The aggressive spatial spectrum reuse (SSR) by network densification using smaller cells has successfully driven the wireless communication industry onward in the past decades. In our future journey toward ultra-dense networks (UDNs), a fundamental question needs to be answered. Is there a limit to SSR? In other words, when we deploy thousands or millions of small cell base stations (BSs) per square kilometer, is activating all BSs on the same time frequency resource the best strategy? In this paper, we present theoretical analyses to answer such question. In particular, we find that both the signal and interference powers become bounded in practical UDNs with a non-zero BS-to-UE antenna height difference and a finite UE density, which leads to a constant capacity scaling law. As a result, there exists an optimal SSR density that can maximize the network capacity. Hence, the limit to SSR should be considered in the operation of future UDNs.
First, if we consider a practical non-zero BS-to-UE antenna height difference @math , then the coverage probability is shown to crash as the BS density increases in a fully-loaded UDN. This is caused by a severe in UDNs @cite_12 . The intuition of such is that the signal power becomes in UDNs due to the lower-bound on the BS-to-UE distance, as a UE cannot be closer than @math to its serving BS.
@cite_12
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In this paper, we present a new and significant theoretical discovery. If the absolute height difference between base station (BS) antenna and user equipment (UE) antenna is larger than zero, then the network performance in terms of both the coverage probability and the area spectral efficiency will continuously decrease toward zero as the BS density increases in ultra-dense networks (UDNs). Such findings are completely different from the conclusions in the existing works, both quantitatively and qualitatively. In particular, this performance behavior has a tremendous impact on the deployment of the 5th-generation UDNs. Network operators may invest large amounts of money in deploying more network infrastructure only to obtain even less network capacity. This paper’s results reveal that one way to address this issue is to lower the BS antenna height to the UE antenna height. However, this requires a revolutionized approach of the BS architecture and deployment, which is also explored in this paper. The concept of Ultra Dense Networks (UDN) is often seen as a key enabler of the next generation mobile networks. However, existing analysis of UDNs, including Stochastic Geometry, has not been able to fully determine the potential gains and limits of densification. In this paper we study performance of UDNs in downlink and provide new insights on the impact of antenna height and careful site selection on the network performance. We focus our investigation on the probability of coverage, average cell rate and average area spectral efficiency for networks with regular and random BS deployments. We show that under a path-loss model which considers antenna height there exists an upper limit on network performance which is dependent on the path-loss model parameters. Our analysis shows an interesting finding that even for over-densified networks a non-negligible system performance can be achieved. Very recent studies showed that in a fully loaded dense small cell network (SCN), the coverage probability performance will continuously decrease with the network densification. Such new results were captured in IEEE ComSoc Technology News with an alarming title of "Will Densification Be the Death of 5G?". In this paper, we revisit this issue from more practical views of realistic network deployment, such as a finite number of active base stations (BSs) and user equipments (UEs), a decreasing BS transmission power with the network densification, etc. Particularly, in dense SCNs, due to an oversupply of BSs with respect to UEs, a large number of BSs can be put into idle modes without signal transmission, if there is no active UE within their coverage areas. Setting those BSs into idle modes mitigates unnecessary inter-cell interference and reduces energy consumption. In this paper, we investigate the performance impact of such BS idle mode capability (IMC) on dense SCNs. Different from existing work, we consider a realistic path loss model incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions. Moreover, we obtain analytical results for the coverage probability, the area spectral efficiency (ASE) and the energy efficiency (EE) performance for SCNs with the BS IMC and show that the performance impact of the IMC on dense SCNs is significant. As the BS density surpasses the UE density in dense SCNs, the coverage probability will continuously increase toward one, addressing previous concerns on "the death of 5G". Finally, the performance improvement in terms of the EE performance is also investigated for dense SCNs using practical energy models developed in the Green-Touch project. For an arbitrarily-located user terminal (UE) in a multi-tier heterogeneous cellular wireless network, the joint distribution of the downlink SINR at the UE from the candidate serving base stations (BSs) in the accessible tiers of the network has been derived in closed form for the cases where the candidate serving BS from each accessible tier is chosen as either the one nearest to the UE [1] or the one that is received strongest (equivalently, with maximum SINR) at the UE [2], when the locations of the BSs in the tiers are modeled by independent Poisson Point Processes, and the fading on all links is assumed independent identically distributed (iid) and Rayleigh. The actual serving BS for the UE is chosen as the nearest strongest max-SINR candidate serving BS after imposing selection bias across the tiers. The above joint distributions can be used to yield the distribution of the