Patent Publication Number: US-8995575-B2

Title: Modulation signals for a satellite navigation system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 10/595,128, filed Nov. 15, 2006, which was the National Stage of International Application No, PCT/GB04/003745, filed Sep. 1, 2004, which claims priority to GB Patent Application No. 0320352.8, filed Sep. 1, 2003. 
    
    
     FIELD OF THE INVENTION 
     The invention relates to modulation signals, systems and methods such as, for example, navigation and positioning signals, systems and methods. 
     BACKGROUND TO THE INVENTION 
     Satellite Positioning Systems (SPS) rely on the passive measurement of ranging signals broadcast by a number of satellites, or ground-based or airborne equivalents, in a specific constellation or group of constellations. An on-board clock is used to generate a regular and usually continual series of events, often known as ‘epochs’, whose time of occurrence is coded into a random or pseudo-random code (known as a spreading code). As a consequence of the pseudo-random or random features of the time epoch encoding sequence, the spectrum of the output signal is spread over a frequency range determined by a number of factors including the rate of change of the spreading code elements and the waveform used for the spreading signal, Typically, the spreading waveform is rectangular and has a sinc function power spectrum. 
     The ranging signals are modulated onto a carrier signal for transmission to passive receivers. Applications are known that cover land, airborne, marine and space use. Typically, binary phase shift keying is employed to modulate the carrier signal, which, itself, has a constant magnitude, Usually, at least two such signals are modulated onto the same carrier in phase quadrature. The resulting carrier signal retains its constant envelope but has four phase states depending upon the two independent input signals. However, it will be appreciated that two modulating signals do not need to have the same carrier magnitude. It is possible for a constant carrier magnitude of the combined signal to be maintained by appropriate selection of corresponding phases other than π/2 radians. 
     An example of such a satellite positioning system is the Global Positioning System (GPS). Generally, the GPS operates using a number of frequencies such as, for example, L 1 , L 2  and L 5 , which are centred at 1575.42 MHz, 1227.6 MHz and 1176.45 MHz respectively. Each of these signals is modulated by respective spreading signals. As will be appreciated by those skilled in the art, a Coarse 
     Acquisition (CA) code signal emitted by the GPS Satellite Navigation System is broadcast on the L 1  frequency of 1575,42 MHz with a spreading code rate (chip rate) of 1.023 MHz, The CA has a rectangular spreading waveform and is categorised as BPSK-R 1  The GPS signal structure is such that the signal broadcast by the satellites on the L 1  frequency has a second component in phase quadrature, which is known as the precision code (P(Y) code) and made available to authorised users only The P(Y) signal is BPSK modulated with a spreading code at 10.23 MHz with a magnitude which is 3 dB lower in signal power than the CA code transmission. Consequently, the Q component has a magnitude which is 0.7071 (−3 dB) of the magnitude of the I component. It will be appreciated by those skilled in the art that the phase angles of these states of these signals are ±35.265° in relation to the ±I axis (phase of the. CA code signal as specified in ICD GPS 200 C). One skilled in the art also appreciates that the P code is a function of or is encrypted by the Y code. The Y code is used to encrypt the P code. One skilled in the art appreciates that the L 1  signal, containing both I &amp; Q components, and the L 2  signal can be represented, for a given satellite, i, as
 
 S   L1i ( t )= A   p   P   i ( t ) d   i ( t )cos(ω 1   t )+ A   c   c   i ( t ) d   i ( t )sin(ω 1   t ),
 
and
 
 S   L2i ( t )= B   p   P   i ( t ) d   i ( t )cos(ω 2   t )
 
where
 
     A p  and A c  are the amplitudes of the P and CA codes, typically A p =2A c ; 
     Bp is the amplitude of the L 2  signal; 
     ω 1  and ω 2  are the L 1  and L 2  carrier frequencies; 
     p i (t) represents the P(Y) ranging code and is a pseudo-random sequence with a chip rate of 10.23 Mcbps. The P code has a period of exactly 1 week, taking values of +1 and −1; 
     c i (t) represents the CA ranging code and is a  1023  chip Gold code, taking values of +1 and −1; 
     d i (t) represents the data message, taking values of +1 and −1. 
     A satellite constellation typically comprises 24 or more satellites often in similar or similarly shaped orbits but in a number of orbital planes. The transmissions from each satellite are on the same nominal carrier frequency in the case of code division access satellites (such as GPS) or on nearby related frequencies such as GLONASS. The satellites transmit different signals to enable each one to be separately selected even though several satellites are simultaneously visible. 
     The signals from each satellite, in a CDMA system like GPS, are distinguished from each one another by means of the different spreading codes and/or differences in the spreading code rates, that is, the p i (t) and c i (t) sequences. Nevertheless, as will be appreciated from the power spectrum  100  shown in  FIG. 1  there remains significant scope for interference between the signals transmitted by the satellites.  FIG. 1  shows power spectra  100  for the CA and P(Y) codes. The power spectrum  102  for the CA code has maximum power at the carrier frequency L 1  and zeros at multiples of the fundamental frequency, 1.023 MHz, of the CA code. For example, it can be appreciated that zeros occur either side of the carrier frequency at ±1.023 MHz, ±2.046 MHz etc. Similarly, the power spectrum  104  for the P(Y) code has a maximum amplitude centred on the L 1  and L 2  frequencies, with zeros occurring at multiples of ±10.23 MHz as is expected with a sine function waveform. 
     It is known to further modulate the ranging codes using a sub-carrier, that is, a further signal is convolved with the P codes and/or CA codes to create Binary Offset Carrier (BOC) modulation as is known within the art see, for example, J, W. Betz, “ Binary Offset Carrier Modulation for Radionavigation ”, Navigation, Vol. 48, pp227-246, Winter 2001-2002, Standard BOC modulation  200  is illustrated in  FIG. 2 .  FIG. 2  illustrates the combination of a portion of a CA code  202  with a subcarrier signal to produce the BOC signal  204  used to modulate a carrier such as, for example, L 1 . It can be appreciated that the BOC signal is a rectangular square wave and can be represented as, for example, c i (t)*sign(sin(2πf s t)), where f s  is the frequency of the subcarrier. One skilled in the art understands that BOC(f s ,f c ) denotes Binary Offset Carrier modulation with a subcarrier frequency of f s , and a code rate (or chipping rate) of f c . Using binary offset carriers results in the following signal descriptions of the signals emitted from the satellite:
 
