Exact Spectral Analysis of Single-h and Multi-h CPM Signals through PAM decomposition and Matrix Series Evaluation

In this paper we address the problem of closed-form spectral evaluation of CPM. We show that the multi-h CPM signal can be conveniently generated by a PTI SM. The output is governed by a Markov chain with the unusual peculiarity of being cyclostationary and reducible; this holds also in the single-h context. Judicious reinterpretation of the result leads to a formalization through a stationary and irreducible Markov chain, whose spectral evaluation is known in closed-form from the literature. Two are the major outcomes of this paper. First, unlike the literature, we obtain a PSD in true closed-form. Second, we give novel insights into the CPM format.Comment: 31 pages, 10 figure

A (Simplified) Bluetooth Maximum a Posteriori Probability (Map) Receiver

In our software-defined radio project, we aim at combining two standards luetooth and HIPERLAN/2. The HIPERLAN/2 receiver requires more computational power than Bluetooth. We choose to use this computational power also for Bluetooth and look for more advanced demodulation algorithms such as a maximum a posteriori probability (MAP) receiver. The paper discusses a simplified MAP receiver for Bluetooth GFSK signals. Laurent decomposition provides an orthogonal vector space for the MAP receiver. As the first Laurent waveform contains the most energy, we have used only this waveform for our (simplified) MAP receiver. This receiver requires a E/sub b//N/sub 0/ of about 11 dB for a BER of 10/sup -3/, required by the Bluetooth standard. This value is about 6 dB better than single bit demodulators. This performance is only met if the receiver has exact knowledge of the modulation index

MMSE-optimal approximation of continuous-phase modulated signal as superposition of linearly modulated pulses

The optimal linear modulation approximation of any M-ary continuous-phase modulated (CPM) signal under the minimum mean-square error (MMSE) criterion is presented in this paper. With the introduction of the MMSE signal component, an M-ary CPM signal is exactly represented as the superposition of a finite number of MMSE incremental pulses, resulting in the novel switched linear modulation CPM signal models. Then, the MMSE incremental pulse is further decomposed into a finite number of MMSE pulse-amplitude modulated (PAM) pulses, so that an M-ary CPM signal is alternatively expressed as the superposition of a finite number of MMSE PAM components, similar to the Laurent representation. Advantageously, these MMSE PAM components are mutually independent for any modulation index. The optimal CPM signal approximation using lower order MMSE incremental pulses, or alternatively, using a small number of MMSE PAM pulses, is also made possible, since the approximation error is minimized in the MMSE sense. Finally, examples of the MMSE-optimal CPM signal approximation and its comparison with the Laurent approximation approach are given using raised-cosine frequency-pulse CPM schemes

Equalization Techniques of Control and Non-Payload Communication Links for Unmanned Aerial Vehicles

In the next years, several new applications involving unmanned aerial vehicles (UAVs) for public and commercial uses are envisaged. In such developments, since UAVs are expected to operate within the public airspace, a key issue is the design of reliable control and non-payload communication (CNPC) links connecting the ground control station to the UAV. At the physical layer, CNPC design must cope with time- and frequency-selectivity (so-called double selectivity) of the wireless channel, due to lowaltitude operation and flight dynamics of the UAV. In this paper, we consider the transmission of continuous phase modulated (CPM) signals for UAV CNPC links operating over doubly-selective channels. Leveraging on the Laurent representation for a CPM signal, we design a two-stage receiver: the first one is a linear time-varying (LTV) equalizer, synthesized under either the zero-forcing (ZF) or minimum mean-square error (MMSE) criterion; the second one recovers the transmitted symbols from the pseudo-symbols of the Laurent representation in a simple recursive manner. In addition to LTV-ZF and LTV-MMSE equalizers, their widely-linear versions are also developed, to take into account the possible noncircular features of the CPM signal. Moreover, relying on a basis expansion model (BEM) of the doubly-selective channel, we derive frequency-shift versions of the proposed equalizers, by discussing their complexity issues and proposing simplified implementations. Monte Carlo numerical simulations show that the proposed receiving structures are able to satisfactorily equalize the doubly-selective channel in typical UAV scenarios

Synchronisation, détection et égalisation de modulation à phase continue dans des canaux sélectifs en temps et en fréquence