actual SINR at the UE (i.e., when receiving from this serving BS) when no selection bias exists across tiers. However, for the practically important case of selection bias, analytical calculation of the distribution of the actual SINR presents significant challenges. This work derives and summarizes the distribution of actual downlink SINR for all the above criteria for selection of the serving BS accounting for selection bias. We then explore some implications of these results for design and operation of a heterogeneous network. A recent way to model and analyze downlink cellular networks is by using random spatial models. Assuming user equipment (UE) distribution to be uniform, the analysis is performed at a typical UE located at the origin. At least one shortcoming of this approach is its inability to model non-uniform UE distributions, especially when there is dependence in the UE and the base station (BS) locations. To facilitate analysis in such cases, we propose a new tractable method of sampling UEs by conditionally thinning the BS point process and show that the resulting framework can be used as a tractable generative model to study current capacity-centric deployments, where the UEs are more likely to lie closer to the BSs. Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control as well as the maximum power limitations for UEs. More specifically, for interference mitigation and robust uplink communication, each UE is required to control its transmit power such that the average received signal power at its serving base station (BS) is equal to a certain threshold ρ o . Due to the limited transmit power, the UEs employ a truncated channel inversion power control policy with a cutoff threshold of ρ o . We show that there exists a transfer point in the uplink system performance that depends on the following tuple: BS intensity λ, maximum transmit power of UEs P u , and ρ o . That is, when P u is a tight operational constraint with respect to (w.r.t.) λ and ρ o , the uplink outage probability and spectral efficiency highly depend on the values of λ and ρ o . In this case, there exists an optimal cutoff threshold ρ o *, which depends on the system parameters, that minimizes the outage probability. On the other hand, when P u is not a binding operational constraint w.r.t. λ and ρ o , the uplink outage probability and spectral efficiency become independent of λ and ρ o . We obtain approximate yet accurate simple expressions for outage probability and spectral efficiency, which reduce to closed forms in some special cases. The forthcoming 5G cellular network is expected to overlay millimeter-wave (mmW) transmissions with the incumbent micro-wave ( @math ) architecture. The overall mm- @math resource management should, therefore, harmonize with each other. This paper aims at maximizing the overall downlink (DL) rate with a minimum uplink (UL) rate constraint, and concludes: mmW tends to focus more on DL transmissions while @math has high priority for complementing UL, under time-division duplex (TDD) mmW operations. Such UL dedication of @math results from the limited use of mmW UL bandwidth due to excessive power consumption and or high peak-to-average power ratio (PAPR) at mobile users. To further relieve this UL bottleneck, we propose mmW UL decoupling that allows each legacy @math base station (BS) to receive mmW signals. Its impact on mm- @math resource management is provided in a tractable way by virtue of a novel closed-form mm- @math spectral efficiency (SE) derivation. In an ultra-dense cellular network (UDN), our derivation verifies mmW (or @math ) SE is a logarithmic function of BS-to-user density ratio. This strikingly simple yet practically valid analysis is enabled by exploiting stochastic geometry in conjunction with real three-dimensional (3-D) building blockage statistics in Seoul, South Korea. In this paper, we investigate the downlink performance of dense cellular networks with elevated base stations (BSs) using a channel model that incorporates line-of-sight (LOS) non-line-of-sight (NLOS) propagation into both small-scale and large-scale fading. Modeling LOS fading with Nakagami- @math fading, we provide a unified framework based on stochastic geometry that encompasses both closest and strongest BS association. This paper is particularized to two distance-dependent LOS NLOS models of practical interest. Considering the effect of LOS propagation alone, we derive closed-form expressions for the coverage probability with Nakagami- @math fading, showing that the performance for strongest BS association is the same as in the case of Rayleigh fading, whereas for closest BS association it monotonically increases with the shape parameter @math . Then, focusing on the effect of elevated BSs, we show that network densification eventually leads to near-universal outage even for moderately low BS densities: in particular, the maximum area spectral efficiency is proportional to the inverse of the square of the BS height. Massive multiuser (MU) multiple-input multiple-output (MIMO) is foreseen to be one of the key technologies in fifth-generation wireless communication systems. In this paper, we investigate the problem of downlink precoding for a narrowband massive MU-MIMO system with low-resolution digital-to-analog converters (DACs) at the base station (BS). We analyze the performance of linear precoders, such as maximal-ratio transmission and zero-forcing, subject to coarse quantization. Using Bussgang’s theorem, we derive a closed-form approximation on the rate achievable under such coarse quantization. Our results reveal that the performance attainable with infinite-resolution DACs can be approached using DACs having only 3–4 bits of resolution, depending on the number of BS antennas and the number of user equipments (UEs). For the case of 1-bit DACs, we also propose novel nonlinear precoding algorithms that significantly