Abstract:
The present invention discloses an apparatus and a method of modulating a carrier with digital information having a series of datums represented in a plurality of symbols, the method comprising selecting a first number of half-periods of a first phase distinguished carrier signal for representing a corresponding symbol of a first one of the datums, selecting a second number of half-periods of a second phase distinguished carrier signal for representing a corresponding symbol of the datum following the first datum, determining at least one matching carrier signal having a third number of half-periods of a format to conform to a transition of the first phase distinguished carrier signal to the second phase distinguished carrier signal, and sequentially arranging the first number of half-periods of the first phase distinguished carrier signal, the third number of half-periods of the matching carrier signal and the second number of half-periods of the second phase distinguished carrier signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present application claims the benefits of U.S. provisional patent application No. 60/430,459 filed Dec. 3, 2002, which is hereby incorporated by reference. 

   TECHNICAL FIELD 
   The invention relates to digital communication, or more particularly to the modulation of a carrier with digital information. 
   BACKGROUND 
   Digital modulation of signals is a necessary component of communication of digital information across a network. Generally, the object of modulation is efficient transmission of information across a channel. Modulation operates by keying shifts in analog characteristics in response to the encoded modulation input. Modulation in its simplest form shifts frequency, amplitude or phase. 
   A sequence of modulated signals may give rise to sharp discontinuities of slope in the modulated carrier. Such discontinuities are associated with high harmonics. This is bandwidth intensive. Such use of bandwidth may be incompatible with efficient communication system design. Further, random occurrence of discontinuities within the communication may add bandwidth without introducing ancillary benefits such as reliable synchronization. 
   Accordingly, it is an object of the present application to obviate or mitigate some or all of the above disadvantages. 
   SUMMARY 
   According to the present invention, there is provided a method of modulating a carrier with digital information having a series of datums represented in a plurality of symbols, said method comprising:
         selecting a first number of half-periods of a first phase distinguished carrier signal for representing a corresponding symbol of a first one of said datums;   selecting a second number of half-periods of a second phase distinguished carrier signal for representing a corresponding symbol of the datum following said first datum;   determining at least one matching carrier signal having a third number of half-periods of a format to conform to a transition of said first phase distinguished carrier signal to said second phase distinguished carrier signal; and   sequentially arranging said first number of half-periods of a first phase distinguished carrier signal, said third number of half-periods of said matching carrier signal and said second number of half-periods of said second phase distinguished carrier signal.       

   
     BRIEF DESCRIPTION OF THE FIGURES 
     Embodiments of the invention will be described by way of example only with reference to the accompanying drawings, in which: 
       FIG. 1  is a table of datum representation in digital modulation. 
       FIG. 2  is a table of datum representation in digital modulation. 
       FIG. 3  an example of a Phase Shift Keying (PSK) modulated wave. 
       FIG. 4  is a table comparing a Yaw Shift Keying (YSK) enhanced version of PSK to un-enhanced PSK. 
       FIG. 5  is a comparison of two matching signals: one higher and one lower frequency. 
       FIG. 6  is a diagram of a YSK modulation apparatus. 
       FIG. 7  is a timing diagram associated with the apparatus of  FIG. 6 . 
       FIG. 8  is a timing diagram illustrating the implications of non-coherent detection. 
       FIG. 9  is a diagram of a YSK demodulation apparatus. 
       FIG. 10  is a diagram of another embodiment of a YSK demodulation apparatus. 
       FIG. 11  is a diagram of a YSK demodulation apparatus illustrating one frequency filtering method. 
       FIG. 12  is a schematic diagram of a shaped RYSK signal. 
   

   DETAILED DESCRIPTION 
   Digital information is composed of a series of datum. Each datum is represented by one of n symbols. Typically such symbols are, themselves, a series of m binary digits. In this way a series of m binary digits may form up to 2 m  symbols i.e. n&lt;=2 m . Referring to  FIGS. 1 and 2  (prior art) we have tables of two such representations  80  and  90 . In the first representation  80 , the possible datum of digital information  100  are binary (A,B) and represented by two possible symbols  110 . In the second representation  90 , the possible symbols of digital information  120  are quaternary and represented by four possible symbols  130  (A,B,C,D). 
