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Modeling and analysis of Ktier downlink heterogeneous cellular networks
 IEEE J. Sel. Areas Commun
, 2012
"... Abstract—Cellular networks are in a major transition from a carefully planned set of large towermounted basestations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this pap ..."
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Cited by 154 (38 self)
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Abstract—Cellular networks are in a major transition from a carefully planned set of large towermounted basestations (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 SignaltoInterferenceplusNoiseRatio (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 closedform 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 12 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 interferencelimited 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 targetSINR. Index Terms—Femtocells, heterogeneous cellular networks, stochastic geometry, point process theory, coverage probability. I.
Massive MIMO in the UL/DL of cellular networks: How many antennas do we need?
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2013
"... We consider the uplink (UL) and downlink (DL) of noncooperative multicellular timedivision duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot con ..."
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Cited by 109 (13 self)
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We consider the uplink (UL) and downlink (DL) of noncooperative multicellular timedivision duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N →∞while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η % of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum meansquare error (MMSE) detection and regularized zeroforcing (RZF), respectively.
Seven Ways that HetNets are a Cellular Paradigm Shift
, 2012
"... Imagine a world with more base stations than cell phones: this is where cellular technology is headed in 1020 years. This megatrend requires many fundamental differences in visualizing, modeling, analyzing, simulating and designing cellular networks versus the current textbook approach. In this pa ..."
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Cited by 64 (10 self)
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Imagine a world with more base stations than cell phones: this is where cellular technology is headed in 1020 years. This megatrend requires many fundamental differences in visualizing, modeling, analyzing, simulating and designing cellular networks versus the current textbook approach. In this paper, the most important shifts are distilled down to seven key factors, with the implications described and new models and techniques proposed for some, while others are ripe areas for future exploration.
LoadAware Modeling and Analysis of Heterogeneous Cellular Networks
 IEEE TRANS. ON WIRELESS COMMUN
, 2013
"... Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assu ..."
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Cited by 22 (10 self)
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Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For aKtier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the ith tier are assumed to transmit independently with probability pi, which models the load. Assuming – reasonably – that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage.
Modeling, analysis, and design for carrier aggregation in heterogeneous cellular networks
 IEEE Tran. Commun
, 2013
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Downlink MIMO HetNets: Modeling, Ordering Results and Performance Analysis
 IEEE TRANS. ON WIRELESS COMMUN
, 2013
"... We develop a general downlink model for multiantenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signaltointerferenceratio (SIR), deployment density, number of transmit antennas and the type of multiantenna tr ..."
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Cited by 14 (6 self)
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We develop a general downlink model for multiantenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signaltointerferenceratio (SIR), deployment density, number of transmit antennas and the type of multiantenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SUBF), and baseline singleinput singleoutput (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, that for a given total number of transmit antennas in the network, it is preferable to spread them across many singleantenna BSs vs. fewer multiantenna BSs. Another observation is that SUBF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE.
Spatial Modulation for Generalized MIMO: Challenges, Opportunities and Implementation
, 2013
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An analytical framework for heterogeneous partial feedback design in heterogeneous multicell ofdma networks
 IEEE Transactions on Signal Processing
, 2013
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Average rate of downlink heterogeneous cellular networks over generalized fading channels – A stochastic geometry approach
 IEEE Trans. Commun
, 2013
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