outperform linear precoders at the cost of an increased computational complexity. Specifically, we show that nonlinear precoding incurs only a 3 dB penalty compared with the infinite-resolution case for an uncoded bit-error rate of 10−3, in a system with 128 BS antennas that uses 1-bit DACs and serves 16 single-antenna UEs. In contrast, the penalty for linear precoders is about 8 dB. Distance-based attenuation is a critical aspect of wireless communications. As opposed to the ubiquitous power-law path loss model, this paper proposes a stretched exponential path loss model that is suitable for short-range communication. In this model, the signal power attenuates over a distance @math as @math , where @math and @math are tunable parameters. Using experimental propagation measurements, we show that the proposed model is accurate for short to moderate distances in the range @math meters and so is a suitable model for dense and ultradense networks. We integrate this path loss model into a downlink cellular network with base stations modeled by a Poisson point process, and derive expressions for the coverage probability, potential throughput, and area spectral efficiency. Although the most general result for coverage probability has a double integral, several special cases are given, where the coverage probability has a compact or even closed form. We then show that the potential throughput is maximized for a particular BS density and then collapses to zero for high densities, assuming a fixed signal-to-interference-plus-noise ratio (SINR) threshold. We next prove that the area spectral efficiency, which assumes an adaptive SINR threshold, is nondecreasing with the BS density and converges to a constant for high densities. The millimeter wave frequencies (roughly above 10 GHz) offer the availability of massive bandwidth to greatly increase the capacity of fifth generation (5G) cellular wireless systems. However, to overcome the high isotropic pathloss at these frequencies, highly directional transmissions will be required at both the base station (BS) and the mobile user equipment (UE) to establish sufficient link budget in wide area networks. This reliance on directionality has important implications for control layer procedures. Initial access in particular can be significantly delayed due to the need for the BS and the UE to find the initial directions of transmission. This paper provides a survey of several recently proposed techniques. Detection probability and delay analysis is performed to compare various techniques including exhaustive and iterative search. We show that the optimal strategy depends on the target SNR regime. Millimeter-wave (mm-wave) frequency bands provide an opportunity for much wider channel bandwidth compared with the traditional sub-6-GHz band. Communication at mm-waves is, however, quite challenging due to the severe propagation pathloss incurred by conventional isotropic antennas. To cope with this problem, directional beamforming both at the base station (BS) side and at the user equipment (UE) side is necessary in order to establish a strong path conveying enough signal power. Finding such beamforming directions is referred to as beam alignment (BA). This paper presents a new scheme for efficient BA. Our scheme finds a strong propagation path identified by an angle-of-arrival (AoA) and angle-of-departure (AoD) pair, by exploring the AoA–AoD domain through pseudo-random multi-finger beam patterns and constructing an estimate of the resulting second-order statistics (namely, the average received power for each pseudo-random beam configuration). The resulting under-determined system of equations is efficiently solved using non-negative constrained least-squares, yielding naturally a sparse non-negative vector solution whose maximum component identifies the optimal path. As a result, our scheme is highly robust to variations of the channel time dynamics compared with alternative concurrent approaches based on the estimation of the instantaneous channel coefficients, rather than of their second-order statistics. In the proposed scheme, the BS probes the channel in the downlink and trains simultaneously an arbitrarily large number of UEs. Thus, “beam refinement,” with multiple interactive rounds of downlink uplink transmissions, is not needed. This results in a scalable BA protocol, where the protocol overhead is virtually independent of the number of UEs, since all the UEs run the BA procedure at the same time. Extensive simulation results illustrate that our approach is superior to the state-of-the-art BA schemes proposed in the literature in terms of training overhead in multi-user scenarios and robustness to variations in the channel dynamics. 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 a K-tier 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 i^ th tier are assumed to transmit independently with probability p_i, 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. Cellular systems in general suffer from co-channel interference, when simultaneous transmissions in other cells use the same physical resources. In order to mitigate such co-channel interference cooperating Base Stations (BSs) can perform joint multi-antenna signal processing across cell borders. This paper describes a concept of distributed cooperation, where BSs communicate directly via a BS-BS interface without central control. A serving BS can serve its terminals on its own or it can request cooperation from one or more supporting BSs. By collecting IQ samples from the supporting BSs' antenna elements, the serving BS can virtually increase its number of receive antennas. Exchanging additional parameters allows applying advanced receiver algorithms, e.g., interference rejection or cancelation. Performance evaluations by means of simulation show the capability of BS cooperation applied to 3GPP LTE in terms of cell and user