 S   L1i ( t )= A   m   sc   im ( t ) m   i ( t ) d   i ( t )cos(ω 1   t )+ A   C   sc   ig ( t ) g   i ( t ) d   i ( t )sin(ω 1   t )= I   SL1i ( t )+ Q   SL1i ( t ),
 
and
 
 S   L2i ( t )= B   m   sc   im ( t ) m   i ( t ) d   i ( t )cos(ω 2   t )
 
where
 
     A m , A c  and B m  are amplitudes; 
     m i (t) is an m-code BOC( 10 , 5 ) signal; 
     g i (t) is a Galileo open service range code; 
     sc im (t) represents the sub-carrier signal for m i (t); 
     sc ig (t) represents a subcarrier signal for g i (t); and 
     ω 1  and ω 2  are the L 1  and L 2  carrier frequencies. 
       FIG. 2  also illustrates power spectra for a BPSK-R 1  code and pair of BOC signals, that is, BOC( 2 , 1 ) and BOC( 10 , 5 ). The first spectrum  202  corresponds to BPSK-R 1  code. The second power spectrum  204  corresponds to the BOC( 2 , 1 ) code and the third power spectrum  206  corresponds to the BOC( 10 , 5 ) code. It can be appreciated that the side lobes  208  of the BOC( 2 , 1 ) signal have a relatively large magnitude. Similarly, the illustrated side lobe  210  of the BOC( 10 , 5 ) signal has a relatively large magnitude. One skilled in the art appreciates that the energy in the side lobes are a source of interference. 
     It is an object of embodiments of the present invention to at least mitigate the problems of the prior art. 
     SUMMARY OF INVENTION 
     Accordingly, a first aspect of embodiments of the present invention provides an in-level modulation signal comprising m signal amplitudes, where m&gt;2, for modulating a first signal. 
     A second aspect of embodiments of the present invention provides a method of generating a transmission signal comprising a carrier signal, the method comprising the step of combining a plurality of subcarrier modulation signals with the carrier signal. 
     A third aspect of embodiments of the present invention provides a ranging system comprising means for generating a ranging code; means for generating a signal; means for transmitting the signal. 
     A fourth aspect of embodiments of the present invention provides a system comprising memory for storing at least one of a plurality of selectable phase states and selectable amplitude states; the memory being responsive to at least one of a ranging code signal, a system clock signal and a subcarrier signal to produce a carrier signal bearing at least one of phase and amplitude modulation to produce a transmission signal. 
     Advantageously, embodiments of the present invention provide significantly more control over the shape of the power spectra of signals, that is, the distribution of energy within those signals. 
     Other aspects of the present invention are described and defined in the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE INVENTION 
       Embodiments of the present invention will now be described, by way of example, only with reference to the accompanying drawings in which: 
         FIG. 1  shows a power spectrum of a pair of ranging code; 
         FIG. 2  illustrates power spectra of a ranging code (BPSK-R 1 ) and BOC( 10 , 5 ) signals; 
         FIG. 3  illustrates a multi-level sub-carrier; 
         FIG. 4  illustrates the phase states for at least a pair of multilevel subcarriers according to embodiments of the present invention; 
         FIG. 5  depicts a power spectrum of a prior art subcarrier and a subcarrier according to embodiments of the present invention; 
         FIG. 6  illustrates phase states for a subcarrier according to embodiments of the present invention; 
         FIGS. 7A and 7B  illustrate in phase and quadrature phase subcarriers according to embodiments of the present invention; 
         FIG. 8  illustrates phase states of a subcarrier according to an embodiment of the present invention; 
         FIG. 9  shows subcarriers according to embodiments of the present invention; 
         FIG. 10  depicts power spectra of subcarriers according to embodiments of the present invention; 
         FIG. 11  illustrates subcarriers according to embodiments of the present invention; 
         FIG. 12  shows an alternative subcarrier waveform according to an embodiment of the present invention; 
         FIG. 13  illustrates a further alternative waveform according to embodiments of the present invention; 
         FIG. 14  illustrates, schematically, a transmitter using subcarriers according to embodiments of the present invention; and 
         FIG. 15  illustrates a further embodiment of a transmitter according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS 
     Referring to  FIG. 3 , there is shown a first embodiment of a subcarrier  300 . It can be appreciated that the sub-carrier is a 5-level approximation of a sinusoidal signal  302 . It can be appreciated that the signal levels are (+1, +1/√2, 0, −1/√2, −1). Furthermore, it will be appreciated that the levels are the projections onto the x or I axis of a rotating vector at angles of π/4 radians having a unit magnitude. It will be further appreciated that, given the in-phase and quadrature-phase components of, for example, S L1i , that is, A m sc im (t)m i (t)d i (t)cos(ω i t)=I SL1i (t) and A C sc ig (t)g i (t)d i (t)sin(ω i t)=Q SL1i  (t), the magnitude of the signal will be such that it is constant since the projection of the quadrature phase component onto the y or Q axis will also take the values (+1, +1/√2, 0, −1/√2, −1). 
     It will be appreciated that there are preferably restrictions on the combinations of signals, at least one of which is that a constant modulus signal should be maintained. The constraints are (1) that “+1” or “−1” on the in-phase component can only occur in conjunction with “0” on the quadrature phase component and visa versa and (2) “±1/√2” can only occur on both phases simultaneously. The magnitudes of the in-phase and quadrature phase components of the spreading signals, sc, ig (t) or sc im (t), can be plotted on an Argand diagram  400  such as is shown in  FIG. 4 . The waveforms for the I and Q components are thus built from the following signal element sequences:
         I phase—(+1/√2, +1, +1/√2, 0) representing a +1 signal   I phase—(−1/√2, −1, −1/√2, 0) representing a −1 signal   Q phase—(+1/√2, 0, −1/√2, −1) representing a +1 signal   Q phase—(−1/√2, 0, +1/√2, +1) representing a −1 signal.       

