Sayandev Mukherjee

Distribution of Downlink SINR in Heterogeneous Cellular Networks

The Signal to Interference Plus Noise Ratio (SINR) on a wireless link is an important basis for consideration of outage, capacity, and throughput in a cellular network. It is therefore important to understand the SINR distribution within such networks, and in particular heterogeneous cellular networks, since these are expected to dominate future network deployments . Until recently the distribution of SINR in heterogeneous networks was studied almost exclusively via simulation, for selected scenarios representing pre-defined arrangements of users and the elements of the heterogeneous network such as macro-cells, femto-cells, etc. However, the dynamic nature of heterogeneous networks makes it difficult to design a few representative simulation scenarios from which general inferences can be drawn that apply to all deployments. In this paper, we examine the downlink of a heterogeneous cellular network made up of multiple tiers of transmitters (e.g., macro-, micro-, pico-, and femto-cells) and provide a general theoretical analysis of the distribution of the SINR at an arbitrarily-located user. Using physically realistic stochastic models for the locations of the base stations (BSs) in the tiers, we can compute the general SINR distribution in closed form. We illustrate a use of this approach for a three-tier network by calculating the probability of the user being able to camp on a macro-cell or an open-access (OA) femto-cell in the presence of Closed Subscriber Group (CSG) femto-cells. We show that this probability depends only on the relative densities and transmit powers of the macro- and femto-cells, the fraction of femto-cells operating in OA vs. Closed Subscriber Group (CSG) mode, and on the parameters of the wireless channel model. For an operator considering a femto overlay on a macro network, the parameters of the femto deployment can be selected from a set of universal curves.

Distributions of Transmit Power and SINR in Device-to-Device Networks

We study the spatial distribution of transmit powers and signal to interference plus noise ratio (SINR) in device-to-device (D2D) networks. Using homogeneous Poisson Point Processes (PPP), cumulative distribution function (CDF) of the transmit power and SINR are analytically derived for a D2D network employing power control. Then, computer simulations are performed for the same network architecture and it is shown that device location modeling and analytical methods from stochastic geometry can enable us to obtain transmit power and SINR distributions of a D2D network.

Dynamic TDD support in the LTE-B enhanced Local Area architecture

The Third Generation Partnership Project (3GPP) has been studying dynamic allocation of sub-frames to uplink (UL) or downlink (DL) in Time Division Duplex (TDD), called `Dynamic TDD, since the Long Term Evolution (LTE) Rel. 11 timeframe. At the same time, 3GPP is also standardizing Enhanced Local Area (eLA) small-cell heterogeneous architectures for inclusion in LTE-B (LTE Rel. 12) as a solution offering high data rate to user terminals (UEs) along with high system capacity through spatial reuse of spectrum. In this paper, we focus on a particular eLA architecture proposed by DOCOMO, called the Phantom Cell architecture, that has the option to support dynamic TDD. For an arbitrarily-located UE in an eLA cell network, we apply results from stochastic geometry to derive expressions for the distribution of DL signal to interference plus noise ratio (SINR) at an arbitrary UE and the distribution of UL SINR at its serving eLA base station (BS). We use these results to study aspects of eLA cell system design, and the sensitivity of SINR to the extent of coordination across eLA cells employing dynamic TDD.

Downlink SINR distribution in a heterogeneous cellular wireless network with biased cell association

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.

Effects of range expansion and interference coordination on capacity and fairness in heterogeneous networks

Range expansion and inter-cell interference coordination can improve the capacity and fairness of heterogeneous networks by off-loading macrocell users to low-power nodes like picocells. In contrast to previous studies, which rely mostly on simulations, we here consider analytical models for base station and user (UE) locations in a macro network with pico-cell overlay and derive closed-form expressions for the distribution of the signal to interference plus noise ratio (SINR) and spectral efficiencies (SEs) of UEs associated with macro- and pico-cells. These results illuminate the effects on SE of (i) duration of the macro almost blank subframes (ABSs), (ii) the SINR threshold for a UE to be served by a picocell during ABSs, and (iii) the range expansion bias. They also help determine the optimum settings of these parameters.

