Asymptotic Capacity Allocation for an Out-of-Cell User in Non-Orthogonal Multiple Access With Coordinated Direct and Relay Transmission

Abstract

An out-of-cell user (referred to UE2) is usually required to receive or send signals from or to a base station (BS) that is connected to wider area networks. In order to provide a wireless connection between BS and UE2 and hence extend their radio coverage, putting a relay between BS and UE2 is widely accepted. The relayed UE2 signal occupies a part of bandwidth that is originally allocated to an in-cell user (referred to UE1) and then UE2 shares UE1's capacity. Especially for single-antenna users, the asymptotic capacity that can be achieved when signal-to-noise power ratio (SNR) ρ goes to infinity is given by log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (ρ) for UE1. By using the in-cell relay, the capacity is divided into β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (ρ) and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (ρ) for UE1 and UE2, respectively, where β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ≤ 1, 0 ≤ β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ≤ 1. A certain portion of the capacity is sometimes lost and then β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <; 1. In order to keep the sum-capacity growth rate (i.e., keeping β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 1), a coordinated direct and relay transmission (CDRT) with non-orthogonal multiple access (NOMA) principles is devised in the downlink, but β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is just fixed at either 0 or 1/2. In the uplink, however, the full rate 1 is not yet restored. Regardless of whether in the downlink or in the uplink, so far there exists no way to manipulate β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> while keeping β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 1. Motivated by designing the UE2 capacity flexibly, this article proposes a power allocation method used for CDRT-NOMA, which allocates a target positive capacity growth rate to UE2 and the asymptotic capacity accordingly. With the proposed power allocation, we derive exact or approximate expressions for the ergodic capacities, and provide the capacity scaling law with asymptotic analysis. The analysis proves that the capacity growth rate as well as the asymptotic capacity can be manipulated by a power allocation parameter. Moreover, in the uplink, the full rate 1 is restored with a full-duplexing relay by the proposed power allocation. Numerical investigation is also provided to verify the approximation and analysis used in the paper and shows that the proposed power allocation can control UE2 capacity as desired in the high SNR regime.