1
Introduction
In this brief Introduction we will examine the scenario in which we are operating. Starting from the main idea behind digital transmission, we will move towards the historical reasons that made of CPMs the most attractive but the least used modulations in satellite communications.
1.1 The how and why of digital communications
In any communication system, some transmitter wishes to send some information to a receiver. When considering digital communications, the information to transmit takes the form of binary values, usually referred to as bits. The purpose of digital-communication theory consists in designing transmission systems as well as receiving structures which ensure reliable transmissions.
The increasingly complex activities of mankind have forced an exponential growth in communication to sustain them, and revolutions in hardware have decimated the cost of communication so the older methods of analog transmission are being replaced by digital techniques. The rapid expansion of digital communications has various reasons of which we give now a short list [1]:
• New Hardware. The modern electronic technology has caused a revolution in the hardware used in digital communication. Digital circuits have been reduced to microscopic size, weight, power consumption, and cost.
• New Service Demands. A source of information that is digital in its nature obviously requires digital transmission. Many new sources of this type have appeared (facsimile transmissions, electronic data transfer for branch banking systems and airlines etc) and the old analog services are moving toward digital transmission because this offers a cost advantage.
• Compatibility and Flexibility. A complex and costly transmission system is far more useful if it can sustain a variety of information types and patterns of usage. Conversion of all data sources to a common format, bits, means that all can be
handled by the same equipment. Bits can be formed into words or packets at will and different kinds of information can be combined for efficiency. Multiplexing and switching are made easier; new methods of multiple access, such as time division multiple access, become economical.
• Fidelity of Reproduction and Error Control. Digital transmission may be favoured by the nature of the channel. Long distance channels are for the most part of two types, terrestrial channels consisting of long chains of repeaters or of other tandem processors such as switches, and satellite transponders. In either case aspects of the channel favour digital signalling. Satellite channels, on the other hand, are marked by lower power and wide bandwidth. These qualities predispose the channel to digital transmission in another way, as we shall develop. These channels have a special character that tends to favour digital transmission, but a digital format in any communications network makes it easier to guarantee a given data error rate or fidelity of reproduction.
• Cost. In cases where one can choose between digital or analogue means to transmit information, digital transmission may be cheaper. This may be true because of the availability of wide bandwidth, the low cost of manufacturing digital equipment, difficulties with error control, or customer factors, like compatibility, flexibility, or need for security.
1.2 The satellite channel
Starting in 1957 with the launch of Sputnik, satellite communications experienced a long successful history and will further develop into the future. Satellite communications has a number of features. In general, satellites have a broadcast characteristic and can cover large areas. They are useful for TV and radio broadcast, as well as for (reliable) data multicast (content distribution).
• Satellites are advantageous for building wide area (closed) networks inside companies and institutions.
• Because of their large coverage area, satellites are useful for providing rural areas and developing countries with information and communications services (bridging the digital divide).
• Similarly, satellites are useful for providing wide area mobile users (land, maritime, aeronautical) with broadcast and two-way communications.
So, satellite communications are an important source that needs to be developed. In this section we will analyze the main features of the satellite channel and how they involve digital transmission.
Satellite communications are one of the most motivating causes of digital transmission research [1]. Indeed the need for efficient utilization of orbital space has led to satellites with large traffic capacities and enhanced reuse of the allocated bandwidth. New bandwidth-efficient digital modulation formats with coding specially designed to complement the modulation method combined with on-board demodulation and demodulation (to separate uplink and downlink signal degradations) offer more interference resistance.
So, the satellite channel consists of relatively linear high-power amplifiers in the ground that feeds the uplink and a highly nonlinear low-power amplifier in the satellite that feeds the downlink to the ground. So it is characterized by wide bandwidth, a nonlinear amplitude response and low power by very long distances, at relatively low cost. These factors all point to digital transmission, but the most telling constraint is the low-power one. Continuous Phase Modulations appear to be the most suitable modulations in the satellite field, due to the issues of the satellite channel. Indeed, to ensure good performance even with the low SNRs encountered in this kind of transmission, a bandwidth-spreading technique is needed; moreover due to the nonlinearity of the amplifiers, signals with little or no envelope variation are recommended. This is the case of CPMs.