     Any combination of I or Q signal sequences can be chosen from the above set within the constraint of a constant magnitude carrier signal, computed as (I 2 +Q 2 ) 1/2 . It will be clear to those skilled in the art, that there are many other equivalent sets of sequences which may be chosen from the set of 5-levels satisfying the criterion of a constant carrier envelope. It can be appreciated that the magnitudes of the subcarriers on the I and Q channels can be thought of as being analogous to the states of an 8-PSK signal. Therefore, such a pair of 5-level subcarrier carrier signals can be thought of as 8 phase subcarrier signals. 
       FIG. 5  illustrates the effect of using a stepped or m-level, m&gt;2, subcarrier waveform, Referring to  FIG. 5  there is shown a pair  500  of power spectra. The first power spectrum  502 , illustrated using the dotted line, represents the spectrum of a BOC( 2 , 2 ) subcarrier. It can be appreciated that the energy of the subcarrier is contained within progressively reducing side lobes  504 ,  506 ,  508  and  510 . The second power spectrum  512  represents the power spectrum of a BOC( 2 , 2 ) signal that used 8 phase subcarrier signals, that is, 8 phase amplitudes, represented by BOC 8 ( 2 , 2 ). More generally, BOCm(f s ,f c ) represents an m-phase subcarrier signal of having a frequency of f s  and a chipping rate of f c . It can be appreciated that the spectrum  512  of the BOC 8 ( 2 , 2 ) signal has a number of side lobes  514 ,  516 ,  518 ,  520 ,  522  and  524 . Of those side lobes, it can be seen that the 1 st  to 4 th  side lobes are significantly reduced, that is, they comprise significant less energy, as compared to the side lobes of the BOC( 2 , 2 ) signal spanning the same frequencies. The significant reduction in the 1 st  to 4 th  side lobes can be beneficial in situations in which one skilled in the art wishes to use the frequency spectrum spanned by the side lobes for other transmissions. 
     It will be appreciated by those skilled in the art the BOC 8 ( 2 , 2 ) has significantly improved interference properties as determined using Spectral Separation Coefficients (SSC) and self SSCs as is well understood by those skilled in the art, that is, the spectral coupling between a reference signal and BOC( 2 , 2 ) is greater than the spectral coupling between a reference signal and BOC 8 ( 2 , 2 ), For example, a BOC 8 ( 2 , 2 ) signal exhibits a 10-12 dB improvement in spectral isolation as compared to a conventional BOC( 2 , 2 ) signal, Further information on the relationship between SSC and signals according to embodiments of the present invention can be found in, for example, Pratt &amp; Owen; BOC Modulation Waveforms, IoN Proceedings, GPS 2003 Conference, Portland, September 2003, which is incorporated herein by reference for all purposes and filed herewith as in the appendix, 
     Furthermore, embodiments of the present invention utilise the magnitude and duration of the subcarrier to influence, that is, control the energy in harmonics of the resulting modulating waveform. 
     For example, referring still to  FIG. 5 , it can be appreciated that additional spectral nulls appear in the BOC 8 ( 2 , 2 ) spectrum at substantially 6 MHz and 10 MHz offset from the carrier whereas there are no such nulls in the conventional BOC( 2 , 2 ) signal. The location of the nulls is influenced by at least one of the magnitude and duration of the steps in the multilevel subcarrier. More specifically, the nulls can be steered to desired locations by changing either of these two elements, that is, the position of the nulls is influenced by these two elements, Appendix A contains an indication of the relationship between the spectra of signals according to embodiments of the present invention and the magnitude and duration of the steps. 
     Referring to  FIG. 6 , there is shown subcarrier states or amplitudes for I and Q signals for a further BOC 8  signal, that is, a binary offset carrier having eight states. It can be appreciated that the eight states can be represented by, or correspond to, subcarrier amplitudes chosen from the set (−√{square root over (3)}/2, −1/2, +1/2, +√{square root over (3)}/2) ie four states or signal amplitudes rather than the five states or signal amplitudes described above. Therefore, the I and Q components, constructed from the following signal elements such that √{square root over ((cos 2 Θ+sin 2 Θ))}=1, that is, ±√{square root over (3)}/2 can only occur in conjunction with ± 1 / 2  , are as follows:
         I phase—(+1/2, +√3/2, +√3/2, +1/2) representing a +1 chip of a ranging code signal   I phase—(−1/2, −√3/2, −√3/2, −1/2) representing a −1 chip of a ranging code signal   Q phase—(+√3/2, +1/2, −1/2, −√3/2) representing a +1 chip of a ranging code signal   Q phase—(−√3/2, −1/2, +1/2, +√3/2) representing a −1 chip of a ranging code signal.       

