Capacity of Cellular Uplink with Multiple Tiers of Users and Path Loss

Abstract-With the emergence and continuous growth of wireless data services, the value of a wireless network is not only defined by how many users it can support, but also by its ability to deliver higher data rates. Information theoretic capacity of cellular systems with fading is usually estimated using models originally inspired by Wyner's Gaussian Cellular Multiple Access Channel (GCMAC). In this paper we extend this model to study the cellular system with users distributed over the cellular coverage area. Based on the distance from the cellsite receiver, users are grouped as tiers, and received signals from each tier are scaled using a distance dependent attenuation factor. The optimum capacity in fading environment is then found by calculating the path-loss for users in each tier using a specific path-loss law and some interesting insights are derived. The results correspond to a more realistic model which boils down to Wyner's model with fading, with appropriate substitutions of parameter values. The results are verified using Wyner's model with fading and Monte-Carlo simulations. Insights are provided for the real world scenarios

Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC

This article presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs). This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading matrix G and the channel path gain matrix Ω. This article demonstrates that the actual capacity converges to the theoretical upper bound under the constraints like low signal-to-noise ratios and limiting channel path gain among the MTs and the respective base station of interest. In order to determine the usefulness of the HUB, the behavior of the theoretical upper bound is critically observed specially when the inter-cell and the intra-cell time sharing schemes are employed. In this context, we derive an analytical form of HUB by employing an approximation approach based on the estimation of probability density function of trace of Hadamard product of two matrices, i.e., G and Ω. A closed form of expression has been derived to capture the effect of the MT distribution on the optimum joint decoding capacity of C-GCMAC. This article demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity of Wyner GCMAC

Fundamental limits of GCMAC with fading.

The scientific field of information theory provides a mathematical framework which aims to quantify the maximum achievable data rate over a communication channel. The underlying mathematical concepts to predict the capacity of a single communication link were developed by Shannon more than half a century ago. The first important attempt to study the capacity of a cellular system was carried out in the last decade. That work by Wyner introduced the concept of Base Station co-operation. The available information theoretic findings are not directly usable to provide realistic estimates for the capacity of practical systems since they cannot model the effect of changes in physical parameters in the environment like path loss exponent and the distance between the adjacent cell sites. The objective of this work is to extend the known formulations for the capacity of the Gaussian Cellular Multiple Access Channel (GCMAC) with joint processing by incorporating path loss and other channel conditions that represent a real communication system and thus to provide a more realistic analytical upper bound for the capacity of the wireless cellular network. In this direction, the available GCMAC model with joint processing and small scale fading is extended by adding multiple antennas at the Base Stations (BSs) and User Terminals (UTs) and by removing the assumption that UTs are co-located at the BS position. Since it is concluded that the available GCMAC model is not sufficient to analyse more complex systems a new model is built which enables the evaluation of the achievable capacity of more realistic systems. Based on this model a new geometric and mathematical model is also developed which enables the study of fairness and user rate distribution in joint processing systems with small and large scale fading. The analysis provides several achievable capacity formulae and some very useful insights on the behavior of the sum rate as well as the fairness, when certain system parameters change, are derived. The formulae can be used to evaluate the achievable sum rate of practical systems employing full BS co-operation, given the parameters that control that capacity

Uplink Capacity of Variable-Density Cellular System with Distributed Users and Fading

In this paper, we extend the well-known model for Gaussian Cellular Multiple Access Channel originally presented by Wyner and later extended by Somekh et al. with fading. The extension to the model, incorporates the distance dependent path loss (maintaining a close relevance to path loss values in real world cellular systems) experienced by the users distributed in a planar cellular array. The density of base stations and hence the cell sizes are variable. In the context of Hyper-receiver joint decoder, a closed form expression for the information theoretic capacity is obtained assuming large number of users in each cell. The effect of the path loss factor, on the information theoretic capacity of the cellular system, is quantified and it is observed that higher path loss factor results in lower capacity. The results validate that larger cell sizes result in lower spectral efficiency. The closed form formula derived by the mathematical analysis is also validated by Monte Carlo simulations

Information theoretic capacity of Gaussian cellular multiple-access MIMO fading channel

Higher spectral efficiency can be achieved by exploiting the space dimension inherent to any wireless communication system using multiple receiver and multiple transmitter antennas (MIMO). There are several results that provide closed form solutions for acellular system with a single antenna at each base station and each user terminal. Results are also available for the single cell case with MIMO. A cellular system with multiple antennas at the transmitter and the receiver nodes has not been investigated to obtain a closed form solution for the capacity limit. The main information theoretic theorems are not directly applicable to this system because of the form of the channel matrix of such a system. In this paper we extend the well known Wyner's model to a MIMO cellular system. It is observed that the achievable rate is bound by an upper limit and lower limit corresponding to two extreme fading conditions: channel with Rayleigh fading and with no fading. The analytical results are verified using Monte Carlo simulations. The analysis provides the insight that for a cellular system, increasing the number of transmitting antennas is not beneficial to increase the achievable rate, and this is reflected in the results obtained

Information Theoretic Capacity of a Gaussian Cellular Multiple-Access MIMO Fading Channel

Information Theoretic Capacity of a Gaussian Cellular Multiple-Access MIMO Fading Channe