1.3 CPMs for satellite communications
Us showed before, Continuous phase modulation (CPM) has two favourable features that made of them a good modulation format for wireless transmission. The first of these is that the transmitted signal has no variations in its amplitude (it is constant envelope). In applications where power supply constraints force the use of fully saturated, non-linear RF power amplifiers, like satellite communications, the use of constant envelope modulations is a necessity. Another application where constant envelope modulations are useful is when simple and inexpensive transmitters are needed. Examples of this include digital FM
land-mobile radio and Bluetooth systems. Overall, the constant envelope nature of the modulation makes CPM very transmitter-friendly.
The second advantage CPM enjoys is bandwidth and power efficiency. A particular CPM format is specified by three parameters: the size of the data alphabet (binary, M-ary, etc.), the modulation index(es), and the duration and shape of the frequency pulse. By carefully selecting these parameters, one can control the power efficiency (minimum distance) and the spectrum of the signal. This makes CPM very versatile and spectrum friendly.
These advantages - constant envelope, power efficiency, and spectral efficiency - are favourable to satellite transmission and in general for the first two parts of the communications link: the transmitter and the transmission medium. However the receiver is not treated favourably by CPM.
The constant envelope nature of the signal means that it is nonlinear (i.e. the signal is not a linear function of the transmitted data). This makes the signal difficult to demodulate and difficult to synchronize. Furthermore, spectral efficiency is often achieved by increasing the size of the data alphabet and by using longer, smoother frequency pulses. These also increase the complexity of the receiver. So the primary disadvantage of CPM is high complexity on the receiving end.
In this work, we are interested in finding ways to well synchronize a general CPM signal.
1.4 What we are dealing with
Us underlined in the previous sections, Continuous-phase modulations (CPMs) have been studied for many years [1]. They found their first relevant practical application in mobile communications where they represent the standard signal format for GSM, because of the attractive property of constant envelope. In spite of the huge literature that is available on the subject, more elaborate CPM schemes have found no application until now because of the implementation complexity of the detector, and of synchronization problems [2].
In the last few years several methods have been proposed to solve synchronization issues related to Continuous Phase Modulations (CPMs). Unfortunately most of these techniques are ad-hoc algorithms, developed to meet synchronization problems for a particular subclass of signals [1] – [10].
In this thesis, we tackle the issue of synchronization with CPM signals. In particular we handle the problem of timing and phase recovery, by means of two different methods, both already applied to linear modulations.
Now we want to give a small overview on synchronization in general and on our work. Apart from the transmitted information bits, the signal to be processed by the receiver depends on a variety of other unknown parameters. These ones, often referred to as
nuisance parameters, include the channel impulse response, the channel propagation delay,
the carrier phase offset, the carrier frequency offset. The uncertainty associated to nuisance parameters has to be taken into account by the receiver. In order to do so, the most common approach consists in first computing an estimate of the nuisance parameters and then performing bit detection by considering the estimate as the actual parameter value. When applied to the estimation of the carrier phase offset, frequency offset or timing epoch, this approach is commonly referred to as synchronization.
During the last decade, synchronization was not a major source of degradations, in fact communication systems operated at fairly high SNR. The recent discovery of powerful error-correcting codes and iterative decoding techniques enables communication systems to operate at very low SNRs. So the synchronization task has become of major importance in the design of any communication system. New synchronization algorithms delivering very accurate parameter estimates while operation at very low SNRs are required to properly synchronise state-of-the-art receivers. State-of-the-art synchronization algorithms should therefore take benefits from the a priori information available from the code structure. This approach as been referred to as code-aided synchronization.
As first, we examine the timing synchronization algorithm. In modern data modem, symbol timing has to be recovered without any prior information about framing, fine carrier frequency and carrier phase, since the most efficient algorithms for those functions rely just on symbol timing information. For generalized MSK modulations, a popular processing is to pass the in-phase component of the complex envelope through a nonlinearity such as a squaring device and then to extract by means of a PLL or a filter the clock-synchronous periodic component contained by the output of the nonlinearity [3]. A different approach is to pass the IF signal through a (second order) nonlinearity to generate periodic components, at carrier and clock frequencies, that are extracted by a couple of PLLs [4]. Another approach is to make use of maximum likelihood estimation methods [5]. Lambrette and Meyr suggested two algorithms that allow efficient timing recovery for MSK based on the
computation of the Fourier spectrum of the absolute value of the differential phases [6]. Another scheme that can also be used with generalized MSK modulations extracts a clock reference by passing the sampled base band waveform through the cascade of a nonlinearity, followed by a digital differentiator whose average output represents the error signal to be employed in a tracking loop [7]. No general solution to the symbol timing recovery issue is know for higher-order or partial-response CPM.
