Abstract
We address the issue of the parametric performance of the Hierarchical-Decode-and-Forward (HDF) strategy in a wireless 2-way relay channel. Promising HDF, representing the concept of wireless network coding, performs well with a pre-coding strategy that requires Channel State Information (CSI) on the transceiver side. Assuming a practical case when CSI is available only on the receiver side and the channel conditions do not allow adaptive strategies, the parametrization causes significant HDF performance degradation for some modulation alphabets. Alphabets that are robust to the parametrization (denoted Uniformly Most Powerful (UMP)) have already been proposed restricting on the class of non-linear multi-dimensional frequency modulations. In this work, we focus on the general design of unrestricted UMP alphabets. We formulate an optimization problem which is solved by standard non-linear convex constrained optimization algorithms, particularly by Nelder-Mead global optimization search, which is further refined by the local interior-pointsmethod.
Highlights
Cooperative wireless network protocols which utilize network coding in the physical layer have recently attracted strong research interest due the significant capacity gains that they offer; for citations see [1] and the references therein
In [3] and [4], the authors show that a two-stage DeNoise-and-Forward (DNF)/Hierarchical-Decodeand-Forward (HDF) strategy is very promising in 2-Way Relay Channel (2-WRC) since it can reliably operate outside the classical Multiple-ACcess (MAC) capacity region [5]
We have applied canonical convex constrained nonlinear optimization methods for general unrestricted design of Uniformly Most Powerful (UMP) alphabets, which are convenient for the Hierarchical-Decodeand-Forward (HDF) strategy in a wireless 2-way relay channel with Channel State Information (CSI) on the receiver side, where the channel conditions do not allow adaptive strategies
Summary
Cooperative wireless network protocols which utilize network coding in the physical layer have recently attracted strong research interest due the significant capacity gains that they offer; for citations see [1] and the references therein. Even in a wireless 2-Way Relay Channel (2-WRC), which is the simplest cooperative network, WNC almost doubles the achievable communication sum-rates. Assuming canonical linear (one complex dimension; PSK, ASK, QAM) modulation alphabets, HDF strategy suffers from unavoidable wireless channel parametrization in the practical case when only Channel State Information at the Receiver side (CSIR) is available. It has been shown that the parametrization is not harmful when the terminals use binary alphabets, but non-binary linear alphabets always suffer from this effect. In this case, more dimensions need to be accommodated to meet the UMP condition. Paper [9] exploits additional dimensions of non-linear multi-dimensional frequency alphabets to fulfill the UMP condition.
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