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\begin{document}

\title{Flipped Modulation Superposition Coding for Broadcast Channel}
\author{%
  \IEEEauthorblockN{Laurent Mazet}
  \IEEEauthorblockA{Motorola-Labs Paris -- Parc Les  Algorithmes, Saint Aubin -- 91193 Gif sur Yvette Cedex -- France \\
    laurent.mazet@motorola.com}
}

\maketitle

\begin{abstract}
In wireless broadband networks where coordination between base stations is not required, users in neighboring of several cells interfere each other, and this impacts dramatically the average throughput of a cell. Superposition Coding is a down-link transmission technique which is nowadays considered to increase the average throughput by unloaded resources usually allocated to users close to the base-station. Thus, others technique can be applied for border cell users.

We propose a new scheme of superposition coding which simplifies the receiver at the near user side. When far user transmission is on QPSK, we propose to flip superimposed near user transmission. This will not affect performance of the original scheme, but it will allow us to decode near user without doing a SIC.
\end{abstract}

\begin{IEEEkeywords}
Multi-user transmission, Superposition Coding, QPSK Modulation, WMAN
\end{IEEEkeywords}

\section{Introduction}
\label{sec:introduction}
Latest WMAN standard 3GPP2 Ultra Mobile Broadband\cite{3ggp2.umb07} (one can also find several contributions into the recently opened IEEE~802.16m study group) proposes a  Multi User (MU) Multiple Input Multiple Output (MIMO) scheme: Superposition Coding (SC).
In this type of networks where coordination between base stations is not required, users in neighboring cells interfere with the transmission in a given cell. Thus, the average throughput of a cell is limited by the achievable throughput for border cell users.

In \cite{ieeeIT.cover72}, Cover proposed and analyzed a solution, denoted ``superposition coding'' for reliable transmission over broadcast channel (a a single source attempting to communicate information simultaneously to several receivers). Moreover,  Cover showed that it outperforms time-sharing techniques in term of throughput. This has been enforced by Bergmans studies in \cite{ieeeIT.bergmans74,ieeeIT.bergmans74a} which demonstrated the optimality of SC scheme. At last, some recent works of Shamai \cite{isit.shamai97} and Liu \cite{isit.liu02} show its feasibility with a reduce number of coding level.

SC relies on piggybacking far user resource block to send message to near users. This is essentially a single stream concept dealing with far/near user pairing. It uses two transmit power levels ($\alpha$ and $1-\alpha$ ) and superimpose transmissions i.e.
\begin{displaymath}
  x = \sqrt{\alpha}\,s_n + \sqrt{1-\alpha}\,s_f
\end{displaymath}
where $s_n$ and $s_f$ are respectively symbols for near and far users. Far user perceives near message as additional noise (hidden message). So, near user apply Successive Interference Cancellation (SIC) procedure to retrieve the embedded message and this is fully transparent to far users.

In order to simplify the near user receiver, we propose a new scheme which doe not require a SIC at the near user receiver side. This scheme only assumes that far user uses Quadrature Phase-Shift Keying (QPSK) modulation. Moreover this scheme provides extra protection for outer constellation point of the far user.

This contribution is organized as follow. We begin, in section \ref{sec:superposition-coding}, by recalling SC scheme.Then, in section \ref{sec:flipp-modul-superp}, we details our innovative scheme and a simple receiver process. At last, in section \ref{sec:perf-eval}, we present some performance evaluation to assess it.

\section{Superposition coding}
\label{sec:superposition-coding}

Superposition coding consists of sending a loud message to the far near and simultaneously sending a soft message the near user. The resulting transmission can be model by $x$ such as
\begin{equation}
  \label{eq:superposition_coding}
  x = \sqrt{\alpha} s_n + \sqrt{1-\alpha} s_f
\end{equation}
where $\alpha$ sets the power level of the message sent to far user and  $s_n$ and $s_f$ are respectively the symbol sent to near user and to far user.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=.5\linewidth]{sp_std}
  \caption{A QPSK superimposed over a QPSK}
  \label{fig:qpsk-super-over}
\end{figure}

At the far user side, the receiver does not see the message sent to the near user and it decodes its message as usual. At the near user side, the receiver decodes the far user message, then it subtracts it and decodes its destined message, i.e. near user receiver proceed a Successive Interference Cancellation (SIC) procedure.

It has been shown\cite{book.tse05} that the linear superposition encoding of the signals of the two users at the base-station and the SIC decoding procedure achieves the capacity. However, at the near user receiver side, applying a SIC on coded modulation implies an extra complexity as it need to completely decode and re-encode the far user message before decoding its own message.