   Modulation is a variation of a carrier wave in response to a modulating wave. Modulation may involve a variation of one or more aspects of the carrier. Phase Shift Keying (PSK) modulation is a digital modulation format. Referring again to the tables of  FIGS. 1 and 2  we see the PSK carrier signals  140 ,  150 , respectively, of the PSK modulated wave as associated with the corresponding symbols  110 , 130 , respectively, they represent, and the corresponding possible datums of digital information  100 , 120 , respectively. These different carrier wave signals  140  and  150 , have identical frequency and amplitude, but different phase. In this way they are phase distinguished. The signals  140  of the first table are antipodal (180 degree phase shifted). The signals  150  of the second are 90 degree phase shifted. It is traditional that the carrier itself be sinusoidal. PSK has a constant envelope, giving it the desirable quality of imperviousness to non-linearity. Referring to  FIG. 3  (prior art) we have an example of a PSK modulated wave  160  (composed of signals  165 ), the series  170  of digital symbols  175  the signals represent, and the digital information  180  used to modulate it (composed of the datums  185  that correspond to symbols  175 ). This example uses the representation  80  of  FIG. 1 . In PSK modulation, it is convenient, but not necessary, for each modulated datum of information to be signaled with one, or multiple, half period(s) of carrier wave i.e. an integral number of periods. To simplify the generation of the modulated signal when a Digital to Analog Converter (DAC) is used to convert a table of values, it is convenient to make use of waveforms that include integral number of periods. When the number of periods is a non-integral number, the transmission of the fraction of period of the carrier waveforms at the end of each symbol causes the phase of the signal to vary from one starting point of a symbol to the other. An integral number of period eases the waveform generation since it is sufficient to repeatedly transmit the same waveform to a sine wave with no phase discontinuities. If an integral number of half-periods is used, generation of a continuous wave is as simple as for the integral case as long as the polarity of the waveform is toggled from one transmission to the other when this number is odd. For an even number of half-periods, we have an integral number of periods. 
   For simplicity, we have illustrated one integral number of periods per datum. Those skilled in the art will understand the other possible PSK modulation schemes involving M-ary (binary, tertiary, etc.) data or use of differential shift keying (symbol determined by change of phase rather than phase.) 
   In a traditional PSK modulated signal, as per  FIG. 3 , sharp discontinuities of slope  190  may arise at the point of transition between successive signals. The resulting high harmonics are undesirable in communication systems. One aspect of the invention is a method of modulation in which two sets of symbols are employed. The first (data) symbol set is information oriented. The symbol sets are interleaved, and the second (matching) symbol set is chosen to avoid sharp discontinuities. Referring to  FIG. 4  such a method, hereinafter referred to as Yaw-Shift Keying (YSK), is discussed as applied to PSK. 
     FIG. 4  is a table  200  comparing YSK enhanced version of PSK to PSK. Column one shows all the permutations of successive digital information  210  to be modulated for the modulation representation  80 . Column two is the corresponding PSK Modulated carrier. The transitions from preceding carrier waves  220  to successive carrier waves  230  may give rise to discontinuities of slope  190 . Column three shows possible corresponding YSK enhanced modulation. In this enhancement, similar to PSK:
         each symbol of the digital information  210  is represented, in part, by a different carrier wave signal,  220 ,  230 ; these carrier wave signals  220 ,  230  have identical frequency and amplitude, but can have different phase. (phase distinguished);   and the carriers themselves are sinusoidal.       
   However, in the inventive method, between two successive carrier wave signals (data) a matching carrier signal (support)  240  is inserted. Such a wave signal:
         conforms to (i.e. has no discontinuity or discontinuity of slope), at its beginning, the preceding carrier wave,  220 , and at its end, the successive carrier wave,  230 ;   and has duration equal to an integral number of carrier ½ sinusoids (one is illustrated in the table  200 ).       

   Note that matching waves of both higher and lower general frequency (than the carrier) are shown. Either of these waves are compatible. This implementation (discontinuity reduction) reduces bandwidth. Other implementations could use waveforms that facilitate synchronization (e.g. Spikes or high frequency burst for carrier recovery as for the color burst in TV signals.) 
