The performance analysis of heterogeneous cellular networks (HetNets), that relied mostly on the homogeneous Poisson point process (PPP) for the spatial distribution of the users and base stations (BSs), has seen a major transition with the emergence of the Poisson cluster process (PCP)-based models. With the combination of PPP and PCP, it is possible to construct a general HetNet model which can capture formation of hotspots and spatial coupling between the users and the BSs. While the downlink coverage analysis of this model in terms of the distribution of the received downlink signal-to-interference ratio ($\tt SIR$) is well understood by now, more fine grained analysis in terms of the meta distribution of ${\tt SIR}$ is an open problem. In this letter, we solve this problem by deriving the meta distribution of the downlink ${\tt SIR}$ assuming that the typical user connects to the BS providing the maximum received power.
The growing complexity of heterogeneous cellular networks (HetNets) has necessitated a variety of user and base station (BS) configurations to be considered for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models proposed by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry-based approach, modeling the locations of the users and the K tiers of BSs as independent and homogeneous Poisson point processes (PPPs), has gained prominence in the past f…
Load balancing by proactively offloading users onto small and otherwise lightly-loaded cells is critical for tapping the potential of dense heterogeneous cellular networks (HCNs). Offloading has mostly been studied for the downlink, where it is generally assumed that a user offloaded to a small cell will communicate with it on the uplink as well. The impact of coupled downlink-uplink offloading is not well understood. Uplink power control and spatial interference correlation further complicate the mathematical analysis as compared to the downlink. We propose an accurate and tractable model to …
We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with K classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing s…
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 ra…
Intelligent load balancing is essential to fully realize the benefits of dense heterogeneous networks. Current techniques have largely been studied with single slope path loss models, though multi-slope models are known to more closely match real deployments. This paper develops insight into the performance of biasing and uplink/downlink decoupling for user association in HetNets with dual slope path loss models. It is shown that dual slope path loss models change the tradeoffs inherent in biasing and reduce gains from both biasing and uplink/downlink decoupling. The results show that with the…
The problem of joint downlink cell association (CA) and wireless backhaul bandwidth allocation (WBBA) in two-tier cellular heterogeneous networks (HetNets) is considered. Large-scale antenna array is implemented at the macro base station (BS), while the small cells within the macro cell range are single-antenna BSs and they rely on over-the-air links to the macro BS for backhauling. A sum logarithmic user rate maximization problem is investigated considering wireless backhauling constraints. A duplex and spectrum sharing scheme based on co-channel reverse time-division duplex (TDD) and dynamic…
We derive a general and closed-form result for the success probability in downlink multiple-antenna (MIMO) heterogeneous cellular networks (HetNets), utilizing a novel Toeplitz matrix representation. This main result, which is equivalently the signal-to-interference ratio (SIR) distribution, includes multiuser MIMO, single-user MIMO and per-tier biasing for $K$ different tiers of randomly placed base stations (BSs), assuming zero-forcing precoding and perfect channel state information. The large SIR limit of this result admits a simple closed form that is accurate at moderate SIRs, e.g., above…
In this paper, a comprehensive study of the the downlink performance in a heterogeneous cellular network (or hetnet) is conducted. A general hetnet model is considered consisting of an arbitrary number of open-access and closed-access tier of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs of each tier have a constant transmission power, random fading coefficient with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability and aver…
Heterogeneous networks (HetNets) with offloading is considered as an effective way to meet the high data rate demand of future wireless service. However, the offloaded users suffer from strong inter-tier interference, which reduces the benefits of offloading and is one of the main limiting factors of the system performance. In this paper, we investigate an interference nulling (IN) scheme in improving the system performance by carefully managing the inter-tier interference to the offloaded users in downlink two-tier HetNets with multi-antenna base stations. Utilizing tools from stochastic geom…
The joint user association and spectrum allocation problem is studied for multi-tier heterogeneous networks (HetNets) in both downlink and uplink in the interference-limited regime. Users are associated with base-stations (BSs) based on the biased downlink received power. Spectrum is either shared or orthogonally partitioned among the tiers. This paper models the placement of BSs in different tiers as spatial point processes and adopts stochastic geometry to derive the theoretical mean proportionally fair utility of the network based on the coverage rate. By formulating and solving the network…
Heterogeneous networks (HetNets) with offloading is considered as an effective way to meet the high data rate demand of future wireless service. However, the offloaded users suffer from strong inter-tier interference, which reduces the benefits of offloading and is one of the main limiting factors of the system performance. In this paper, we investigate the use of an interference nulling (IN) beamforming scheme to improve the system performance by carefully managing the inter-tier interference to the offloaded users in downlink two-tier HetNets with multi-antenna base stations. Utilizing tools…
