Christian Hofbauer

Non-Systematic Complex Number RS Coded OFDM by Unique Word Prefix

In this paper, we expand our recently introduced concept of unique word orthogonal frequency division multiplexing (UW-OFDM). In UW-OFDM the cyclic prefixes (CPs) are replaced by deterministic sequences, the so-called unique words (UWs). The UWs are generated by appropriately loading a set of redundant subcarriers. By that a systematic complex number Reed-Solomon (RS) code construction is introduced in a quite natural way, because an RS code may be defined as the set of vectors, for which a block of successive zeros occurs in the other domain w.r.t. a discrete Fourier transform. (For a fixed block different to zero, i.e., a UW, a coset code of an RS code is generated.) A remaining problem in the original systematic coded UW-OFDM concept is the fact that the redundant subcarrier symbols disproportionately contribute to the mean OFDM symbol energy. In this paper we introduce the concept of non-systematic coded UW-OFDM, where the redundancy is no longer allocated to dedicated subcarriers, but distributed over all subcarriers. We derive optimum complex valued code generator matrices matched to the best linear unbiased estimator (BLUE) and to the linear minimum mean square error (LMMSE) data estimator, respectively. With the help of simulations we highlight the advantageous spectral properties and the superior bit error ratio (BER) performance of non-systematic coded UW-OFDM compared to systematic coded UW-OFDM and to CP-OFDM in additive white Gaussian noise (AWGN ) as well as in frequency selective environments.

Building blocks of cooperative relaying in wireless systems

SummaryThe concept of cooperative relaying promises gains in robustness and energy efficiency in wireless networks. This survey gives an introduction and overview of promising methods that can be used for cooperative relaying: relay selection protocols, cooperative channel and network coding, and physical layer aspects such as cooperative modulation. The particular methods can be seen as building blocks that can be configured and optionally used for designing a system. They offer a large number of design options for relaying systems. Based on available hardware features, expected environment, and required services an efficient system needs to be tailored using the right subset of available methods.ZusammenfassungDas Konzept des kooperativen Weiterleitens von Nachrichten ermöglicht eine Verbesserung der Robustheit und Energieeffizienz von drahtlosen Netzwerken. Dieser Artikel stellt einige vielversprechende Methoden für Netzwerke mit kooperativem Relaying vor. Im Speziellen werden Protokolle zur Relayauswahl, Kanalcodierung, Network Coding sowie kooperative Modulationstechniken behandelt. Die vorgestellten Methoden sind als Bausteine für ein Netzwerk mit kooperativem Relaying zu verstehen. Jede einzelne Methode kann optional und gemeinsam mit anderen verwendet werden und in den meisten Fällen zusätzlich noch dem Zweck entsprechend konfiguriert werden. Somit ergibt sich eine hohe Anzahl von Möglichkeiten, ein System mit kooperativem Relaying zu entwerfen. Das tatsächliche Design hängt letztendlich von Parametern wie der zur Verfügung stehenden Hardware, den Annahmen über die Zielumgebung sowie den Anforderungen der Applikation ab.

Coded OFDM by unique word prefix

In this paper, we propose a novel transmit signal structure for OFDM (orthogonal frequency division multiplexing). Instead of the conventional cyclic prefix (CP), we use a deterministic sequence, which we call unique word (UW), as guard interval. We show how unique words, which are already well investigated for single carrier systems with frequency domain equalization (SC/FDE), can also be introduced in OFDM symbols. Since unique words represent known sequences, they can advantageously be used for synchronization and channel estimation purposes. Furthermore, the proposed approach introduces a complex number Reed-Solomon (RS-) code structure within the sequence of subcarriers. This either allows for algebraic RS decoding or for applying a highly efficient Wiener smoother succeeding a zero forcing stage at the receiver to further improve the bit error ratio behavior of the system. These beneficial properties are achieved while additionally featuring around the same bandwidth efficiency as conventional CP-OFDM. We present simulation results in an indoor multipath environment to highlight the advantageous properties of the proposed scheme.

Unique word prefix in SC/FDE and OFDM: A comparison

The concept of using unique word (UW) prefixes instead of cyclic prefixes (CPs) is already well investigated for single carrier systems with frequency domain equalization (SC/FDE). In OFDM (orthogonal frequency division multiplexing), where the data symbols are specified in frequency domain, the introduction of UWs — which are specified in time domain — is not that straight forward. In this paper we show how unique words can also be introduced in OFDM symbols. In OFDM our proposed method introduces correlations between subcarrier symbols. This allows to apply a highly efficient LMMSE (linear minimum mean square error) receiver. Throughout this paper we discuss the similarities and differences of UW-SC/FDE and UW-OFDM transmitter/receiver processing, and we present simulation results in indoor multipath environments.

