S. Alireza Banani

Analyzing the Impact of Access Point Density on the Performance of Finite-Area Networks

Assuming a network of infinite extent, several researchers have analyzed small-cell networks using a Poisson point process (PPP) location model, leading to simple analytic expressions. The general assumption has been that these results apply to finite-area networks as well. However, do the results of infinite-area networks apply to finite-area networks? In this paper, we answer this question by obtaining an accurate approximation for the achievable signal-to-interference-plus-noise ratio (SINR) and user capacity in the downlink of a finite-area network with a fixed number of access points (APs). The APs are uniformly distributed within the area of interest. Our analysis shows that, crucially, the results of infinite-area networks are very different from those for finite-area networks of low-to-medium AP density. Comprehensive simulations are used to illustrate the accuracy of our analysis. For practical values of signal transmit powers and AP densities, the analytic expressions capture the behavior of the system well. As an added benefit, the formulations developed here can be used in parametric studies for network design. Here, the analysis is used to obtain the required number of APs to guarantee a desired target capacity in a finite-area network.

Point-Wise Sum Capacity Maximization in LTE-A Coordinated Multi-Point Downlink

Coordinated Multi-Point (CoMP) for Long Term Evolution Advanced (LTE-A) systems refers to a range of techniques to increase the capacity averaged over the cell, and also at the cell edge where the path loss is usually highest. In this paper, the problem of power allocation is first addressed for maximizing the sum capacity at each point of the coverage area in a CoMP multi-user downlink. Then, based on targeting the minimum value of the maximized sum capacity, a design approach is presented for obtaining an optimal size of the cells in a wireless network. The approach guarantees that the sum capacity at each point of the coverage area is above the target value. The path loss model is pivotal for the outcome of this type of performance analysis and the ensuing system design. Here, a simplistic, standard path loss model is used, but the approach can use other models.

Analyzing the reduced required BS density due to CoMP in cellular networks

In this paper we investigate the benefit of base station (BS) cooperation in the uplink of coordinated multi-point (CoMP) networks. Our figure of merit is the required BS density required to meet a chosen rate coverage. Our model assumes a 2-D network of BSs on a regular hexagonal lattice in which path loss, lognormal shadowing and Rayleigh fading affect the signal received from users. Accurate closed-form expressions are first presented for the sum-rate coverage probability and ergodic sum-rate at each point of the cooperation region. Then, for a chosen quality of user rate, the required density of BS is derived based on the minimum value of rate coverage probability in the cooperation region. The approach guarantees that the achievable rate in the entire coverage region is above a target rate with chosen probability. The formulation allows comparison between different orders of BS cooperation, quantifying the reduced required BS density from higher orders of cooperation.

A Perturbed Hexagonal Lattice to Model Basestation Locations in Real-World Cellular Networks

For the emerging heterogeneous networks, the theoretical analysis has been largely limited to using a Poisson point process (PPP) model for the locations of base stations (BSs). This model has been shown to provide a lower bound on the coverage probability (CP) when compared with real-world deployments; as such, in this paper, we focus on a perturbed hexagonal lattice model. We show that, as compared to a PPP, this model better fits the locations of BSs in real-world cellular networks. We provide a tractable analysis for the signal-to-interference (SIR) CP at any point of an interference-limited reuse-1 network. Simulation results help illustrate the accuracy of the theory developed. The resulting average SIR CP (averaged over the network area) lies in between that of the PPP and the perfect hexagonal lattice models. The perturbation allows us to quantify the loss in the CP in moving from a perfect lattice model to a random BS deployment. Finally, we compare the perturbed lattice to real-world BS deployments using data from publicly available databases. Using the method of minimum contrast we show that the average SIR CP from the presented formulation accurately fits that of real-world cellular networks.

The penalty for random deployment in hexagonal lattice networks with perturbed interferers

Base station (BS) locations are usually modelled using one of two extremes: at one end is a deterministic, hexagonal, location model; while at the other is a random deployment following a Poisson point process (PPP). However, real-world networks follow neither extreme; as such, in this paper, we focus on a modified perturbed hexagonal lattice model that, in terms of regularity, lies in between the PPP and the perfect hexagonal lattice models. In our modified perturbed hexagonal lattice, the location of all interfering BSs, except for the serving BS under consideration, are perturbed. We provide a simple and tight upper bound on the average total interference in an interference-limited reuse-1 network. The bound is presented in the form of a polynomial in the distance from the serving BS and another polynomial in the normalized perturbation. The presented formulation is useful in obtaining simple analytical expressions for various network parameters such as SIR and/or coverage probability. As an added benefit, the formulations here quantify the loss in the coverage probability in moving from the perfect lattice model to a random BS deployment. We use simulations to illustrate the accuracy of the theory developed.

Sum Capacity of Block-Diagonalized Multiuser MIMO Downlink with Channel Estimation and Finite-Rate CSI Feedback Link

A multiuser multi-input multi-output (MU-MIMO) downlink system with block diagonalization-based precoding is presented with a study of the impact of limited bandwidth resource for the feedback-links on the sum capacity. The channel estimation is acquired at each user via downlink training, and the linear quantized form of estimated channels is fed back to the base station (BS) via noisy, finite-rate channel state information (CSI) feedback-links. Two architectures for CSI feedback are considered: parallel feedback where there is a feedback-link for each user; and serial feedback where a single feedback-link is used for all the users. The sum capacity is formulated as a function of the link parameters, enabling optimization of the number of training symbols and required feedback bits with the criterion of maximum sum capacity. The approach allows a performance comparison for different feedback architectures, the number of transmit antennas, and the number of users. The effect of time variations of the channel is analyzed via simulation, quantifying the loss of sum capacity relative to the case with perfect CSI for different Doppler frequencies.