Dynamic TDD Support in Macrocell-Assisted Small Cell Architecture

Dynamic allocation of subframes to uplink (UL) or downlink (DL) in time division duplex (TDD), termed `Dynamic TDD, has been studied by the 3rd Generation Partnership Project (3GPP) since the Long Term Evolution (LTE) Release 11 timeframe. At the same time, 3GPP is also standardizing macrocell-assisted small cell heterogeneous architectures for inclusion in LTE Release 12 as a solution offering high data rate to user terminals (UEs) along with high system capacity through spatial reuse of spectrum. In this paper, we focus on a particular small cell architecture proposed by DOCOMO, known as the Phantom Cell architecture, which provides the option to support dynamic TDD. For an arbitrarily-located UE in a small cell network, we apply results from stochastic geometry to derive expressions for the distribution of DL signal to interference plus noise ratio (SINR) at an arbitrary UE and the distribution of UL SINR at its serving base station (BS). The analytical results are verified by system level simulations. These results can be used to study aspects of system design for small cells, and the sensitivity of SINR to the extent of synchronization across small cells employing dynamic TDD. In order to deal with the severe inter-cell interference (ICI) problem in dynamic TDD, we further propose a frequency domain interference coordination technique. Finally, system level simulations based on more realistic system models and assumptions are conducted to evaluate the performance of dynamic TDD systems and the proposed interference coordination technique.

Capacity analysis of LTE-Advanced HetNets with reduced power subframes and range expansion

The use of reduced power subframes in LTE Rel. 11 can improve the capacity of heterogeneous networks (HetNets) while also providing interference coordination to the picocell-edge users. However, in order to obtain maximum benefits from the reduced power subframes, setting the key system parameters, such as the amount of power reduction, carries critical importance. Using stochastic geometry, this paper lays down a theoretical foundation for the performance evaluation of HetNets with reduced power subframes and range expansion bias. The analytic expressions for average capacity and 5th percentile throughput are derived as a function of transmit powers, node densities, and interference coordination parameters in a two-tier HetNet scenario and are validated through Monte Carlo simulations. Joint optimization of range expansion bias, power reduction factor, scheduling thresholds, and duty cycle of reduced power subframes is performed to study the trade-offs between aggregate capacity of a cell and fairness among the users. To validate our analysis, we also compare the stochastic geometry-based theoretical results with the real macro base station (MBS) deployment (in the city of London) and the hexagonal grid model. Our analysis shows that with optimum parameter settings, the LTE Rel. 11 with reduced power subframes can provide substantially better performance than the LTE Rel. 10 with almost blank subframes, in terms of both aggregate capacity and fairness.

Energy Efficiency in the Phantom Cell enhanced Local Area architecture

The Third Generation Partnership Project (3GPP) is presently standardizing Enhanced Local Area (eLA) small-cell heterogeneous architectures for inclusion in Long Term Evolution (LTE) Release 12 as a solution offering high data rate to user terminals (UEs) along with high system capacity through spatial reuse of spectrum. At the same time, Energy Efficiency (EE) is becoming an important metric in evaluating the next generation of small cell networks. In this paper, we focus on a particular eLA architecture proposed by DOCOMO, called the Phantom Cell architecture. We use results from stochastic geometry to compare the EE of the phantom cell architecture versus the baseline small cell network, defined as a conventional frequency division duplex (FDD) LTE pico-cell deployment that uses the same spectrum as the underlying macrocellular network.

Analysis of UE Outage Probability and Macrocellular Traffic Offloading for WCDMA Macro Network with Femto Overlay under Closed and Open Access

Downlink coverage issues for macrocellular users (UEs) in a macrocellular network with Closed Subscriber Group (CSG) femtocellular overlay have so far been investigated almost exclusively via simulation. However, consideration of specific scenarios via simulation may not provide general insights applicable to long-term planning for femto-macro deployments. In this paper, we employ general models for macro Node B and femto access point (AP) locations to derive analytical expressions for the probability that an arbitrary UE cannot be served a macro Node B because of interference on the downlink from a nearby femto AP under CSG, and for the probability that the UE is served by the femto AP instead, if the femto AP operates with Open Access (OA). These expressions depend only on the ranges and densities of the macro Node Bs and femto APs, and on the parameters of the wireless channel model. We then show how to apply these results to compute measures of the fraction of overall macrocellular traffic that could be offloaded to an OA femtocellular network, thereby reducing the load on the macrocellular backhaul and increasing overall system capacity. These results are of interest to operators weighing the capacity vs. coverage tradeoff of a femtocellular overlay on a macrocellular network.

An LTE offload solution using small cells with D2D links

Small cells are an attractive technology for offloading traffic from the macrocellular network. The first small cell architecture for offload was the femto cell, but it was not widely commercially deployed. This is because it had some drawbacks in terms of network planning such as interference handling. In this paper, we propose and study a new concept for a low-cost small cell base station (BS) for traffic offloading from the macrocellular network. The main difference from a femto cell is that the communication with the user terminal (UE, in 3GPP terminology) uses the device-to-device (D2D) radio interface. The D2D radio interface is chosen because of the close proximity between UEs and small-cell BSs and its support for opportunistic access and flexible resource allocation. The proposed concept also increases operational efficiency by reducing the network planning effort required by the projected increased deployment density of BSs to meet future traffic demand. We describe the benefits of this offload solution for LTE networks and quantify the gains via analysis and simulation.