). We compare our scheme with conventional repetition in which the relay retransmits the entire decoded message, with parallel coding, and additionally with dynamic decode-and-forward (DDF). We provide a finite-SNR analysis for all the collaborative schemes. The analysis reveals that the proposed partial repetition method can provide a gain of several dB over conventional repetition. It also shows that in general, power allocation is less important provided that one optimally allocates bandwidth. Surprisingly, the proposed scheme is able to achieve the same performance as that of parallel coding for some relay network configurations, but at a much lower complexity.

• 43.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Queens Univ Belfast, Sch Elect Elect Engn & Comp Sci, Belfast BT3 9DT, Antrim, North Ireland.
Nokia Bell Labs, Murray Hill, NJ 07974 USA. Nokia Bell Labs, NJ 07974 USA. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Nokia Bell Labs, NJ 07974 USA.
Cell-Free Massive MIMO Versus Small Cells2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 3, p. 1834-1850Article in journal (Refereed)

• 44.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linear Multihop Amplify-and-Forward Relay Channels: Error Exponent and Optimal Number of Hops2011In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 10, no 11, p. 3834-3842Article in journal (Refereed)

We compute the random coding error exponent for linear multihop amplify-and-forward (AF) relay channels. Instead of considering only the achievable rate or the error probability as a performance measure separately, the error exponent results can give us insight into the fundamental tradeoff between the information rate and communication reliability in these channels. This measure enables us to determine what codeword length that is required to achieve a given level of communication reliability at a rate below the channel capacity. We first derive a general formula for the random coding exponent of general multihop AF relay channels. Then we present a closed-form expression of a tight upper bound on the random coding error exponent for the case of Rayleigh fading. From the exponent expression, the capacity of these channels is also deduced. The effect of the number of hops on the performance of linear multihop AF relay channels from theerror exponent point of view is studied. As an application of the random coding error exponent analysis, we then find the optimal number of hops which maximizes the communication reliability (i.e., the random coding error exponent) for a given data rate. Numerical results verify our analysis, and show the tightness of the proposed bound.

• 45.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
No Downlink Pilots Are Needed in TDD Massive MIMO2017In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, no 5, p. 2921-2935Article in journal (Refereed)

We consider the Massive Multiple-Input MultipleOutput downlink with maximum-ratio and zero-forcing processing and time-division duplex operation. To decode, the users must know their instantaneous effective channel gain. Conventionally, it is assumed that by virtue of channel hardening, this instantaneous gain is close to its average and hence that users can rely on knowledge of that average (also known as statistical channel information). However, in some propagation environments, such as keyhole channels, channel hardening does not hold. We propose a blind algorithm to estimate the effective channel gain at each user, that does not require any downlink pilots. We derive a capacity lower bound of each user for our proposed scheme, applicable to any propagation channel. Compared with the case of no downlink pilots (relying on channel hardening), and compared with training-based estimation using downlink pilots, our blind algorithm performs significantly better. The difference is especially pronounced in environments that do not offer channel hardening.

• 46.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Huawei Technology Co Ltd, Peoples R China. University of Maryland, MD 20742 USA; University of Maryland, MD 20742 USA. University of Crete, Greece; Fdn Research Technology Hellas FORTH, Greece.
Relay-Assisted Multiple Access With Full-Duplex Multi-Packet Reception2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, no 7, p. 3544-3558Article in journal (Refereed)

The effect of full-duplex cooperative relaying in a random access multiuser network is investigated here. First, we model the self-interference incurred due to full-duplex operation, assuming multi-packet reception capabilities for both the relay and the destination node. Traffic at the source nodes is considered saturated and the cooperative relay, which does not have packets of its own, stores a source packet that it receives successfully in its queue when the transmission to the destination has failed. We obtain analytical expressions for key performance metrics at the relay, such as arrival and service rates, stability conditions, and average queue length, as functions of the transmission probabilities, the self interference coefficient, and the links outage probabilities. Furthermore, we study the impact of the relay node and the self-interference coefficient on the per-user and aggregate throughput, and the average delay per packet. We show that perfect self-interference cancelation plays a crucial role when the SINR threshold is small, since it may result to worse performance in throughput and delay comparing with the half-duplex case. This is because perfect self-interference cancelation can cause an unstable queue at the relay under some conditions.