Complex number RS coded OFDM with systematic noise in the guard interval

Recently we presented a novel OFDM (orthogonal frequency division multiplexing) signaling concept, where the cyclic prefixes (CPs) are replaced by deterministic sequences which we call unique words (UWs). The UWs are generated by appropriately loading so-called redundant subcarriers. By that a complex number Reed Solomon (RS) code construction is introduced which can advantageously be exploited in an LMMSE (linear minimum mean square error) receiver. The overall concept clearly outperforms CP-OFDM in frequency selective channels. In this paper we introduce a method that significantly reduces the energy of the redundant subcarrier symbols by allowing some systematic noise in the UWs. The concept features a notable performance and bandwidth efficiency gain compared to our original UW-OFDM approach.

On the impact of redundant subcarrier energy optimization in UW-OFDM

Unique word - orthogonal frequency division multiplexing (UW-OFDM) is a novel OFDM concept that uses deterministic sequences, which we call unique words, as guard intervals instead of the conventional cyclic prefixes. Since unique words represent known sequences, they can advantageously be used for sychronization, channel estimation, but also for improving the bit error ratio (BER) behavior of a system. These UWs are created by appropriately loading so-called redundant subcarriers. In this paper, we investigate methods to improve the BER behavior of UW-OFDM by increasing the number of redundant subcarriers (while keeping the length of the UW constant). This gain in the BER performance comes with an increase of the redundancy part and thus with a decrease of the data rate. As such, we present methods to vary the coding rate in UW-OFDM. We present results for the additive white Gaussian noise (AWGN) channel as well as for indoor multipath environments to highlight the advantages of the proposed methods.

Iterative detection for unique word OFDM

In this paper we consider a unique word OFDM (UW-OFDM) system with iterative detection, for which we explore two soft-input soft-output (SISO) detection algorithms: A LMMSE detector and a detector based on the generalized approximate message passing (GAMP) algorithm. For the GAMP based detector we propose additional simplifications suitable for UW-OFDM to further reduce the complexity while exhibiting only a small BER performance loss. As verified by computer simulations, both algorithms show a significant BER performance improvement over the iterations. Moreover, the GAMP based detector with the proposed simplifications outperforms the computational more complex LMMSE detector.

Component-wise conditionally unbiased widely linear MMSE estimation

Biased estimators can outperform unbiased ones in terms of the mean square error (MSE). The best linear unbiased estimator (BLUE) fulfills the so called global conditional unbiased constraint when treated in the Bayesian framework. Recently, the component-wise conditionally unbiased linear minimum mean square error (CWCU LMMSE) estimator has been introduced. This estimator preserves a quite strong (namely the CWCU) unbiased condition which in effect sufficiently represents the intuitive view of unbiasedness. Generally, it is global conditionally biased and outperforms the BLUE in a Bayesian MSE sense. In this work we briefly recapitulate CWCU LMMSE estimation under linear model assumptions, and additionally derive the CWCU LMMSE estimator under the (only) assumption of jointly Gaussian parameters and measurements. The main intent of this work, however, is the extension of the theory of CWCU estimation to CWCU widely linear estimators. We derive the CWCU WLMMSE estimator for different model assumptions and address the analytical relationships between CWCU WLMMSE and WLMMSE estimators. The properties of the CWCU WLMMSE estimator are deduced analytically, and compared by simulation to global conditionally unbiased as well as WLMMSE counterparts with the help of a parameter estimation example and a data estimation/channel equalization application. HighlightsExtension of CWCU linear estimators to CWCU widely linear estimators.Derivation of the CWCU WLMMSE estimator for different model assumptions.Improper parameter estimation example and a data estimation/channel equalization application for estimator comparison.

A study of data rate equivalent UW-OFDM and CP-OFDM concepts

Unique word - orthogonal frequency division multiplexing (UW-OFDM) is a novel transmit signal structure for OFDM where the usual cyclic prefixes (CPs) are replaced by deterministic sequences, the so-called UWs. Since unique words represent known sequences, they can advantageously be used for synchronization and estimation tasks, but also for improving the bit error ratio (BER) behavior of an UW-OFDM system. Recent research results have demonstrated the superior BER behavior of UW-OFDM over conventional CP-OFDM used for real-world communication systems, e.g. for the IEEE 802.11a WLAN standard. In this paper we extend these investigations by considering different and data rate equivalent UW-OFDM and CP-OFDM configuration setups. We show simulation results for various frequency selective environments and additionally compare UW-OFDM with UW based single carrier/frequency domain equalization (UW-SC/FDE) systems.

From dedicated redundant subcarriers to distributed redundancy in UW-OFDM

Unique word orthogonal frequency division multiplexing (UW-OFDM) is based on introducing redundancy, either on dedicated redundant subcarriers leading to systematically encoded UW-OFDM, or spread over the entire bandwidth resulting in the non-systematically encoded UW-OFDM concept. The waveform design of the latter has originally been optimized by incorporating transmitter and receiver processing steps, while the systematic approach primarily focuses on the redundant transmit energy minimization. This work closes the gap between both by introducing a design procedure for non-systematically encoded UW-OFDM that is also predicated on redundant energy arguments. Furthermore, this approach provides a simple way to increase the bandwidth efficiency.