Achievable rates optimization for broadcast channels using finite size constellations under transmission constraints
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Achievable rates optimization for broadcast channels using finite size constellations under transmission constraints Zeina Mheich1,2,3 , Florence Alberge1,2,3* and Pierre Duhamel1,2,3
Abstract In this paper, maximal achievable rate regions are derived for power-constrained AWGN broadcast channel involving finite constellations and two users. The achievable rate region is studied for various transmission strategies including superposition coding and compared to standard schemes such as time sharing. The maximal achievable rates are obtained by optimizing over both the joint distribution of probability and over the constellation symbol positions. A numerical solution is proposed for solving this non-convex optimization problem. Then, we consider several variations of the same problem by introducing various constraints on the optimization variables. The aim is to evaluate efficiency vs. complexity tradeoffs of several transmission strategies, some of which (the simplest ones) can be found in actual standards. The improvement for each scheme is evaluated in terms of SNR savings for target achievable rates or/and percentage of gain in achievable rates for one user compared to a reference scheme. As an application, two scenarios of coverage areas and user alphabets are considered. This study allows to evaluate with practical criteria the performance improvement brought by more advanced schemes. Keywords: AWGN broadcast channels; Achievable rate region; Hierarchical modulation; Superposition modulation; Superposition coding; Constellation shaping; Non-convex optimization
1 Introduction During the past few decades, information networks have witnessed tremendous and rapid advances, based on the important growth in the adoption of new wireless technologies, applications and services, first from cellular networks and more recently for computer networks (WLANs). Consequently, wireless networks are exposed to capacity and coverage problems, and the focus is now shifting towards capturing some of the aspects of realistic networks by studying natural network models such as models with broadcasting. In 1972, achievable rate region is obtained by Cover in [1] for Gaussian broadcast channels with two outputs and generalized by Bergmans to broadcast channels with any number of outputs [2]. Roughly a year later, the optimality of the sets of achievable rates was established *Correspondence: [email protected] 1 University Paris-Sud, UMR8506 Orsay, F-91405, France 2 CNRS, Gif-sur-Yvette, F-91192, France
by Bergmans [3] and Gallager [4]. Superposition coding is a possible solution to achieve good rate regions in which information intended for high-noise receivers and information intended for low-noise receivers are superimposed and transmitted simultaneously on the same radio resource. The low-noise receivers can always decode messages intended for the high-noise receivers. Thus, they effectively cancel out the interference due to the signal intended for the high-noise receivers, and then decode their ow
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