throughput but it also shows the trade-off in terms of increased backhaul requirement due to BS-BS communication. We develop a general downlink model for multi-antenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signal-to-interference-ratio (SIR), deployment density, number of transmit antennas and the type of multi-antenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (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 single-antenna BSs vs. fewer multi-antenna BSs. Another observation is that SU-BF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE. Dense deployment which brings small base stations (BS) closer to mobile devices is considered as a promising solution to the booming traffic demand. Meanwhile, the utilization of new frequency bands and spectrum aggregation techniques provide more options for spectrum choice.Whether to increase BS density or to acquire more spectrum is a key strategic question for mobile operators. In this paper, we investigate the relationship between BS density and spectrum with regard to individual user throughput target. Our work takes into account load-dependent interference model and various traffic demands. Numerical results show that densification is more effective in sparse networks than in already dense networks. In sparse networks, doubling BS density results in almost twofold throughput increase. However, in dense networks where BSs outnumber users, more than 10 times of BS density is needed to double user throughput. Meanwhile, spectrum has a linear relationship with user throughput for a given BS density. The impact of traffic types is also discussed. Even with the same area throughput requirement, different combination of user density and individual traffic amount leads to different needs for BS density and spectrum. An uplink–downlink two-cell cellular network is studied in which the first base station (BS) with @math antennas receives independent messages from its @math serving users, while the second BS with @math antennas transmits independent messages to its @math serving users. That is, the first and second cells operate as uplink and downlink, respectively. Each user is assumed to have a single antenna. Under this uplink–downlink setting, the sum degrees of freedom (DoFs) is completely characterized as the minimum of @math , @math , @math , and @math , where @math denotes @math . The result demonstrates that, for a broad class of network configurations, operating one of the two cells as uplink and the other cell as downlink can strictly improve the sum DoF compared with the conventional uplink or downlink operation, in which both cells operate as either uplink or downlink. The DoF gain from such uplink–downlink operation is further shown to be achievable for heterogeneous cellular networks having hotspots and with delayed channel state information. Massive MIMO is attractive for wireless information and energy transfer due to its ability to focus energy toward desired spatial locations. In this paper, the overall power transfer efficiency (PTE) and the energy efficiency (EE) of a wirelessly powered massive MIMO system are investigated, where a multi-antenna base-station (BS) uses wireless energy transfer to charge single-antenna energy harvesting users on the downlink. The users may exploit the harvested energy to transmit information to the BS on the uplink. The overall system performance is analyzed while accounting for the nonlinear nature of practical energy harvesters. First, for wireless energy transfer, the PTE is characterized using a scalable model for the BS circuit power consumption. The PTE-optimal values for the number of BS antennas and users are derived. Then, for wireless energy and information transfer, the EE performance is characterized. The EE-optimal BS transmit power is derived in terms of the key system parameters, such as the number of BS antennas and the number of users. As the number of antennas becomes large, increasing the transmit power improves the EE for moderate to large number of antennas. Simulation results suggest that it is energy efficient to operate the system in the massive MIMO regime. In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum instantaneous biased received power under the open access cell association scheme. For such a general setting, we provide an analytical characterization of the coverage probability at the MS. In this paper, we study the problem of (AD) in a massive MIMO setup, where the Base Station (BS) has @math antennas. We consider a block fading channel model where the @math -dim channel vector of each user remains almost constant over a (CB) containing @math signal dimensions. We study a setting in which the number of potential users @math assigned to a specific CB is much larger than the dimension of the CB @math ( @math ) but at each time slot only @math of them are active. Most of the previous results, based on compressed sensing, require that @math , which is a bottleneck in massive deployment scenarios such as Internet-of-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we show that one can overcome this fundamental limitation when the number of BS antennas @math is sufficiently large. More specifically, we derive a on the parameters @math and also (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension @math , and a sufficient number of BS antennas @math with @math , one can identify the activity of @math active users, which is much larger than the previous bound @math obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a poly-logarithmic penalty @math for increasing the number of potential users @math , which makes it ideally suited for AD in IoT setups. We propose low-complexity algorithms for AD and provide numerical simulations to illustrate our results. We also compare the performance of our proposed AD algorithms with that of other competitive algorithms in the literature.