\section{Flipped Modulation Superposition coding}
\label{sec:flipp-modul-superp}

We propose a new scheme to superimpose signal when the far user modulation is QPSK. It consists in flipping the near user constellation point with respect of the far user signal as illustrated in figure \ref{fig:flipp-modul-super}. In the following, our scheme will be denoted as FM-SC (Flipped Modulation Superposition coding).

\begin{figure}[htbp]
  \centering
   \includegraphics[width=.5\linewidth]{sp_fsm2}
  
  \caption{Flipped Modulation superimposed over a QPSK}
  \label{fig:flipp-modul-super}
\end{figure}

It can be written as:
\begin{equation}
  \label{eq:fm-sc}
  x = \sqrt{\alpha} f(s_n, s_f) + \sqrt{1-\alpha} s_f
\end{equation}
where $f(s, r) = \sig(\Re(r)) \Re(s) + i \times \sig(\Im(r)) \Im(s)$ is the flip function and $\sig(.)$ return 1 for positive number and -1 for negative number.

Let remarks, that the FM-SC does not impact far user: the receiver decoding process is exactly the same than for standard SC and its achievable performance does not change. For the near user, one can replace the SIC procedure by an alternative decoding procedure (illustrated in figure \ref{fig:decoding-fm-sc}):
\begin{itemize}
\item[(a)] received signal is folded in the upper right quadrant,
\item[(b)] resulting signal is translated by a factor $\sqrt{1-\alpha}$
\end{itemize}
This decoding procedure allows us to reduce the receiver complexity but it does not take advantage on the far user coding which leads to a penalty of less than 0.1dB on coded PER as we will show later.

\begin{figure}[htbp]
  \centering
   \subfigure[Folding]{\includegraphics[width=0.49\linewidth]{sp_fsm3}}
   \subfigure[Translating]{\includegraphics[width=0.49\linewidth]{sp_fsm4}}
  \caption{Decoding FM-SC near signal message}
  \label{fig:decoding-fm-sc}
\end{figure}

On another hand, when the power ratio is high, the FM-SC scheme provides extra protection for outer constellation point for uncoded modulation. Especially when two QPSK are superimposed and the power ration is to $1/4$, so the resulting signal appears as a regular 16QAM.

\section{Performance evaluations}
\label{sec:perf-eval}

As written before, our scheme does not impact the performance of the far user. Thus, in this section, we only compare the near user performance curves for different power ratio ($\alpha$ is set to $1/4$ and $1/10$). 

Figures \ref{fig:uncoded-ber-sc} and \ref{fig:coded-per-sc} present the performance curves for both modulation/decoding schemes (that means three curves):
\begin{enumerate}
\item curves named `SC + SIC' present the performance of the standard Superposition Coding scheme using a SIC at the near user receiver,
\item curves named `FM-SC' present the performance of our Flipped Modulation Superposition Coding scheme using out low complexity decoding procedure,
\item curves named `FM-SC + SIC' present the performance of our Flipped Modulation Superposition Coding scheme using a SIC.
\end{enumerate}

\begin{figure}[htbp]
  \centering
  \includegraphics[width=\linewidth]{ber_fsm_nocc}
  \caption{Uncoded BER for SC and FM-SC}
  \label{fig:uncoded-ber-sc}
\end{figure}

Performance of uncoded modulations are presented on figure \ref{fig:uncoded-ber-sc}. First, in the special case where the two superimposed QPSK formed a regular 16QAM (i.e. $\alpha=1/4$), our scheme outperform by 3dB the standard Superposition scheme at a BER of $10^{-3}$. Second, when the power ratio decreases, both scheme achieve same performance. Obviously, for uncoded modulation, adding a SIC to our scheme does not provide any gain.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=\linewidth]{per_fsm_cc}
  
  \caption{Coded PER for SC and FM-SC}
  \label{fig:coded-per-sc}
\end{figure}

Performance of coded modulations are presented on figure \ref{fig:coded-per-sc}. Both scheme achieve same performance however, using a SIC over our FM-SP scheme provides 0.1dB gain at PER of $10{-2}$ for $\alpha=1/4$.


\section{Conclusions}
\label{sec:conclusion}

In this contributions, we propose a new scheme of SC in order to simplify the near user receiver as it does not require a SIC at the near user receiver side. It only assumes that far user uses Quadrature Phase-Shift Keying (QPSK) modulation and we proposed that a flip function is applied to the superimposed near user modulated symbols. This will not affect performance of the original scheme, but it will allow us to decode near user without doing a SIC.

%We shown that by only folding received signal and recenter it by a factor of $\sqrt{1-\alpha}$, near user can demodulate flipped and superimposed symbols with very few performance loss compared to a full SIC procedure.

Moreover, for uncoded modulation, we show that this scheme provides extra protection for far user outer constellation points. Indeed, then a received symbol corresponding to an outer constellation point crosses real or imaginary axes due to effect noise, it will still correspond to the same constellation point thank to the fold.

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