Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC
- PDF / 414,766 Bytes
- 13 Pages / 595.28 x 793.7 pts Page_size
- 28 Downloads / 176 Views
RESEARCH
Open Access
Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC Muhammad Zeeshan Shakir1,2*, Tariq S Durrani2 and Mohamed-Slim Alouini1
Abstract 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. 1. Introduction The ever growing demand for communication services has necessitated the development of wireless systems with high bandwidth and power efficiency [1,2]. In the last decade, recent milestones in the information theory of wireless communication systems with multiple antenna and multiple users have offered additional newfound hope to meet this demand [3-11]. Multiple input multiple output (MIMO) technology provides substantial gains over single antenna communication systems, however the cost of deploying multiple antennas at the mobile terminals (MTs) in a cellular network can be prohibitive, at least in the immediate future [3,8]. In this context, distributed MIMO approach is a means of realizing the gains of MIMO with single antenna terminals in a cellular network allowing a gradual migration to a * Correspondence: [email protected] 1 Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology, KAUST, Thuwa1 23599-6900, Makkah Province, Kingdom of Saudi Arabia Full list of author information is available at the end of the article
true MIMO cellular network. This approach requires some level of cooperation among the network terminals which can be accomplished through suitably designed protocols [4-6,12-16]. Toward this end, in the last few decades, numero
Data Loading...