• 47.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Uplink Performance of Time-Reversal MRC in Massive MIMO Systems subject to Phase Noise2015In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, p. 711-723Article in journal (Refereed)

Multi-user multiple-input multiple-output (MU-MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information (CSI) and M BS antennas. In particular, we consider two distinct operation modes, namely when the phase noise processes at the BS antennas are identical (synchronous operation) and when they are independent (non-synchronous operation). We analyze a linear and low-complexity time-reversal maximum-ratio combining (TR-MRC) reception strategy. For both operation modes we derive a lower bound on the sum-capacity and we compare the performance of the two modes. Based on the derived achievable sum-rate, we show that with the proposed receive processing an O($\sqrt{M}$) array gain is achievable. Due to the phase noise drift the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users.

• 48.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Singapore University of Technology and Design, Singapore. Department of Electrical and Computer Engineering, New York University, New York, USA.
Joint Unicast and Multi-group Multicast Transmission in Massive MIMO Systems2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 10, p. 6375-6388Article in journal (Refereed)

We study the joint unicast and multi-group multicast transmission in massive multiple-input-multiple-output (MIMO) systems. We consider a system model that accounts for channel estimation and pilot contamination, and derive achievable spectral efficiencies (SEs) for unicast and multicast user terminals (UTs), under maximum ratio transmission and zero-forcing precoding. For unicast transmission, our objective is to maximize the weighted sum SE of the unicast UTs, and for the multicast transmission, our objective is to maximize the minimum SE of the multicast UTs. These two objectives are coupled in a conflicting manner, due to their shared power resource. Therefore, we formulate a multiobjective optimization problem (MOOP) for the two conflicting objectives. We derive the Pareto boundary of the MOOP analytically. As each Pareto optimal point describes a particular efficient trade-off between the two objectives of the system, we determine the values of the system parameters (uplink training powers, downlink transmission powers, etc.) to achieve any desired Pareto optimal point. Moreover, we prove that the Pareto region is convex, hence the system should serve the unicast and multicast UTs at the same time-frequency resource. Finally, we validate our results using numerical simulations.

• 49.
Singapore Univ Technol and Design, Singapore.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering. Singapore Univ Technol and Design, Singapore. NYU, NY 10003 USA.
Max-Min Fair Transmit Precoding for Multi-Group Multicasting in Massive MIMO2018In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 17, no 2, p. 1358-1373Article in journal (Refereed)

This paper considers the downlink precoding for physical layer multicasting in massive multiple-input multiple-output (MIMO) systems. We study the max-min fairness (MMF) problem, where channel state information at the transmitter is used to design precoding vectors that maximize the minimum spectral efficiency (SE) of the system, given fixed power budgets for uplink training and downlink transmission. Our system model accounts for channel estimation, pilot contamination, arbitrary path-losses, and multi-group multicasting. We consider six scenarios with different transmission technologies (unicast and multicast), different pilot assignment strategies (dedicated or shared pilot assignments), and different precoding schemes (maximum ratio transmission and zero forcing), and derive achievable spectral efficiencies for all possible combinations. Then, we solve the MMF problem for each of these scenarios, and for any given pilot length, we find the SE maximizing uplink pilot and downlink data transmission policies, all in closed forms. We use these results to draw a general guideline for massive MIMO multicasting design, where for a given number of base station antennas, number of users, and coherence interval length, we determine the multicasting scheme that shall be used.

• 50.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Single-User Beamforming in Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints: The Doughnut Channel2012In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 11, no 11, p. 3992-4005Article in journal (Refereed)

Large antenna arrays at the transmitter (TX) have recently been shown to achieve remarkable intra-cell interference suppression at low complexity. However, building large arrays in practice, would require the use of power-efficient RF amplifiers, which generally have poor linearity characteristics and hence would require the use of input signals with a very small peak-to-average power ratio (PAPR). In this paper, we consider the single-user Multiple-Input Single-Output (MISO) channel for the case where the TX antennas are constrained to transmit signals having constant envelope (CE). We show that, with per-antenna CE transmission the effective channel seen by the receiver is a SISO AWGN channel with its input constrained to lie in a doughnut-shaped region. For a broad class of fading channels, analysis of the effective doughnut channel shows that under a per-antenna CE input constraint, i) compared to an average-only total TX power constrained MISO channel, the extra total TX power required to achieve a desired information rate is small and bounded, ii) with N TX antennas an O(N) array power gain is achievable, and iii) for a desired information rate, using power-efficient amplifiers with CE inputs would require significantly less total TX power when compared to using highly linear (power-inefficient) amplifiers with high PAPR inputs.

