A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.

Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

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Multi-Cell MIMO Cooperative Networks: A New Look at Interference

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given \sinr, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.

Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

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Pilot Contamination and Precoding in Multi-Cell TDD Systems

In this article we consider network coordination as a means to provide spectrally efficient communications in cellular downlink systems. When network coordination is employed, all base antennas act together as a single network antenna array, and each mobile may receive useful signals from nearby base stations. Furthermore, the antenna outputs are chosen in ways to minimize the out-of-cell interference, and hence to increase the downlink system capacity. When the out-of-cell interference is mitigated, the links can operate in the high signal-to-noise ratio regime. This enables the cellular network to enjoy the great spectral efficiency improvement associated with using multiple antennas

Network coordination for spectrally efficient communications in cellular systems

Intercell interference limits the capacity of wireless networks. To mitigate this interference we explore coherently coordinated transmission (CCT) from multiple base stations to each user. To treat users fairly, we explore equal rate (ER) networks. We evaluate the downlink network efficiency of CCT as compared to serving each user with single base transmission (SBT) with a separate base uniquely assigned to each user. Efficiency of ER networks is measured as total network throughput relative to the number of network antennas at 10% user outage. Efficiency is compared relative to the baseline of single base transmission with power control, (ER-SBT), where base antenna transmissions are not coordinated and apart from power control and the assignment of 10% of the users to outage, nothing is done to mitigate interference. We control the transmit power of ER systems to maximise the common rate for ER-SBT, ER-CCT based on zero forcing, and ER-CCT employing dirty paper coding. We do so for (no. of transmit antennas per base, no. of receive antennas per user) equal to (1,1), (2,2) and (4,4). We observe that CCT mutes intercell interference enough, so that enormous spectral efficiency improvement associated with using multiple antennas in isolated communication links occurs as well for the base-to-user links in a cellular network.

Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency

We investigate optimum zero-forcing beamforming in multiple antenna broadcast channels with per-antenna power constraints. We show that standard zero-forcing techniques, such as the Moore-Penrose pseudo-inverse, considered mainly in the context of sum-power constrained systems are suboptimal when there are per-antenna power constraints. We formulate convex optimization problems to find the optimum zero-forcing beamforming vectors. Our results indicate that optimizing the antenna outputs based on the per-antenna constraints may improve the rate considerably when the number of transmit antennas is larger the number of receive antennas. Having more transmit antennas gives rise to additional signal space dimensions that may be exploited effectively to reduce transmit power at particular antennas with limited power budget.

Optimum Zero-forcing Beamforming with Per-antenna Power Constraints

Recently, there has been considerable interest in the potential of inter-base station cooperation techniques to manage excessive out-of-cell interference in evolving cellular networks. It has been observed that on the uplink, significant improvements in interference rejection can be attained by exchanging complex-valued received signal samples across a cluster of cells and employing joint multi-antenna receiver processing. However, such processing incurs substantial increases in backhaul overhead, exceeding the actual information delivered by at least an order of magnitude. In this paper, we propose and describe a signal processing approach based on a novel Network Interference Cancellation Engine (NICE), which opportunistically cancels out-of-cell interference by exchanging decoded dominant interferer data among cooperating cells and reconstructing interfering signals. Simulation results with NICE processing in cellular networks show that substantial improvements (5-7 dB) in signal-to-interference-plus-noise ratio may be achieved over current non-cooperative multi-antenna receiver processing techniques while allowing backhaul overhead to be reduced by factors on the order of 40 to 50 relative to joint processing techniques employing the exchange of complex-valued received signal samples.

NICE: A Network Interference Cancellation Engine for Opportunistic Uplink Cooperation in Wireless Networks

In this paper, we propose a cross layer optimization framework for multi-hop routing and resource allocation design in an orthogonal frequency division multiple access (OFDMA) based wireless mesh network. The network under consideration is assumed to consist of fixed mesh routers (or base station routers) inter-connected using OFDMA wireless links with some of the mesh routers functioning as gateways to a wired network. The objective of our cross-layer formulation is to allow joint determination of power control, frequency-selective OFDMA scheduling and multi-hop routing in order to maximize the minimum throughput that can be supported to all mesh routers. Results of our investigations under typical cellular deployment, propagation and channel model assumptions show that this approach achieves significant mesh throughput improvements primarily due to the following: (a) frequency selective scheduling with OFDMA which provides improved tone diversity thus allowing more efficient bandwidth utilization relative to single carrier methods; and (b) multi-hop routing which provides improved path diversity relative to single hop transmissions.

Cross-Layer Optimization for OFDMA-Based Wireless Mesh Backhaul Networks

As the demand for wireless data grows to unprecedented levels, cellular service providers have been investigating different ways to meet this growing demand. The deployment of small cells with reduced transmission powers and reduced coverage areas is being considered as one possible way of meeting the growing demand. Using the same spectrum employed by existing macro cells, small cells would allow increased spatial reuse of bandwidth thus providing the potential for improved user rates. One challenge for small cells, though, is that due to their weaker signals (lower transmission powers, antennas with smaller antenna gains), the coverage area tends to be significantly reduced and the incremental benefit of deploying each small cell is limited. In this paper, resource partitioning is proposed along with suitably modified cell selection criteria to improve the performance of heterogeneous networks comprising small and macro cells that operate in the same swath of spectrum. Our simulation results demonstrate that with four small cells deployed per sector, 5%-ile and 50%-ile user throughputs both improve by ~150% relative to the same case without resource partitioning.

Kemal M. Karakayali

Papers

Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency

Optimum Zero-forcing Beamforming with Per-antenna Power Constraints

NICE: A Network Interference Cancellation Engine for Opportunistic Uplink Cooperation in Wireless Networks

Cross-Layer Optimization for OFDMA-Based Wireless Mesh Backhaul Networks

Cell Selection with Downlink Resource Partitioning in Heterogeneous Networks