     It will be appreciated that the states  1  to  8  shown in  FIG. 6  are not equidistantly disposed circumferentially. The transitions between states  2 &amp; 3 ,  4 &amp; 5 ,  6 &amp; 7 ,  8 &amp; 1  are larger in angular step than the transitions between states  1 &amp; 2 ,  3 &amp; 4 ,  5 &amp; 6 ,  7 &amp; 8 . It will be appreciated that when these states are translated into subcarrier amplitudes, the duration of a given amplitude will depend on the duration or dwell time of a corresponding state, that is, the durations for which the subcarrier remains in any given state may no longer be equal unlike the states of  FIG. 4  above, The dwell times are a matter of design choice such as, for example, to minimise the mean square difference between a stepped waveform and a sinusoid,  FIG. 7   a  illustrates the subcarriers  700  and  702  corresponding to the states shown in  FIG. 6 . It can be appreciated that the durations of within each state the subcarriers  700  and  702  are equal. The Q channel subcarrier magnitudes will follow substantially the same pattern as described above but phase shifted by π/2 radians. The subcarrier  702  for the Q channel is shown in dotted form in  FIG. 7 . It will be appreciated that such subcarriers provide a constant envelope magnitude since (I 2 +Q 2 ) 1/2 =1 for all amplitude combinations. However, referring to  FIG. 7   b , there is shown a pair of subcarriers  704  and  706  in which the durations at each state are unequal. It will be appreciated that not all amplitude combinations satisfy (I 2 +Q 2 ) 1/2 =1. Therefore, the transmitted signal will not have a constant envelope. 
     It will be appreciated by those skilled in the art that a stepped half cycle of the subcarrier corresponds to one chip. However, other embodiments can be realised in which other multiples of half cycles correspond to a chip. For example, embodiments can be realised in which two half cycles of a subcarrier correspond to a chip. In such embodiments the signals for the I and Q channels would be 
     I phase—(+1/2, +√3/2, +√3/2, +1/2, −1/2, −√3/2, −√3/2, −1/2) representing a +1 signal 
     I phase—(−1/2, −√3/2, −√3/2, −1/2, +1/2, +√3/2, +√3/2, +1/2) representing a −1 signal 
     Q phase—(+√3/2, +1/2, −1/2, −√3/2, −√3/2, −1/2, +1/2, +√3/2) representing a +1 signal 
     Q phase—(−√3/2, −1/2, +1/2, +√3/2, +√3/2, +1/2, −1/2, −√3/2) representing a −1 signal. Similarly, embodiments realised using three half cycles per chip would produce 
     I phase—(+1/2, +√3/2, +√3/2, +1/2, −1/2, −√3/2, −√3/2, −1/2, +1/2, +√3/2, +√3/2, +1/2) representing a +1 signal 
     I phase—(−1/2, −√3/2, −√3/2, −1/2, +1/2, +√3/2, +√3/2, +1/2, −1/2, −√3/2, −√3/2, −1/2) representing a −1 signal 
     Q phase—(+√3/2, +1/2, −1/2, −√3/2, −√3/2, −1/2, +1/2, +√3/2, +√3/2, +1/2, −1/2, −√3/2) representing a +1 signal 
     Q phase—(−√3/2, −1/2, +1/2, +√3/2, +√3/2, +1/2, −1/2, −√3/2, −√3/2, −1/2, +1/2, +√3/2) representing a −1 signal. 
     One skilled in the art will appreciate that the above can be extended to n half cycles of a subcarrier per ranging code chip. 
     It will be appreciated that other phases can be used to describe the subcarriers. For example, phase and amplitude components of 16-PSK can be used to create BOC 16  subcarriers having 9 levels, assuming that the first state is at (+1,0), Using m-PSK phase states can be used to produce (m+2)/2level subcarrier signals. Therefore, setting m=2 gives the conventional BPSK and a two-level subcarrier. Setting m=4 provides a 3 level subcarrier, that is BOC 4  modulation, setting m=8 produces a 5 level subcarrier, that is, BOC 8  modulation, setting m=16 produces a 9 level subcarrier, which corresponds to BOC 16  modulation. 
     It will be appreciated that several further variations in the assignment of code and data states to the phase locations can be realised, For example, rotation of the states shown in  FIG. 4  by 22.5° leads to a reassignment of angles associated with the states from the angles (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°)to the angles (22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5°). Again, it will be appreciated that this does not cause a change in the modulus of the spectrum and, again, the required number of amplitude levels reduces from 5 to 4, that is, m-PSK can be used to realise [(m+2)/231 1] amplitudes according to appropriate rotation and alignment of the phase states. The resulting waveforms for the I and Q components are built, in this case, from the following signal element sequences:
         I phase—(+cos(67.5°),+cos(22.5°),+cos(22.5°),+cos(67.5°)) representing a +1 signal   I phase—(−cos(67.5°),−cos(22.5°),−cos(22.5°),−cos(67.5°)) representing a −1 signal   Q phase—(+sin(67.5°),+sin(22.5°),−sin(22.5°),−sin(67.5°)) representing a +1 signal   Q phase—(−sin(67.5°),−sin(22.5°),+sin(22.5°),+sin(67.5°)) representing a −1 signal,       