Considering a heterogeneous network (HetNet) where both macro base station (BS) and small cell (SC) nodes are equipped with massive antennas, this paper studies the performance for multiple-input multiple-output (MIMO) downlinks when the macro and small cells share the same spectrum and hence interfere with each other. Suppose that the large-scale antenna arrays at both macro BS and SC nodes employ maximum-ratio transmission (MRT) or zero-forcing transmission (ZFT) precoding, and transmit data streams to the served users simultaneously. A new pilot reuse pattern among SCs is proposed for chann…
This paper considers joint uplink/downlink of an orthogonal frequency division multiple access (OFDMA)-based heterogeneous network (HetNet) consisting of a single macro base station (MBS), multiple femto base stations (FBSs) and access points (APs) where base stations (BSs) can offload data to APs and each mobile user (MU) is able to harvest the received energy using the simultaneous wireless information and power transfer (SWIPT) technique. We also suppose that the harvested energy of MUs are used for their uplink information transmission. We devise a radio resource allocation (RRA) algorithm…
This paper characterizes the statistics of effective fading gain in multi-tier cellular networks with strongest base station (BS) cell association policy. First, we derive the probability of association with the $n$-th nearest BS in the $k$-th tier. Next, we use this result to derive the probability density function (PDF) of the channel fading gain (effective fading) experienced by the user when associating with the strongest BS. Interestingly, our results show that the effective channel gain distribution solely depends upon the original channel fading and the path-loss exponent. Moreover, we …
We study multiple-input multiple-output (MIMO) based downlink heterogeneous cellular network (HetNets) with joint transmit-receive diversity using orthogonal space-time block codes at the base stations (BSs) and maximal-ratio combining (MRC) at the users. MIMO diversity with MRC is especially appealing in cellular networks due to the relatively low hardware complexity at both the BS and user device. Using stochastic geometry, we develop a tractable stochastic model for analyzing such HetNets taking into account the irregular and multi-tier BS deployment. We derive the coverage probability for …
In this paper, we investigate an application of two different beamforming techniques and propose a novel downlink power minimization scheme for a two-tier heterogeneous network (HetNet) model. In this context, we employ time reversal (TR) technique to a femtocell base station (FBS) whereas we assume that a macrocell base station (MBS) uses a zero-forcing-based algorithm and the communication channels are subject to frequency selective fading. Additionally, HetNet's backhaul connection is unable to support a sufficient throughput for signaling information exchange between two tiers. Given the c…
This paper exploits the potential of physical layer security in massive multiple-input multiple-output (MIMO) aided two-tier heterogeneous networks (HetNets). We focus on the downlink secure transmission in the presence of multiple eavesdroppers. We first address the impact of massive MIMO on the maximum receive power based user association. We then derive the tractable upper bound expressions for the secrecy outage probability of a HetNets user.We show that the implementation of massive MIMO significantly improves the secrecy performance, which indicates that physical layer security could be …
Heterogeneous networks (HetNets) have strong interference due to spectrum reuse. This affects the signal-to-interference ratio (SIR) of each user, and hence is one of the limiting factors of network performance. However, in previous works, interference management approaches in HetNets are mainly based on interference level, and thus cannot effectively utilize the limited resource to improve network performance. In this paper, we propose a user-centric interference nulling (IN) scheme in downlink two-tier HetNets to improve network performance by improving each user's SIR. This scheme has three…
Considering both small-scale fading and long-term shadowing, we characterize the downlink rate distribution at a typical user equipment (UE) in a heterogeneous cellular network (HetNet), where shadowing, following any general distribution, impacts cell selection while fading does not. Prior work either ignores the impact of channel randomness on cell selection or lumps all the sources of randomness into a single variable, with cell selection based on the instantaneous signal strength, which is unrealistic. As an application of the results, we study the impact of shadowing on load balancing in …
The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models considered by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry based approach modeling the user and BS locations as independent and homogeneous Poisson point processes (PPPs) has gained prominence in the past few years. Despite its …
Real-time distributed control is a promising application of 5G in which communication links should satisfy certain reliability guarantees. In this letter, we derive closed-form maximum average rate when a device (e.g. industrial machine) downloads a sequence of n operational commands through cellular connection, while guaranteeing a certain signal-to-interference ratio (SIR) coverage for all n messages. The result is based on novel closed-form n-successive SIR coverage bounds. The proposed bounds provide simple approximations that are increasingly accurate in the high reliability region.