   In YSK enhancement, modulation is staggered between waveforms (like the carrier waves  220 ,  230 ) devoted to transporting information, and waveforms (like the matching carrier  240 ) devoted to easing recovery (bandwidth control, synchronization). 
   Both these examples use a single carrier wave period for the carrier waves  220 ,  230 . However, for ease of generation, one can envision using any integral number of ½ periods for YSK enhanced PSK, as is the case in PSK. In cases where generating fractional period phase shifts is not an issue, the number of periods is, in fact, immaterial. 
   For a given representation (e.g. representation  80 ,  90 ) the set of transitions (for all permutations of preceding  220  and successive  230  carrier signals) will require matching signals  240  for each transition. Where the successive waves are identical, a third identical wave is a simple choice for the matching carrier signal  240 . (provided bandwidth reduction is the goal. A totally different waveform might be preferred if ease of synchronization is the priority.) In the table  200  we have shown a shaped waveform for the matching carrier signal  240  where the successive waves  220 ,  230  are antipodal. 
   This is not to imply the shown matching waveforms  240  are the only choices. One possible basis of matching wave signals  240  is sinusoidally modulated quadrature carriers from which linear combinations may be derived to satisfy the various transitions. Such signals are used in minimum-shift keying (MSK). One advantage of using such particular sinusoids is they produce an overall signal that is phase continuous. To satisfy this criteria, the matching signals  240  do not give rise to a discontinuity or change in slope that substantially negatively influences the communication system. Another advantage of using MSK signals relies in the fact that it involves the minimum frequency spacing that leads to a signal which is phase continuous. Since this method represents the maximum reduction in bandwidth, this particular shaping of the matching signals is referred to as Reduced Yaw Shift Keying (RYSK). Note that MSK is applicable only if the matching signal differs by ½ period from the signaling waveform In other cases a broader spectrum results. As it can be seen from  FIG. 4 , the matching carrier signal  240  may be of higher or lower frequency than the carrier waves  220 ,  230 . Thus the average frequency of the YSK signal may be equal to the frequency of the carrier waves  220 ,  230 . Instantaneously, it may drift from this center frequency to higher or lower values in a manner that depends on the data symbol. Due to this frequency “yawing” that the present invention is termed “yaw shift keying” (YSK). In regard to the signal&#39;s bandwidth, it is an advantage to have matching signals  240  of higher and lower frequency than the center frequency (of waves  220 ,  230 ) since it leads to a average spectrum of the signal which is symmetrical when one support waveform is used as often as the other. Other implementations may make use of support waveforms that are both of higher, or lower, frequency than the frequency of the signaling waveform depending on the desired spectrum of the signal. More than two support waveforms can also be considered in order to spread the signal&#39;s energy across a wider bandwidth. 
   In the example  250  of  FIG. 5 , waveforms are used for the matching signals  240   a  and  240   b  that respectively, are composed of substantially, lower and higher frequency components than the base carrier frequency of the preceding and successive carriers  220 ,  230 , respectively. It is possible to allow for multiple satisfactory matching wave signals  240  (such as examples  240   a  and  240   b ) per individual transition, and to chose between them on a transition by transition basis. For a given transition, one matching signal  240  of the possible satisfactory matching wave signals may then be chosen. In this manner, the frequency side-bands of the carrier may be balanced by alternating between a higher and lower spectral matching signal  240 . This balancing is desirable. Alternatively, another information signal (based on the matching choice) may be superimposed upon the modulated carrier by deliberately choosing amongst possible matching signals  240 . In this sense, it is possible to interleave two sets of digital information in one phase continuous carrier. The first (communicated with signals including  220 ,  230 ) is phase encoded; the second (communicated with signals including  240 ) is frequency encoded. 
   It may be understood by one skilled in the art that the principles of YSK extend to other modulation formats. PSK is used here for illustration, but the idea could be applied to frequency or amplitude shift keying as well. The central principle is a modulated signal composed of interspersed matching signals between information, in such a manner as to maintain continuous phase. 