     It should be noted that the I and Q signal element sequences for the cases described above are orthogonal over the duration of one spreading pulse (chip). Clearly, other rotations are possible and will yield orthogonal signal element sets. 
     An alternative way of representing the above is via a state table. Assume that an embodiment of a BOC 8  modulation has been realised with equidistant states and the first state having a phase angle of π/8 radians(22.5°) as shown in  FIG. 8 , which correspond to the above values. The sequence of phase states required for each I and Q ranging code signal components, assuming that the ranging codes transition substantially simultaneously and a desire to maintain a substantially constant output envelope, that is, the states for the subcarriers would be given by 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Sequence of States for BOC8(x,x) I &amp; Q signal elements 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 I 
                 Q 
                 t1 
                 t2 
                 t3 
                 t4 
               
               
                   
                   
               
               
                   
                 +1 
                 +1 
                 2 
                 1 
                 8 
                 7 
               
               
                   
                 −1 
                 +1 
                 3 
                 4 
                 5 
                 6 
               
               
                   
                 +1 
                 −1 
                 7 
                 8 
                 1 
                 2 
               
               
                   
                 −1 
                 −1 
                 6 
                 5 
                 4 
                 3 
               
               
                   
                   
               
            
           
         
       
     
     It will be appreciated that the subcarrier corresponding to the phase states in Table 1 comprises a half cycle per ranging code chip. Furthermore, the sense of the phasor is clockwise when I and Q are equal and anticlockwise otherwise. It will be apparent that the signal element sequences or state sequences are sections (specifically half cycle sections in the aspect of the invention disclosed above) of a sampled or quantised sinusoid. The concept can, therefore, be extended to include a multiplicity of such samples. Those variants, which appear to be useful, include the cases with samples from a finite number of half cycles, that is, rather than, for example, an I channel value of +1 being represented by the states of  2 ,  1 ,  8  and  7 , it can be represented using some other number of states such as, for example,  2 ,  1 ,  8 ,  7 ,  6 ,  5 ,  4 ,  3 ,  2 ,  1 ,  8 ,  7  ie by three half cycles of the sample or quantised sinusoid. Table 2 illustrates the phase states for such an embodiment and is based on the phase state diagram of  FIG. 4  for samples but using three half cycles (or an arbitrary number of half cycles) of the sinusoid waveform. The sinusoid or portion or multiple of half cycles thereof is known as the ‘basis waveform’. One skilled in the art realises that other basis waveforms can be used such as, for example, a triangular waveform or a set of mutually orthogonal waveforms. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Sequence of States for 8-PSK I &amp; Q Signal Elements with 1½ cycles 
               
               
                 of sub-carrier per chip modulation 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 I 
                 Q 
                 t1 
                 t2 
                 t3 
                 t4 
                 t5 
                 t6 
                 t7 
                 t8 
                 t9 
                 t10 
                 T11 
                 t12 
               
               
                   
               
               
                 +1 
                 +1 
                 2 
                 1 
                 8 
                 7 
                 6 
                 5 
                 4 
                 3 
                 2 
                 1 
                 8 
                 7 
               
               
                 −1 
                 +1 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                 +1 
                 −1 
                 7 
                 8 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 1 
                 2 
               
               
                 −1 
                 −1 
                 6 
                 5 
                 4 
                 3 
                 2 
                 1 
                 8 
                 7 
                 6 
                 5 
                 4 
                 3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Sequence of States for 8-PSK I &amp; Q Signal Elements with two half 
               
               
                 cycles of sub-carrier per chip modulation. 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 I 
                 Q 
                 t1 
                 t2 
                 t3 
                 t4 
                 t5 
                 t6 
                 t7 
                 t8 
               
               
                   
               
               
                 +1 
                 +1 
                 2 
                 1 
                 8 
                 7 
                 6 
                 5 
                 4 
                 3 
               
               
                 −1 
                 +1 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 1 
                 2 
               
               
                 +1 
                 −1 
                 7 
                 8 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                 −1 
                 −1 
                 6 
                 5 
                 4 
                 3 
                 2 
                 1 
                 8 
                 7 
               
               
                   
               
            
           
         
       
     