Massive multiple-input multiple-output (massive MIMO) and small cell densification are complementary key 5G enablers. Given a fixed number of the entire base-station antennas per unit area, this paper fairly compares (i) to deploy few base stations (BSs) and concentrate many antennas on each of them, i.e. massive MIMO, and (ii) to deploy more BSs equipped with few antennas, i.e. small cell densification. We observe that small cell densification always outperforms for both signal-to-interference ratio (SIR) coverage and energy efficiency (EE), when each BS serves multiple users via L number of …
We consider the spatial stochastic model of single-tier downlink cellular networks, where the wireless base stations are deployed according to a general stationary point process on the Euclidean plane with general i.i.d. propagation effects. Recently, Ganti & Haenggi (2016) consider the same general cellular network model and, as one of many significant results, derive the tail asymptotics of the signal-to-interference ratio (SIR) distribution. However, they do not mention any conditions under which the result holds. In this paper, we compensate their result for the lack of the condition and e…
The meta distribution of the signal-to-interference ratio (SIR) provides fine-grained information about the performance of individual links in a wireless network. This paper focuses on the analysis of the meta distribution of the SIR for both the cellular network uplink and downlink with fractional power control. For the uplink scenario, an approximation of the interfering user point process with a non-homogeneous Poisson point process is used. The moments of the meta distribution for both scenarios are calculated. Some bounds, the analytical expression, the mean local delay, and the beta appr…
Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and …
In heterogeneous networks (HetNets), strong interference due to spectrum reuse affects each user's signal-to-interference ratio (SIR), and hence is one limiting factor of network performance. In this paper, we propose a user-centric interference nulling (IN) scheme in a downlink large-scale HetNet to improve coverage/outage probability by improving each user's SIR. This IN scheme utilizes at most maximum IN degree of freedom (DoF) at each macro-BS to avoid interference to uniformly selected macro (pico) users with signal-to-individual-interference ratio (SIIR) below a macro (pico) IN threshold…
We develop an analytical framework to derive the meta distribution and moments of the conditional success probability (CSP), which is defined as {success probability for a given realization of the transmitters}, in large-scale co-channel uplink and downlink non-orthogonal multiple access (NOMA) networks with one NOMA cluster per cell. The moments of CSP translate to various network performance metrics such as the standard success or signal-to-interference ratio (SIR) coverage probability (which is the $1$-st moment), the mean local delay (which is the $-1$-st moment in a static network setting…
One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing K-tier Poisson Point Process (PPP) HetNet model by consideri…
Motivated by heterogeneous networks (HetNets) design in improving coverage and by millimeter-wave (mmWave) transmission offering an abundance of extra spectrum, we present a general analytical framework shedding light to the downlink of realistic mmWave HetNets consisting of $K$ tiers of randomly located base stations (BSs). Specifically, we model, by virtue of stochastic geometry tools, the \textit{multi-tier} \textit{multi-user multiple-input multiple-output (MU-MIMO) mmWave} network degraded by the inevitable \textit{residual additive transceiver hardware impairments (RATHIs)} and \textit{c…
One of the goals of 5G wireless systems stated by the NGMN alliance is to provide moderate rates (50+ Mbps) everywhere and with very high reliability. We term this service Ultra-Reliable Ubiquitous-Rate Communication (UR2C). This paper investigates the role of frequency reuse in supporting UR2C in the downlink. To this end, two frequency reuse schemes are considered: user-specific frequency reuse (FRu) and BS-specific frequency reuse (FRb). For a given unit frequency channel, FRu reduces the number of serving user equipments (UEs), whereas FRb directly decreases the number of interfering base …
In this paper, we investigate the downlink performance of a three-tier heterogeneous network (HetNet). The objective is to enhance the edge capacity of a macro cell by deploying unmanned aerial vehicles (UAVs) as flying base stations and small cells (SCs) for improving the capacity of indoor users in scenarios such as temporary hotspot regions or during disaster situations where the terrestrial network is either insufficient or out of service. UAVs are energy-constrained devices with a limited flight time, therefore, we formulate a two layer optimization scheme, where we first optimize the pow…
