BOC Modulation Waveforms

This paper is concerned with the evolution of modulation waveforms finding application in recent navigation satellite transmissions. Specifically, we focus on the waveforms used for sub carrier modulation with binary signals, and the spectra of the resulting waveforms. These are generalized to multi-level waveforms that can be simply implemented by multi-phase constant envelope signals, well adapted to high power amplifiers used in satellite payloads. A family of equations is derived for the spectra of such signals. These include the spectra of both 3-level and 5-level BOC sub carriers. The theory is general and is extendible to sub carrier modulation with higher numbers of levels and the use of non-binary spreading code waveforms. One important suggestion, (J-L Issler, CNES), is the use of cosine sub carrier phasing, rather than sine phasing. The results of analysis are also applied to this case for the first time. Spectral Separation Coefficients (SSC) are one of the metrics used to compare the interactions between signals in the same spectrum space. A section is included, therefore, on developments in SSC Theory. There are two useful enhancements. One introduces the effects of protection filters that further isolate different signal types whilst the second derives SSC’s computable in the time domain – this is useful for complex signal shapes. The combination of the two is a more complete theory providing an armory of techniques useful in designing navigation signals able to compete within the current crowded spectra. This is useful in the design of candidate signals for Galileo, able to occupy the E1-L1-E2 frequency band alongside CA code transmissions from GPS and the BOC(10,5) spectrum proposed for M-code. BIOGRAPHY Dr Tony Pratt graduated with a B.Sc. and Ph.D. in Electrical and Electronic Engineering from Birmingham University, UK. He was on the teaching staff at Loughborough University, UK from 1967 to 1980. He held visiting professorships at Yale University; IIT, New Delhi and University of Copenhagen. In 1980, he joined Navstar Ltd, as Technical Director. In 1995, with Peek plc, he was involved in the formation of Tollstar Ltd, a 5 company consortium developing Electronic Road Tolling. He left Peek in 1997, starting OrbStar Consultants and joining Navstar Systems Ltd as Technical Consultant. He is now Technical Director (GPS) with ParthusCeva Ltd. He is also Special Professor at the IESSG at the University of Nottingham, UK. He is a Consultant to the UK Government in the development of Galileo Satellite System and it is in this role that the present work has been conducted. Mr J I R Owen is Leader of Navigation Systems, Air Systems Department, Dstl. He is a Dstl Fellow, a Fellow of the Royal Institute of Navigation. He gained a BSc (Hons) in Electrical and Electronic Engineering, Loughborough University, and joined the Royal Aircraft Establishment to research aspects of aircraft antennas. He helped develop the first GPS adaptive antenna system. He moved to the satellite navigation research group in 1982 and was responsible for the technical development of GPS receivers, antenna systems and simulators in the UK. Following the formation of DERA, he was responsible for the satellite navigation aspects of UK MOD’s research programmes for aircraft and missiles. He is technical adviser to UK Government Departments for GPS and the European Galileo programme, where he is active on the Signal Working Group, the Security Board and the European Space Agency Programme Board for Navigation. He chairs the ICAO Global Navigation Satellite Systems spectrum subgroup. Dr Pratt and Mr Owen are both Members of the European Commissions’s Signal Task Force for Galileo. INTRODUCTION Considerable efforts have been made to develop and qualify signals for the Galileo satellite navigation system. These have reached baseline status in all the proposed transmission bands (E5, E6, E1-L1-E2) but concerns remain in the E1-L1-E2 band as this is already occupied with GPS signals. Levels of intra-system and intersystem interference have been computed by a number of agencies in Europe and the USA. The additional interference generated by Galileo is not considered to be at a level that significantly degrades other satellite navigation systems and is less than ITU levels for the interference between geo-stationary satellite systems. This is not the only measure of interaction between the signals and receivers of 2 satellite systems and issues of jamming need also to be considered. This is especially appropriate for Galileo where it is intended that the system include ‘local elements’ – some of which may take the form of ground or near ground transmitters with identical signal formats to those of the satellites. This has motivated the search for improved satellite waveforms exhibiting lower levels of interference with existing systems whilst still providing good performance. However, the main metric for establishing the interaction between the signals from one satellite system and receiver performance designed for another satellite system or different service within the same system, is the Spectral Separation Coefficient. This seems to have been introduced originally by Betz (ref 1, 2) but there may have been earlier origins. He used it to deduce performance degradations in received signal to noise levels. The SSC concept provides a measure of the noise power output from a receiver when certain signals with given spectra are incident at its input. This shows that the fundamental measure is a cross power spectral density. This has particular utility in designing signal structures with good opportunities for co-existence within a given frequency band. We introduce the concept of Partial Spectral Separation Coefficients in which the frequency bands for the accumulation of noise energy are split into disjoint regions (non-disjoint regions or even overlapping regions could be used) as a diagnostic tool to establish the relative contributions of each sub-band numerically. Finally, a form of SSC’s is derived in the time domain using a ‘cross autocorrelation’ function. This term is the Fourier Transform of the cross power spectral density. The time domain method of SSC computation has two advantages it computes the SSC over an infinite frequency spectrum. This is the fundamental normalization for SSC’s. Secondly, when the modulation waveforms are complicated, it provides a simpler method of computation. The theory of SSC’s is extended to include the effects of filters prior to the main signal processing in satellite navigation receivers. This one of the techniques which can be employed to separate the effects of satellite signals with different spectra. The filters improve the effective Spectral Separation Coefficients (broadly read as performance in jamming) but at the (slight) cost of suboptimum system performance against a white noise background. SPECTRAL SEPARATION COEFFICIENTS Spectral Separation Coefficients represent the power at the output of a receiver matched filter when subject to certain input signals. The general arrangement is shown in figure 1. The input to the receiver might be from a variety of possible sources as shown. These include a signal source whose spectrum (HS(ω)), is matched to that of the receiver (in the signal processing sense – this specifies that the receiver filter is the complex conjugate of the signal spectrum HS*(ω)) or an interfering signal with spectrum HI(ω). The figure also has a ‘protection’ filter between the signal inputs and the receiver matched filter. This can be considered as having a frequency transfer response of 1 everywhere when it is not required. Figure 1 – Arrangement of signals incident on protected receiver The spectrum at the output of the (spreading waveform) matched filter is: ) ( ). ( )). ( . ) ( . ( ) ( 2 / 1 2 / 1 ω ω ω ω ω ∗ + = S P S S I I O H H H P H P S (1.1) Note that the definitions of HI(.) and HS(.) are general and could encompass also the spreading codes as well as the spreading waveform. This allows for a further development of the SCC theory including the complex code signals. The PI and PS multipliers represent the power levels (signal levels) of the two sources respectively. The power output is just the integral (over frequency) of this spectrum, assuming that the protection filter is absent: 2 2 2 / 1 2 / 1 2 2 2 ) ( )}. ( . ) ( . { ) ( ). ( ). ( . . 2 ) ( }. ) ( . ) ( . { ) (