     FIG. 6  is an apparatus  401  for generating the YSK modulation. The apparatus consists of a preceding symbol memory  405 , a matching signal lookup  415 , a carrier signal lookup  425 , switches  435 , and  445 , and summation unit  455 . The symbol memory  405  is input coupled to the input symbol port  400 , and the carrier/matching clock port  420 . The symbol memory  405  output is coupled to the preceding input of the matching signal lookup  415  via connection  410 . Matching signal lookup  415  is also coupled to a synchronizing clock port  430  and to the input symbol port  400  at the successive input. The carrier signal lookup  425  is input coupled to the input symbol port  400 , the synchronizing clock port  430 , and the carrier/matching clock  420 . Switches  445  and  435  are control coupled to the carrier/matching clock port  420  and its complementary port  421 , respectively. Switch  435  couples the matching signal lookup  415  output to a summation unit  455  input. Switch  445  couples the carrier signal lookup  425  output to a summation unit  455  input. The output of the summation unit  455  is the YSK modulation apparatus output  460 . 
     FIG. 7  shows a signal operation example of apparatus  401 . The input symbol  500  is asserted on the input symbol port  400 , and must be valid as shown. The carrier/matching clock  520  is asserted on the carrier/matching clock port  420 , and must be valid as shown. The symbol memory  405  records the current input symbol  500 , on the rising edge of the carrier/matching clock  520  and asserts this information  510  on connection  410 . Due to this, the matching signal lookup  415  has, at the falling edge of the carrier/matching clock  520 , access to the current input symbol  500  at its successive input and the preceding input symbol  500  at its preceding input. The matching signal lookup  415  with these signals along with synchronizing clock  530 , (via synchronizing clock port  430 ) generates matching signals  565  in accordance with the YSK method q.v. The carrier signal lookup  425  has access to input symbol  500 , the carrier/matching clock  520 , and the synchronizing clock  530 . These allow it to generate carrier signals for the appropriate number of periods of carrier. This example shows 3 carrier periods and 1 matching period. The switches  445 ,  435  are governed by the carrier/matching clock  520  (via the carrier/matching clock port  420  and its complementary port  421 ). Along with the summation unit  455 , the switches  445 ,  435 , merge the output of the lookups  415 ,  425  to produce a single YSK wave  560  at the YSK modulation apparatus output  460 . 
   Those skilled in the art will understand that YSK may be coherently detected with standard means i.e. where there is no question of synchronization between modulation and demodulation, the portion of the YSK wave containing the information may be directly demodulated. In the case non-coherent demodulation, however, YSK poses specific challenges. 
   Referring again to the examples of YSK modulated carrier signals  250  of  FIG. 5 , efforts to demodulate a carrier signal,  220 , 230 , are complicated by the need to locate them amongst the matching signals  240   a ,  240   b.    
     FIG. 9  illustrates an apparatus  900  for demodulating YSK signals. A YSK signal input  905  is input coupled to a switch  910 . The switch  910  is output coupled to a support demodulator  920  and a data demodulator  940 . A synchronizer  930  is input coupled to the support demodulator  920  and output coupled to the control terminal of the switch  910 . A Clock output  950  and data output  960  are coupled to the synchronizer  930  and data demodulator  940 , respectively. There is a need to de-interleave the matching signal (support)  240  and carrier signal (data)  220 , 230  before attempting to recover the information. When the reception starts, a switch  910  is in the position that allows the signal to reach the support symbol demodulator  920 . This demodulator triggers the synchronizer  930  each time it detects an incoming matching signal  240 . The synchronizer  930  then activates the switch  910  at the appropriate time in order to make carrier signal(s)  220 ,  230  reach the data symbol demodulator  240  for the duration of one data signal  220 ,  230 . At the same time, the synchronizer  930  generates a clock signal (on clock output  950 ) that indicates when an information symbol is available at the data output  960 . 
   The architecture shown in  FIG. 9  is not the only one that may be used to demodulate YSK signals. Referring to  FIG. 10 , there is shown an alternate embodiment of a demodulation apparatus  1000 , consisting of matched filters  1010 , output coupled to a decision making circuit  1020 , and input coupled to a synchronizer  1030  (which is in turn input coupled to the decision making circuit  1020 ). Data output  1040  is coupled to the decision making circuit  1020 , clock output  1050  is coupled to the synchronizer  1030 . This simplification of the demodulator&#39;s architecture is possible if the waveforms that represent the datum are selected having this in mind i.e. by selecting waveforms that are orthogonal. 