Analyzing Dependent Placements of Small Cells in a Two-Layer Heterogeneous Network with a Rate Coverage Constraint

We consider the downlink of a two-layer heterogeneous network, comprising macrocells (MCs) and small cells (SCs). The existing literature generally assumes independent placements of the access points (APs) in different layers; in contrast, we analyze a dependent placement where SC APs are placed at locations with poor service from the MC layer. Our goal is to obtain an estimate of the number of SCs required to maintain a target outage rate. Such an analysis is trivial if the MCs are located according to a Poisson point process (PPP), which provides a lower bound on performance. Here, we consider MCs placed on a hexagonal grid, which complements the PPP model by providing an upper bound on performance. We first provide accurate bounds for the average interference within an MC when SCs are not used. Then, by obtaining the outage areas, we estimate the number of SCs required within an MC to overcome outage. If resource allocation among SCs is not used, we show that the problem of outage is not solved completely and that the residual outage area depends on whether cochannel or orthogonal SCs are used. Simulations show that a much smaller residual outage area is obtained with orthogonal SCs.

Analyzing the Impact of Inter Cooperation Region Interference in Coordinated Multi-Point Uplink Networks

We analyze the uplink of coordinated multi-point (CoMP) networks in which cooperation can be amongst N = 2 or N = 3 base stations (BSs). We consider a 2-D network of BSs on a regular hexagonal lattice wherein the cooperation tessellates the 2-D plane into cooperation regions (CRs); specifically, we analyze the impact of the interference between the CRs in the network. Our model accounts realistic propagation conditions, particularly including shadowing. We obtain accurate, closed-form, approximations for the user capacity coverage probability (CCP) and the ergodic capacity at each point within the CR. To provide a network-level analysis, we focus on the locations within each CR with the minimum CCP - “the worst-case point(s)”. The worst-case CCP and/or ergodic capacity can be used in parametric studies for network design. Here, the analysis is applied to obtain the relationship between cell size and CCP and, thereby, the required density of BSs to achieve a chosen target capacity coverage. The analysis also allows for a comparison between different orders of BS cooperation, quantifying the reduced required BS density from higher orders of cooperation. Comprehensive simulations are used to illustrate the accuracy of our analysis, including the approximations used for analytic tractability.

Design and Deployment of Small Cell Networks: Required number of small cell access points in heterogeneous wireless networks

How many small cell (SC) access points (APs) are required to guarantee a chosen quality of service in a heterogeneous network? In this chapter, we answer this question considering two different network models. The first is the downlink of a finite-area SC network where the locations of APs within the chosen area are uniformly distributed. A key step in obtaining the closed-form expressions is to generalize the well-accepted moment matching approximation for the linear combination of lognormal random variables. For the second model, we focus on a two-layer downlink heterogeneous network with frequency reuse-1 hexagonal macro cells (MCs), and SC APs that are placed at locations that do not meet a chosen quality of service from macro base stations (BSs). An important property of this model is that the SC AP locations are coupled with the MC coverage. Here, simple bounds for the average total interference within an MC makes the formulation possible for the percentage of MC area in outage, as well as the required average number of SCs (per MC) to overcome outage, assuming isolated SCs. Introduction Heterogeneous cellular networks (HCNs) are being considered as an efficient way to improve system capacity as well as effectively enhance network coverage [1, 2]. Comprising multiple layers of access points (APs), HCNs encompass a conventional macro cellular network (first layer) overlaid with a diverse set of small cells (SCs) (higher layers). Cell deployment is an important problem in heterogeneous networks, both in terms of the number and positioning of the SCs. Traditional network models are either impractically simple (such as the Wyner model [3]) or excessively complex (e.g., the general case of random user locations in a hexagonal lattice network [4]) to accurately model SC networks. A useful mathematical model that accounts for the randomness in SC locations and irregularity in the cells uses spatial point processes, such as Poisson point process (PPP), to model the location of SCs in the network [5–10]. The independent placement of SCs from the MC layer, has the advantage of analytical tractability and leads to many useful SINR and/or rate expressions. However, even assuming that wireless providers would deploy SCs to support mobile broadband services, the dominant assumption remains that SCs are deployed randomly and independent of the MC layer [11].

The density penalty for random deployments in uplink CoMP networks

We consider a coordinated multi-point (CoMP) uplink cellular network with a Poisson point process (PPP) model for the position of BSs. Our model assumes cooperation amongst two BSs and the required density is obtained under shadowing and Rayleigh fading for different LTE-A path loss models. We obtain accurate closed-form approximations for the worst-case rate coverage probability within the cooperation region. The approximations presented are useful for a rapid assessment of network performance and can be utilized in parametric studies for network design. Here, they are applied to obtain the required density of BSs to achieve a target rate coverage probability. As an added benefit, the formulation here quantifies the penalty in moving from a regular BS deployment (the grid model) to a random BS deployment (the PPP model).