     One skilled in the art will appreciated that it is assumed in Tables 1 to 3, that the I and Q chip transitions happen substantially simultaneously and, furthermore, that the I and Q subcarriers take the form of sine and cosine waveforms respectively. However, embodiments can be realised in which the ranging code chip transitions do not occur substantially simultaneously. Furthermore, in circumstances in which the ranging code chip transitions do not occur substantially simultaneously, the subcarriers corresponding to the I and Q ranging code chips can be arranged to take the form of a pair of quantised sine waves. 
     It will seen that there are 4 time samples for each ½ cycle of the waveform. The stepped sinusoidal waveform may be viewed as sub-carrier modulation of the basic spreading waveform. The number of time samples and independent information bearing channels is related to the number of phase states, which the carrier signal has in its representation. Although the examples above have used phase states that are ‘powers of 2’, embodiments can be realised in which some other number is used For example, a 6-PSK carrier signal can be used to carry 2 independent information bearing binary channels, In this case only 3 signal element samples are required per transmitted code chip. 
     One skilled in the art appreciates that the replacement of the stepped sinusoid with a rectangular wave with duration of each element equal to a ½ cycle of the sinusoid is well known within the art. As indicated above, it is known as ‘Binary Offset Carrier’ modulation. There are usually 2 further attributes associated with the BOC description, which relate to the frequency of the code chipping rate and to the frequency of the offset sub-carrier. BOC( 2 , 2 ) consequently is interpreted as a waveform with a 2.046 MHz chipping rate and a 2.046 MHz offset sub-carrier. This arrangement has exactly two ½ cycles of the sub-carrier signal for each code element (chip). 
     A further aspect of embodiments of the present invention relates to using a set of subcarriers to modulate ranging codes, with at least one or more, or all, of the subcarriers being multilevel waveforms, One skilled in the art may think of such embodiments as modulation of the subcarrier signal by a further subcarrier signal. The resulting signal transmitted by an ith satellite or system having a carrier frequency of ω i  for an additional subcarrier, would have the form:
 
 S   i ( t )= A   m   sc   jm ( t ) sc   im ( t ) m   i ( t ) d   i ( t )cos(ω i   t )+ A   c   sc   jg ( t )sc ig ( t ) g   i ( t ) d   i ( t )sin(ω i   t )= I   Si ( t )+ Q   Si ( t )
 
where
 
     sc im (t) and sc jm (t) represent first and second subcarrier signals respectively first ranging codes such as, for example, M-codes; and 
     sc ig (t) and sc jg (t) represent first and second subcarrier signals second ranging codes such as, for example, Gold codes. In general, for n subcarriers, the signal would have the form: 
     It should be noted that embodiments can be realised in which sc im (t) and sc ig (t) are the same or different, Similarly, embodiments can be realised in which sc jm (t) and sc ig (t) are the same of different. 
                   S   i     ⁡     (   t   )       =           A   m     ⁢       ∏     j   =   1     n     ⁢           ⁢         sc   ijm     ⁡     (   t   )       ⁢       m   i     ⁡     (   t   )       ⁢       d   i     ⁡     (   t   )       ⁢   cos   ⁢     (       ω   i     ⁢   t     )           +       A   C     ⁢       ∏     j   =   1     l     ⁢           ⁢         sc   ijg     ⁡     (   t   )       ⁢       g   i     ⁡     (   t   )       ⁢       d   i     ⁡     (   t   )       ⁢     sin   ⁡     (       ω   1     ⁢   t     )               =         I   Si     ⁡     (   t   )       +       Q   Si     ⁢     (   t   )             ,         
where
 
               ∏     j   =   1     n     ⁢           ⁢         sc   ijm     ⁡     (   t   )       ⁢           ⁢   and   ⁢           ⁢       ∏     j   =   1     l     ⁢           ⁢       sc   ijg     ⁡     (   t   )                 
represents the product of the subcarriers for the first and second ranging codes such as, for example, the m and Gold codes.
 