   In this apparatus, some filters  1010  are built to “recognize” the support signals  240  and other filters  1010  detect the data signals  220 ,  230 . The decision making circuit  1020  is required to be able to identify which matched filter produces the largest output. The synchronizer  1030  is then fed with this information. The synchronizer  1030  analyses at what rate and for how long those matched-filters  1010  that are associated to the support signals  240  produce the largest output and then generates a signal that synchronizes the operation of every matched-filter  1010  with the timing of the incoming signals  220 ,  230 ,  240 . This improves the filter reliability and, in turn, helps the decision making circuit  1020  in identifying the origin of largest outputs. Working on more reliable information, the synchronizer  1030  can iteratively improve its timing signal. At the same time, the decision-making circuit  1020  sends to its data output  1040  the demodulated data signal. Aware of the time at which these symbols become available, the synchronizer  1030  also generates a clock signal on the clock output  1050 . 
   When the signaling waveforms that are used to implement YSK modulation are sine waves such as those used for binary phase shift-keying (BPSK), PSK or frequency shift-keying (FSK), the matched filters  1010  that are shown in  FIG. 10  may be built with a mixer  1012  and an integrate &amp; dump circuit  1014  as shown in  FIG. 11 . For such a circuit, the waveform that feeds a given mixer  1012  determines which signaling waveforms the associated filter detects. The integrate &amp; dump circuit  1014  then acts as a low pass filter. Provided that integration begins when a signal starts to come in and ends with the same signal, the integrate &amp; dump circuit  1014  will produce a maximum output for a similar waveform. The output of the integrate &amp; dump circuits  1014  corresponds to the cross-correlation value of the incoming signal with the waveform that drives the mixer.  FIG. 11  thus shows a classical cross-correlation-type demodulator adapted for YSK signals. For such a demodulator  1100 , the synchronizer  1030  controls at what time the integrate &amp; dump circuit  1014  integrates in order for correct demodulation of YSK to take place. 
   In  FIGS. 10 and 11 , the number of matched filters depends on the particular waveforms that are used to implement YSK. This number may be reduced if some of these waveforms share properties. For example, BPSK involves two waveforms that only differ because of their respective polarity. Thus, the outputs of the two matched filters that may be used to demodulate a BPSK only differ because of their polarities. Hence, to eliminate one of these matched filters, a decision-making circuit that processes the magnitude and sign of its input may be used. 
   It may be understood by one skilled in the art that using YSK involves certain trade-offs with respect to the length of the carrier waves  220 ,  230  and the matching carrier  240 . Consider non-coherent demodulation of such a signal using a cross-correlation system (for implementation purposes, a desirable method): The sampling of the succeeding unrelated signals, may cause the response of the cross-correlator to be, for a limited period of time, a blend of both a response that depends on a preceding wave  220  and a matching wave  240 , or a matching wave  240  and a successive wave  230 . Depending on the length of the sampling period, it may be impossible, to guarantee a pure sample of the matching wave. In order to avoid circuit complexity in response to symbol interference, it is highly desirable to achieve a pure sample. This implies a shorter sampling period relative to the successive waves  220 ,  230 . Reducing the length of the correlation sample itself is limited by the correlator ability to successfully identify the necessary signals: improvement here is governed by the state of cross-correlator art. Reducing the length of matching wave  240  may have a positive effect on demodulation, but having matching waves that are relatively too short can cause the bandwidth of the signal to be unnecessarily large. Furthermore, increasing the length of the data bearing preceding and successive signals  220 ,  230 , will have a deleterious effect on the data transfer rate. It can be understood from this that a compromise reflecting circuit complexity, data transfer rate, bandwidth, and data integrity is in order. 
