Abstract
Hierarchical-Decode-and-Forward is a promising wireless-network-coding-based 2-way relaying strategy due to its potential to operate outside the classical multiple-access capacity region. Assuming a practical scenario with channel state information at the receiver and no channel adaptation, there exist modulations and exclusive codes for which even non-zero channel parameters (denoted as catastrophic) cause zero hierarchical minimal distance -- significantly degrading its performance. In this work, we state that non-binary linear alphabets cannot avoid these parameters and some exclusive codes even imply them; contrary XOR does not. We define alphabets avoiding all catastrophic parameters and reaching its upper bound on minimal distance for all parameter values (denoted uniformly most powerful (UMP)). We find that binary, non-binary orthogonal and bi-orthogonal modulations are UMP. We optimize scalar parameters of FSK (modulation index) and full-response CPM (frequency pulse shape) to yield UMP alphabets.
Highlights
Cooperative communication in wireless relay networks can potentially be of great benefit, offering several gains that may decrease required transmission power, increase the system capacity, improve the cell coverage or interference mitigation while balancing the quality of service and keeping relatively low deployment costs [1]
We have found that such modulation is BPSK and definitely not the other linear modulations (PSK, QAM,...) with higher cardinality than 2, because they possess socalled catastrophic parameters
It is interesting that minimal cardinality XC (Latin square) should have symmetrical XC matrix with the same diagonal not to imply catastrophic parameters
Summary
Cooperative communication in wireless relay networks can potentially be of great benefit, offering several gains that may decrease required transmission power, increase the system capacity, improve the cell coverage or interference mitigation while balancing the quality of service and keeping relatively low deployment costs [1]. Future wireless networks are envisaged to include the cooperative relaying techniques. It brings several new challenging problems such as the extra resources (e.g. frequency or time slots) taken for interference-free relay traffic when considering practical halfduplex constraints (each node cannot send and receive at the same time). This is well demonstrated in the simplest cooperative network – 2-way relay channel (2-WRC) comprising two terminals A and B bidirectionally communicating between themselves via a supporting relay R. The exclusive code (XC) permits message decoding at the terminals using their own messages serving as a complementary-side information [7]
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