     Although it is possible to use more than one subcarrier, practical embodiments will typically use 2 subcarriers, Modulation using a pair of subcarriers is known as Double Binary Offset Carrier 
     (DBOC) modulation. Modulation using three subcarriers is known as Triple Binary Offset Carrier (TBOC) modulation and so on such that modulation using a n-tuple of subcarriers is known as N-tuple Binary Offset Carrier (NBOC). As mentioned above, one or more than one of the subcarriers may be stepped, that is, having magnitudes related to respective phase states. 
     As examples of this aspect of the invention,  FIG. 9  illustrates a pair of waveforms  900 . In  FIG. 9 , as an illustration of the NBOC invention, the subcarrier basis waveforms are assumed to be binary and only a single subcarrier waveform  902  is shown, The time duration in  FIG. 9  is 512 samples and exactly matches the duration of one code element duration (chip), The first subcarrier  902  contains 4 half cycles of a subcarrier per ranging code chip, as illustrated by the dashed waveform. If this was the only sub-carrier component, the modulation would be a BOC( 2 x,x) type, where x is the frequency of the code rate (chipping rate), However, it can be appreciated that a second sub-carrier (not shown) having 16 half cycles per 512 samples has been used to produce the modulated waveform  904  to be combined with the carrier of the satellite signal. The modulated waveform is shown by the solid curve. As a result of modulation (multiplication) of the two subcarriers, the resulting waveform  904  has phase reversals for the second subcarrier  904  whenever there is a sign reversal in the first subcarrier  902 , This is clearly evident in  FIG. 9  at points  906 ,  908  and  910 , where the transitions of the second subcarrier (not shown) would have been opposite. The resulting modulation is denoted 
     Double BOC, or DBOC. In the case of  FIG. 9 , the modulation is DBOC(8x,(2x,x)), that is there are 8 half cycles of the second subcarrier per chip of the ranging code (not shown), The main energy is concentrated around frequencies ±8x from the carrier signal, with a BOC like double humped spectrum. 
     Referring to  FIG. 10 , there is shown a pair of power spectra  1000 . A first power spectrum  1002  relates to a DBOC 8 ( 16 ,( 2 , 2 )) signal. It will be appreciated that at least one of the first and second subcarriers used to create the DBOC 8 ( 16 ,( 2 , 2 )) signal comprised amplitudes derived from 8 corresponding phase states. In the specific embodiment shown, the first subcarrier was the multi-level signal. It will be appreciated that the nomenclature for representing DBOC modulation or subcarriers is DBOCa(b,c(d,e)), where a and c represent the number of phase states, that is, amplitudes, of the subcarriers having frequencies b and d respectively. The second spectrum  1004  relates to a BOC 8 ( 2 , 2 ) signal. The spectra shown have been made using a previous aspect of the invention, that is the use of multilevel subcarriers or subcarriers having more than two phase states, in combination with the Double BOC concept. The waveforms for I &amp; Q modulations for the spectrum of  FIG. 10  are shown in  FIG. 11 , Referring to  FIG. 11  there is shown a pairs  1100  of waveforms. The first pair of waveforms  1102 , representing the I channel of the spreading waveform, comprises a stepped or multi-level BOC( 2 , 2 ) signal  1104 , represented by the solid line, and a 16 Mhz subcaffier modulated BOC( 2 , 2 ) signal  1106 , represented by the dashed line. It will be appreciated that the 16 MHz subcarrier modulated BOC( 2 , 2 ) signal has been produced by multiplying the BOC 8 ( 2 , 2 ), that is, stepped BOC( 2 , 2 ) signal, by a 16 MHz rectangular waveform (not shown) having amplitudes of ±1. 
     The second waveform  1108 , representing the Q channel, comprises a quadrature BOC( 2 , 2 ) signal  1110  together with a 16 MHz subcarrier modulated BOC( 2 , 2 ) signal  1112 . It can be appreciated that the first subcarrier  1104  or  1110  is a subcarrier according to an embodiment of the present invention described above whereas the second sub-carrier (not shown) in both cases are conventional binary rectangular waveforms, that is, conventional subcarriers. It can be appreciated that there are regions  1114  of overlap between the two BOC( 2 , 2 ) subcarriers  1104  and  1110  and their resulting products, that is, 16 MHz subcarrier modulated BOC( 2 , 2 ) signals  1106  and  1112 , In the regions of overlap  1114 , the waveforms have the same amplitude profile. 
     An advantage of the embodiments of the signals shown in  FIG. 11  is that the I channel or component has been produced or represents DBOC 8  modulation or signal whereas the Q channel has been produced using or represents BOC 8  modulation. However, this arrangement still preserves or provides a substantially constant envelope carrier signal to be emitted from the satellite. 
     Embodiments of the present invention have been described with reference to the subcarrier signals being periodic, However, embodiments can be realised in which the subcarrier signal comprises a pseudorandom noise signal. Furthermore, embodiments can be realised in which the shape of the subcarrier takes a form other than a stepped, that is, a multilevel wave or quantised approximation of a sinusoidal waveform, For example, multilevel-pulsed waveforms, multilevel-periodic waveforms or multilevel-aperiodic waveforms, could be used such as the signal shown in  FIG. 12  according to the influence one skilled in the art wishes the resulting modulation to have on the power spectrum of the transmitted signal and/or any appropriate measure of interference such as, for example, SSC or self-SSCs. 
     Referring to  FIG. 13 , there is shown a subcarrier waveform  1300  according to a further embodiment of the present invention together with one chip  1302  of a code or other waveform such as, for example, another subcarrier. It can be appreciated that the subcarrier comprises a first portion of a BOC( 5 , 1 ) waveform, in the  100  ns sections, combined with portions of a BOC( 1 , 1 ) waveform, in the  400  ns portions, to produce an overall subcarrier. It will be appreciated that the spectra of the BOC( 5 , 1 ) waveform will have a peak at 5*1.023 MHz and the BOC( 1 , 1 ) waveform will have a peak at 1*1.023 MHz, Therefore, one skilled in the art appreciated that selectively combining the BOC subcarriers allows one skilled in the art to position or relocate the peaks of the overall subcarrier. Again, it can be appreciated that the subcarrier used, for example, to modulate the ranging codes is derived from more than one subcarrier. Although the signal described in relation to  FIG. 13  has been derived from BOC( 5 , 1 ) and B 0 C( 1 , 1 ) subcarriers, embodiments can be realised in which other combinations of BOC subcarriers are used In effect, the BOC( 5 , 1 ) and BOC( 1 , 1 ) signal have been multiplexed or selectively combined to produce an overall subcarrier signal. It will be appreciated that