On the other hand, the problem of blind timing recovery with linear modulations has several efficient solutions, irrespective of the complexity of the signal constellation. The workhorse in this respect is Gardner’s timing error detector to be used with a first or second order closed loop estimator [8]. Open loop symbol timing synchronization can also be carried out by means of the well-known Oerder-Meyr’s (O&M) estimator [11], that calls for signal oversampling. Gini and Giannakis (G&G) [12] showed that the O&M estimator is a particular sample of a larger class of estimators that exploit the cyclostationarity of a data signal. We will show in the following that the G&G approach can be extended to CPM signals, and we will perform an approximate analytical performance evaluation. Although some contributions, [9], [10], based on Laurent’s decomposition [13], have appeared on the cyclic analysis of CPM signals, they are not concerned with timing estimation.
The second part of this work is about another general synchronization method that can be applied to CPM signals, that exploit the trellis structure inherent in the modulator. In particular we focus on phase estimation, being the phase the parameter that shows the lower implementation complexity. Our approach is the so-called code-aided synchronization, that take benefits from the a priori information available from the code structure applied to a linear modulation scheme. We try to extend this approach to CPMs, since this signals share with a coded system the trellis structure, due to the inherent memory of the CPM modulator. The algorithm starts with a first step, called Expectation-Maximisation [14]. It is an iterative method which enables to solve ML optimisation problem.
If we deal with a general nuisance parameter to estimate, due to the non-linearity of the problem, we have to solve the maximisation problem by means of the well-known Newton-Raphson method. After we have to calculate the first and second derivative, required by the NR algorithm, by means of the finite difference approximation.
In the special case of the sole phase, being CPM a phase modulation, the computational complexity decreases and it is possible to find a closed form for the estimator, that is data
aided and makes use of the state transition probabilities given by a symbol-based BCJR [15], developed in an ad-hoc way for an uncoded CPM signal.
1.5 Organization of the dissertation
A deep understanding of the synchronization mathematical frameworks derived in this dissertation requires a number of background knowledge. In particular, the reader should be familiar with communication theory, estimation theory, non linear modulations. Being aware that not all the readers have a full understanding of all these topics, this dissertation includes some chapters dealing with some background information. These chapters will allow us to recall or emphasize some notions the reader should be aware of to fully understand the remainder of the dissertation. As a consequence, not all the chapters are relevant for all the readers: some chapters should be skipped by those having a sufficient knowledge in the corresponding field.
The personal contributions of this work are included in Chapters 4, 5, 6 and 7.
The dissertation is divided into 6 chapters, including this Introduction and the Conclusions. After this Introduction, Chapter 2 introduces signal model and basic notations, while in Chapter 3 the statement of the problem is given. Chapter 4 describes the derived timing estimation algorithm and shows analytical and simulation results. Chapter 5 introduces the soft approach to CPM synchronization; and some conclusions are offered in Chapter 6.
We give now a short overview of each of them.
Chapter 2: Signal Analysis and Basic Notations
In this chapter we introduce the model that will be used for the derivation of synchronization algorithms in the remainder of this thesis. We will introduce the expressions of the transmitted and received signals in the case of a band pass non linearly-modulated transmission scheme.
Chapter 3: Synchronization
In this chapter, we introduce the concept of synchronization and we place it in the context of the optimal reception. It is emphasized that synchronization may be performed under different synchronization modes: data-aided (DA), non-data-aided (NDA) and code-aided (CA). In this chapter we recall the fundamental principles of estimation theory. In particular, we emphasize some of the synchronization issues which may appear in the case
of CPM signals. Finally, the question of the ultimate accuracy of an estimator for CPM is tackled. In particular, we present the expressions for the modified Cramér-Rao bound.
Chapter 4: Cyclostationarity-based Blind Symbol Timing Recovery
In this chapter, we introduce a blind timing estimator that can be used for any CPM scheme. This algorithm is derived by an existing algorithm for linear modulations. We illustrate by simulation results the performance of the derived synchronizer.
Chapter 5: Soft Recovery
In this chapter, we consider iterative procedures enabling to solve unconstrained optimization problems. We then present one of the well-known families of iterative optimization procedures, the Expectation-Maximization algorithms. The properties of these algorithms are presented and discussed and the iterative procedure applied to CPM signals to derive an soft estimation algorithm.