Si les drones militaires connaissent un développement important depuis une quinzaine d’année, suivi depuis quelques années par les drones civiles dont les usages ne font que se multiplier, en réalité les drones ont un siècle avec le premier vol d’un avion équipé d’un système de pilotage automatique sur une centaine de kilomètre en 1918. La question des règles d’usage des drones civiles sont en cours de développement malgré leur multiplication pour des usages allant de l’agriculture, à l’observation en passant par la livraison de colis. Ainsi, leur intégration dans l’espace aérien reste un enjeu important, ainsi que les standards de communication avec ces drones dans laquelle s’inscrit cette thèse. Cette thèse vise en effet à étudier et proposer des solutions pour les liens de communications des drones par satellite.L’intégration de ce lien de communication permet d’assurer la fiabilité des communications et particulièrement du lien de Commande et Contrôle partout dans le monde, en s’affranchissant des contraintes d’un réseau terrestre (comme les zones blanches). En raison de la rareté des ressources fréquentielles déjà allouées pour les futurs systèmes intégrant des drones, l’efficacité spectrale devient un paramètre important pour leur déploiement à grande échelle et le contexte spatiale demande l’utilisation d’un système de communication robuste aux non-linéarités. Les Modulations à Phase Continue permettent de répondre à ces problématiques. Cependant, ces dernières sont des modulations non-linéaire à mémoire entraînant une augmentation de la complexité des récepteurs. Du fait de la présence d’un canal multi-trajet (canal aéronautique par satellite), le principal objectif de cette thèse est de proposer des algorithmes d’égalisation (dans le domaine fréquentiel pour réduire leur complexité) et de synchronisation pour CPM adaptés à ce concept tout en essayant de proposer une complexité calculatoire raisonnable. Dans un premier temps, nous avons considéré uniquement des canaux sélectifs en fréquence et avons étudier les différents égaliseurs de la littérature. En étudiant leur similitudes et différences, nous avons pu développer un égaliseur dans le domaine fréquentiel qui proposant les mêmes performances a une complexité moindre. Nous proposons également des méthodes d’estimation canal et une méthode d’estimation conjointe du canal et de la fréquence porteuse. Dans un second temps nous avons montré comment étendre ces méthodes à des canaux sélectifs en temps et fréquence permettant ainsi de conserver une complexité calculatoire raisonnable

Reduced-Complexity Joint Frequency, Timing and Phase Recovery for PAM Based CPM Receivers

In this thesis, we present a reduced-complexity decision-directed joint timing and phase recovery method for continuous phase modulation (CPM). Using a simple linear modulation--pulse amplitude modulation (PAM)--representation of CPM, more popularly known as the Laurent representation of CPM, we develop formulations of a PAM based joint timing error detector (TED) and a phase error detector (PED). We consider the general M-ary single-h CPM model in our developments and numerical examples. We show by analysis and computer simulations that the PAM based error detector formulations have characteristics similar to the conventional (i.e., non-PAM) formulations and they render reliable performance when applied to specific CPM examples; in fact, we show the error detectors are able to perform close to the theoretical limit given by the modified Cramer-Rao bound (MCRB) and able to provide a bit error rate (BER) close to the theoretical value. Also, we investigate the false lock problem in M-ary CPMs and are able to obtain much improved performance over conventional CPM detectors with our PAM based method. Furthermore, the PAM based receivers perform well in the presence of a large frequency offset (on the order of the symbol rate) and are, in general, much more resistant to small carrier frequency variations compared to conventional CPM receivers. We use an existing PAM based frequency difference detector (FDD) for a large carrier frequency recovery. As such, the proposed method of combining the error detectors (FDD, TED and PED) provides important synchronization components for jointly recovering the respective signal attribute offsets (i.e, carrier frequency, symbol timing and carrier phase) for reduced-complexity PAM based CPM receivers, which have been missing up to this point

A new performance bound for PAM-based CPM detectors

©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.It is well understood that the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) can lead to reduced-complexity detectors with near optimum performance. It has recently been shown that the PAM representation also extends to CPM schemes with multiple modulation indexes (multi-h CPM). In this paper, we present a detector for multi-h CPM which is based on the PAM representation. We also give an exact expression for the pairwise error probability for the entire class of PAM-based CPM detectors (single- and multi-h, optimal, and reduced-complexity) over the additive white Gaussian noise (AWGN) channel and show that this bound is tighter than the previously published bound for approximate PAM-based detectors. In arriving at this expression, we show that PAM-based detectors for CPM are a special case of the broad class of mismatched CPM detectors. We also show that the metrics for PAM-based detectors accumulate distance in a different manner than metrics for other CPM detectors. These distance properties are especially useful in applications with greatly reduced trellis sizes. We give thorough examples of the analysis for different single- and multi-h signaling schemes. We also apply the new bound in comparing the performance of PAM-based detectors with other reduced-complexity detectors for CPM

CPM Training Waveforms With Autocorrelation Sidelobes Close to Zero

Continuous phase modulation (CPM) plays an important role in wireless communications due to its constant envelope signal property and tight spectrum confinement capability. Although CPM has been studied for many years, CPM training waveforms having autocorrelations with zero sidelobes have not been reported before, to the best of our knowledge. Existing works on the CPM system design mostly assume that the channel fading coefficients are either perfectly known at the receiver or estimated using random CPM training waveforms. In this correspondence paper, we propose a novel class of CPM training waveforms displaying autocorrelation sidelobes close to zero. The key idea of our construction is to apply differential encoding to Golay complementary pair having perfect aperiodic autocorrelation sum properties

A highly efficient receiver for satellite-based Automatic Identification System signal detection

An innovative receiver architecture for the satellitebased Automatic Identification System (AIS) has been recently proposed. In this paper, we describe a few modifications that can be introduced on the algorithms for synchronization and detection, that provide an impressive performance improvement with respect to the previous system. The receiver architecture has been designed for an on-board implementation, and for this reason all algorithms have been realized keeping the complexity as low as possible. A prototype for the proposed receiver has been implemented by the University of Parma and CGS S.p.A. Compagnia Generale per 10 Spazio under the ESA project FENICE