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text:
#### Combining learning rate decay and weight decay with complexity gradient descent - Part I

##### Pierre H. Richemond, Yike Guo

The role of $L^2$ regularization, in the specific case of deep neural networks rather than more traditional machine learning models, is still not fully elucidated. We hypothesize that this complex interplay is due to the combination of overparameterization and high dimensional phenomena that take place during training and make it unamenable to standard convex optimization methods. Using insights from statistical physics and random fields theory, we introduce a parameter factoring in both the level of the loss function and its remaining nonconvexity: the \emph{complexity}. We proceed to show that it is desirable to proceed with \emph{complexity gradient descent}. We then show how to use this intuition to derive novel and efficient annealing schemes for the strength of $L^2$ regularization when performing standard stochastic gradient descent in deep neural networks.

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text:
## Algebra 1

$n=4\frac{2}{3}$
Use cross multiplication since the variable is in the denominator. $\frac{9}{14}=\frac{3}{n}$ cross multiply $9n=42$ divide both sides by 9 $9n\div9=42\div9$ simplify $n=4\frac{6}{9}$ simplify $n=4\frac{2}{3}$


text:
Calculus (3rd Edition)

We have $$\lim _{x \rightarrow 0^{-}} \frac{\lfloor x\rfloor}{x}=\frac{-1}{0^-}=\infty$$ so the limit does not exist.


text:
+0

Need help please ASAP

+1
47
1
+263

1) What is the smallest positive integer n such that the rightmost three digits of n! and (n+1)! are the same?

2)  $$N=1991\cdot1993\cdot1995\cdot1997\cdot1999.$$ What is the sum of the hundreds, tens and units digits of N?

3) What is the remainder when $$2+4+6+\cdots+100$$ is divided by 7?

Oct 24, 2020

#1
+1

1 - n = 10! =3,628,800  and (10+1)! = 11! =39,916,800

2 - N=1991*1993*1995*1997*1999 = N = 31601836203377055. Sum = 0 + 5 + 5 = 10

3 - sumfor(n, 1, 50, 2*n) = 2550 mod 7 = 2 - the remainder

Oct 24, 2020


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# How does Scheffe test deal with data snooping?

hypotheses suggested by the data, if tested using the data set that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning would be involved: something seems true in the limited data set, therefore we hypothesize that it is true in general, therefore we (wrongly) test it on the same limited data set, which seems to confirm that it is true. Generating hypotheses based on data already observed, in the absence of testing them on new data, is referred to as post hoc theorizing.

The correct procedure is to test any hypothesis on a data set that was not used to generate the hypothesis.

For Post Hoc analysis of ANOVA,

Henry Scheffé's simultaneous test of all contrasts in multiple comparison problems is the most[citation needed] well-known remedy in the case of analysis of variance.1 It is a method designed for testing hypotheses suggested by the data while avoiding the fallacy described above.

So I was wondering how Scheffé's test avoids the fallacy of data snooping?

• The Wikipedia article you link to states "It can be shown that the probability is $1-\alpha$ that all confidence limits of the type $$\hat{C}\pm s_\hat{C}\sqrt{(r-1)F_{\alpha;r-1;N-r}}$$ are simultaneously correct." That seems like a particularly clear and full answer to me. Do you detect that something is missing in it?
– whuber
Jul 11, 2013 at 1:45
• @whuber: Thanks! (1) Why does the quote in your comment explains Scheffe's test avoids the data snooping? (2) Also does Bonferroni multiple comparison procedure not avoid data snooping problem, and why? See my question here.
– Tim
Jul 11, 2013 at 1:52
• It seems to me that the quotation with which you begin your previous question nicely answers both (1) and (2). The distinction it explicitly draws is between a "family of inferences" specified in advance and a family that is not, or cannot, be so specified. The Wikipedia quotation is in the context of a clearly defined family: namely, all possible contrasts.
– whuber
Jul 11, 2013 at 1:55
• I think this is a beautiful and important question! There is a paper from Berk et al. (2013) that could be interesting for you (the title is 'Valid Post-Selection Inference'). They develop confidence intervals that are robust to any kind of selection/snooping/significance searching, given normal errors and a fixed design. They manage to derive PoSI (Post selection inference) constants that serve as critical values. They are (in absolute value) upper bounded by the Scheffé constant, demonstrating that it in fact provides a 'guarantee against data snooping'. Feb 16, 2016 at 15:46

The Wikipedia article you link to states "It can be shown that the probability is $1−α$ that all confidence limits of the type $$\hat{C}\pm s_\hat{C}\sqrt{(r-1)F_{\alpha;r-1;N-r}}$$ are simultaneously correct." That seems like a particularly clear and full answer to me. Do you detect that something is missing in it? – whuber


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# Is there a Borel subset of $\mathbb{R}^{2}$, with finite vertical cross-sections, whose projection onto the first component is non-Borel?

This question is related to another one that I asked two days ago.

Question. Does there exist a Borel subset $M$ of $\mathbb{R}^{2}$ with the following two properties?