other sequences for the subcarriers can be realised according to a desired effect upon the power spectrum of a transmitted signal. For example, a subcarrier can be realised using a pseudorandom sequence as sub-carrier instead of the stepped modulations, The use of additional sequences to that of the main spreading code has hitherto been limited to use as a tiered code, which changes state after every complete code repetition interval. The GPS L 5  codes are constructed in this manner using Neumann Hoffman sequences of length 10 or 20 to extend a 1 ms code (of 10230 chips or elements) to 10 ms or 20 ms, The use of a subcode chip interval has not previously been considered. A complete sequence (a sub-sequence) has a duration of one code chip, or at most a plurality, of code chips, It fulfills a similar role to the sub-carrier modulation as previously described in that it controls the spectrum of the emissions, One feature of such a sub-sequence is that such sequences may be chosen to be common amongst a satellite constellation or a sub-set of the constellation, One such subset might be a group of ground transmitters providing a local element or augmentation to the space segment of the system, For example, subcarrier amplitudes can be realised that have the sequence -++++----+in 10 subchip intervals or other sequence of +1′s and −1′s per ranging code chip or other subcanier chip according to the desired effect on spectrum of the resulting signal. Examples such as the 7 subchip interval sequences would include ++-----, +++----, +-+-+--, and can be chosen to provide similar control over the emitted spectrum. 
     Referring to  FIG. 14 , there is shown, schematically, a transmitter  1400  according to an embodiment of the present invention. The transmitter  1400  comprises means  1402 , that is, a generator, for generating or selecting the ranging codes for transmission. It will be appreciated by those skilled in the art that such ranging code may be generated by, for example, shift register implementations, It can be appreciated that the ranging code selection and/or generation means  1402  is illustrated as producing g i (t) and p i (t), These codes are fed to respective mixers  1404  and  1406 . The mixers  1404  and  1406  are arranged to combine the ranging codes with subcarriers according to embodiments of the present invention. Respective subcarrier generators  1408  and  1410  generate the subcarriers. Optionally, a data signal, d i (t), is also preferably mixed with the ranging codes and subcarriers, The duration of one bit of the data signal is normally an integer multiple of the code repetition interval. For example, in UPS CA code, it is 20 times the 1 ms code repetition interval, that is, the data rate is 50 bps, The mixed signals  1412  and  1414  are fed to a further pair of mixers  1416  and  1418 , where they are mixed with in-phase and quadrature phase signals produced via an oscillator and phase shifter assembly  1420 . The further mixed signals  1422  and  1424  are combined, via a combiner  1426 , and output for subsequent up conversion by an appropriate up converter  1428 . The output from the up converter  1428  is fed to a high-power amplifier  1430  and then filtered by an appropriate filter  1433  for subsequent transmission by, for example, a satellite or other device arranged to emit or transmit the ranging codes. 
     Referring to  FIG. 15 , there is shown a schematic representation of a modulation system  1500  according to an embodiment. The system  1500  comprises a ranging code generator  1502  for producing a ranging code. The ranging code is fed to a first lookup table  1504  comprising phase states and a second lookup table  1506  comprising amplitude states. The output of the phase state lookup table  1504  is used to drive a phase modulator  1508 , which, in turn, produces a voltage signal to control the phase of a voltage controlled oscillator  1510 . The output of the oscillator  1510  is combined, via, a combiner  1512  such as, for example, a gain controlled amplifier or multiplier, with a signal output from the amplitude state table  1506  to produce a subcarrier having the appropriate characteristics. 
     Although the above embodiments have been described with reference to maintaining a substantially constant signal envelope, embodiments are not limited thereto. Embodiments can be realised in which variable modulus signal envelopes are used. It will be appreciated that the constraints described above, which are aimed at preserving unitary magnitude of (I 2 +Q 2 ) 1/2 , need not necessary apply. 
     The above embodiments have been described with reference to the I and Q channels having the same chipping rates. However, embodiments are not limited to such arrangements. Embodiments can be realised in which different chipping rates are used 
     Although embodiments of the present invention have been described with reference to the L 1  and L 2  frequencies, embodiments are not limited to such arrangements. Embodiments can be realised in which other frequencies or frequency bands can be used according to the requirements of the system using the invention, For example, the lower L band (ie E 5   a  and E 5   b ), the middle (ie E 6 ) and upper L-band (ie E 2 -L 1 -E 1 ) can also benefit from embodiments of the present invention. It will be appreciated that such embodiments may use signals having at least three components rather than the two components described above. 
     Furthermore, embodiments of the present invention have been described with reference to standard 
     BOC. However, one skilled in the art appreciated that embodiments can also be realised using Alternative BOC. 
     Furthermore, it will be appreciated that embodiments can be realised in which the number of half cycles of a subcarrier per chip of a code can be at least one of odd, even, an integer multiple or a non-integer multiple of the chip, that is, there is a rational number relationship between the number of subcarrier half cycles and the chip duration. 
     Embodiments of the present invention described above have focused on the transmission side of the invention, that is, upon the generation, modulation and transmission of ranging codes combined with a subcarrier or subcarriers. However, one skilled in the art appreciated that a converse system and method are required to receive and process the signals. Once one skilled in the art has designed a system for transmitting such signals, designing an appropriate receiver is merely the converse of the transmit operations. Therefore, embodiments of the present invention also relate to a receiver for processing signals such as those described above. 
     The reader&#39;s attention is directed to all papers and documents that are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference. 
     All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. 
     Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise, Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. 
     The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.