Two key traits of 5G cellular networks are much higher base station (BS) densities - especially in the case of low-power BSs - and the use of massive MIMO at these BSs. This paper explores how massive MIMO can be used to jointly maximize the offloading gains and minimize the interference challenges arising from adding small cells. We consider two interference management approaches: joint transmission (JT) with local precoding, where users are served simultaneously by multiple BSs without requiring channel state information exchanges among cooperating BSs, and resource blanking, where some macr…
Full-duplex (FD) transmission in a point-to-point (P2P) link, wherein bidirectional traffic flows simultaneously share the same spectrum, has the capability of doubling the link rate by completely removing self-interferences. However, the rate gain of FD transmission in an interference-limited network is not as clear as a P2P link due to the interferences induced by complex FD and half-duplex (HD) transmission behaviors in the network. To thoroughly investigate the achievable link rates of users and base stations (BSs) in a heterogeneous network (HetNet) with decoupled user association, a gene…
In this paper, we study the downlink performance of a heterogeneous cellular network (HetNet) where both macro and small cells share the same spectrum and hence interfere with each other. We assume that the users are concentrated at certain areas in the cell, i.e., they form hotspots. While some of the hotspots are assumed to have a small cell in their vicinity, the others are directly served by the macrocell. Due to a relatively small area of each hotspot, the users lying in a particular hotspot appear to be almost co-located to the macrocells, which are typically deployed at some elevation. …
We introduce a simple yet powerful and versatile analytical framework to approximate the SIR distribution in the downlink of cellular systems. It is based on the mean interference-to-signal ratio and yields the horizontal gap (SIR gain) between the SIR distribution in question and a reference SIR distribution. As applications, we determine the SIR gain for base station silencing, cooperation, and lattice deployment over a baseline architecture that is based on a Poisson deployment of base stations and strongest-base station association. The applications demonstrate that the proposed approach u…
In this paper, we pioneer the study of physical-layer security in heterogeneous networks (HetNets). We investigate secure communications in a two-tier downlink HetNet, which comprises one macrocell and several femtocells. Each cell has multiple users and an eavesdropper attempts to wiretap the intended macrocell user. Firstly, we consider an orthogonal spectrum allocation strategy to eliminate co-channel interference, and propose the secrecy transmit beamforming only operating in the macrocell (STB-OM) as a partial solution for secure communication in HetNet. Next, we consider a secrecy-orient…
In this paper, we analyze the downlink coverage probability and rate of an aerial user in vertical HetNets (VHetNets) comprising aerial base stations (aerial-BSs) and terrestrial-BSs. The locations of terrestrial-BSs are modeled as an infinite 2-D Poisson Point Process (PPP), while the locations of aerial-BSs are modeled as a finite 2-D Binomial Point Process (BPP). Our cellular-to-air (C2A) channel model incorporates line-of-sight (LoS) and non-LoS transmissions between terrestrial-BSs and a typical aerial user, while we assume LoS transmissions for all aerial links. We assume that the aerial…
In this paper, we present the downlink coverage and rate analysis of a cellular vehicle-to-everything (C-V2X) communication network where the locations of vehicular nodes and road side units (RSUs) are modeled as Cox processes driven by a Poisson line process (PLP) and the locations of cellular macro base stations (MBSs) are modeled as a 2D Poisson point process (PPP). Assuming a fixed selection bias and maximum average received power based association, we compute the probability with which a {\em typical receiver}, an arbitrarily chosen receiving node, connects to a vehicular node or an RSU a…
Meta distribution is a fine-grained unified performance metric that enables us to evaluate the {reliability and latency} of next generation wireless networks, in addition to the conventional coverage probability. In this paper, using stochastic geometry tools, we develop a systematic framework to characterize the meta distributions of the downlink signal-to-interference-ratio (SIR)/signal-to-noise-ratio (SNR) and data rate of a typical device in a cellular network with coexisting sub-6GHz and millimeter wave (mm-wave) spectrums. Macro base-stations (MBSs) transmit on sub-6GHz channels (which w…
This paper characterizes the performance of coordinated beamforming with dynamic clustering. A downlink model based on stochastic geometry is put forth to analyze the performance of such base station (BS) coordination strategy. Analytical expressions for the complementary cumulative distribution function (CCDF) of the instantaneous signal-to-interference ratio (SIR) are derived in terms of relevant system parameters, chiefly the number of BSs forming the coordination clusters, the number of antennas per BS, and the pathloss exponent. Utilizing this CCDF, with pilot overheads further incorporat…