• The projection of $M$ onto the first component is a non-Borel analytic subset of $\mathbb{R}$.
• Every vertical cross-section of $M$ is finite, i.e., the set $\{ y \in \mathbb{R} \mid (x,y) \in M \}$ is finite for every $x \in \mathbb{R}$.

An affirmative answer to this question will provide a counterexample in the topic of measure theory, as explained in the linked post. It therefore holds some importance.

Thank you very much for your help!

• I think the answer is no, and it could be proved with results from Borel equivalence relations. Consider $M$ as a standard Borel space, and the Borel equivalence relation $E$ on $M$ which is $(x,y) E (x', y')$ iff $x=x'$. Since every equivalence class of $E$ is finite, it has a transversal: a Borel set $A \subset M$ containing one element from each $E$-class. (See Proposition 1.4.4 in homepages.math.uic.edu/~kslutsky/papers/cber.pdf.) Then the projection $\pi : A \to \mathbb{R}$ is an injective Borel function, hence its image $\pi(A) = \pi(M)$ is Borel. – Nate Eldredge Nov 2 '16 at 6:45
• But there should be a more elementary argument. – Nate Eldredge Nov 2 '16 at 6:46
• @Nate: Thank you for your comments, Nate. Yes, a more elementary argument might do away with the requirement that $M$ be a standard Borel space. Hopefully, a descriptive set theorist will be able to weigh in. – Transcendental Nov 2 '16 at 9:56
• Oh, that part's not a requirement: since $M$ is a Borel subset of $\mathbb{R}^2$ it is already a standard Borel space. I just mean to think of it as a space in its own right, since we don't really want to work with an equivalence relation on all of $\mathbb{R}^2$. – Nate Eldredge Nov 2 '16 at 12:51

No, no such set exists. This is a special case of the Lusin–Novikov theorem; see e.g. Kechris, Classical Descriptive Set Theory, Theorem 18.10.

In general, let $X,Y$ be standard Borel spaces, and suppose $M \subset X \times Y$ is Borel. (Here we are taking $X=Y=\mathbb{R}$.) For $x \in X$, let $M_x = \{y : (x,y) \in M\}$ be the section of $M$ at $x$. The Lusin–Novikov theorem asserts that if all but at most countably many of the $M_x$ are at most countable (i.e. $|\{x : |M_x| > \aleph_0\}| \le \aleph_0$) , then $M$ has a Borel uniformization: there is a Borel set $M^* \subset M$ such that $M^*$ intersects every nonempty section $M_x$ in exactly one point. In particular, the projection map $\pi : X \times Y \to X$, which is Borel, is injective when restricted to $M^*$; so as a consequence (see Kechris Corollary 15.2) we have that $\pi(M^*) = \pi(M)$ is Borel in $X$.

Any set $M$ satisfying your second condition certainly satisfies the hypothesis of Lusin–Novikov (since $\{x : |M_x| > \aleph_0\} = \emptyset$), so its projection is Borel, and thus it does not satisfy your first condition.

• Or you can even prove it bare-handedly by noticing there is a borel linear ordering of the space, define the uniformizing function by picking the least element under that – Jing Zhang Nov 2 '16 at 16:46
• @JingZhang: So you're suggesting something like let $f(x) = \inf M_x$? I considered that but did not see how to show it's a Borel function. We have to use somewhere the fact that the sections are finite. For general $M$ this will not give a Borel function. – Nate Eldredge Nov 2 '16 at 16:53
• @NateEldredge: Yeah the definition is $(x,y)\in f \Leftrightarrow (x,y)\in B \wedge \forall z<y (x,z)\not \in B$, which is just co-analytic. I believe Luzin-Novikov is needed to reduce $\forall z<y$ to a countable operation. (I thought of Feldman-Moore which states every countable Borel equivalence relation is the same as an orbit equivalence relation generated by some action of a countable group on the space, but I don't think this is any easier than LN). – Jing Zhang Nov 2 '16 at 18:04

The projection is always Borel provided the set is Borel and each cross-section is at most countable. This is an old theorem of Luzin and/or Novikov, valid for sets in any product of two polish spaces, and the countability can be weakened to sigma-compactness (Novikov and/or Kunugui).

There is a pure recursion theoretical proof of the result. The idea is as follows: By Spector-Gandy theorem, a lightface Borel set $(x,y)$ is an r.e set over $L_{\omega_1^{CK}}[x,y]$. If there are at most countably many $y$'s corresponded to the $x$ for every $x$, then it can be reduced to $L_{\omega_1^{CK}}[x]$. Then the projection to the first section becomes a $\Pi^1_1$ statement.