   One aspect of the invention brings a solution to the problem of selecting the proper ratio for non-coherent demodulation. Consider a cross-correlator with a minimum effective sampling period of 1, and length L. We shall make N refer to the length of support bits (e.g: if that cross-correlator processes a given support—or interspersed—signal). If that cross-correlator processes a given signal of length N it produces L+N−1 values that depend on that signal. Therefore, the sampled correlation values must be spaced apart in time by at least L+N sampling intervals if situations for which both samples are affected by interspersed signals are to be avoided. On the other hand, the sampled correlation values must not be too far apart since this could lead to sampling of a correlation value that depends on two successive interspersed signals. By analyzing scenarios that involve various lengths of correlator and signals, it may be shown that the number of consecutive correlation values that only depend on a given data signal of M samples is M−L+1. This second condition means that the sampled correlation values must be spaced apart by at most M−L sampling intervals. Hence, we may write that the sampled correlation values must be spaced apart by a number of sampling interval T such that M−L&gt;=T&gt;=N+L. 
   This spacing must be larger than one to have more than one sampled correlation value per data bit. Therefore, the conditions that apply to the sampling of the correlation values also imply that the correlator&#39;s length must be smaller than the length of the data signal. Thus, the correlator of this embodiment only processes a part of each data signal at a time. To highlight this fact, we refer to it by saying that the embodiment makes use of partial-cross-correlators that computes partial cross-correlation values. 
   To preserve bandwidth, it is required to minimize the length of the data. Because we have a condition that states that the length of the data bits can be lowered down to the point for which we have M−L=T, we can conclude that the minimum length of the data bit can be such that M=T+L. Hence, for a given correlator length, the length of the data bits will be minimized if the sampling interval is kept to a minimum. Based on the conditions that are mentioned above, this is to say that we must have T=N+L. This last result allow us to find that we need to have T=(M+N)/2 to preserve bandwidth. This condition indicates that it is only necessary to evenly sample the correlation values at a rate that corresponds to two samples per duration of a data signal,  220  and  230 , followed by a matching signal  240  to have pairs of sampled correlation values that each includes at least one value that only depends on a single data bit. If this condition is met, it is then only necessary to make use of classical time diversity combining or selection techniques to retrieve the information from the incoming bits. Combining techniques such as those that would involve comparison of the correlation values that form the pairs of value can then be considered as well as selection algorithm that would be based on identification of preamble sequences or detection of correct checksum values in the demodulated messages. 
   If the sampling rate of the correlation value is such that it is not required to demodulate the support signal, it becomes an advantage to reduce the length of the support signal to a minimum since this improves the overall throughput of the communication system. However, in order to have a YSK signal that can also be demodulated by circuits which take the support signal into account, it is better to keep the length of the support signal long enough to allow reliable demodulation of the support signal. The selection of a length for a bit can then be driven by a need to further simplify the design of the demodulators. Because it can be advantageous to have correlators that are all of the same length, one can think about using support signals that are of the same length as the correlators that are to be used to demodulate the data bits. In that case, the number of correlation values that depend on the support bits will be one per support bit. This will be desirable for those demodulators that do not demodulate the support signals and it will be acceptable for the other types of YSK demodulator that make use of the timing information carried by the support signals. Under these circumstances, the conditions given previously imply that N=L=(M+N)/4 which indicates that these types of demodulator will be able to demodulate a YSK signal for which the data signals are 3 times longer than the support signals. Different ratios can also be considered. What is important here is to select a ratio that allows the partial-cross-correlator to produce two or more partial-cross-correlation values per data signal in a way that ensures that at least one value per set depends only on the data signals. 
   A demodulation example in correspondence with these principles is shown in  FIG. 8 . Referring to this is a YSK modulated carrier  600 . Matching signals  620  are interspersed between long carrier signals  610 . The matching signals  620  are shown to be of constant amplitude for simplicity. Shaped waveforms described above could also have been used instead of the constant amplitude matching signals  620 . Referring to  FIG. 12  that shows a shaped RYSK signal  1200 , shaped support waveforms  1210  are used when phase shifts are required and constant amplitude support waveforms  620  are selected otherwise. The shaped support waveforms  1210  have an amplitude that first decreases and later increases in a way that provides a narrower signal bandwidth; the amplitude variation being a result of the multiplication of the support sine waves with one period of a cosine signal which last the same as the support signal  1210 . Digital narrow band filtering techniques can also be involved in the design of the matching signal  1210  to provide additional bandwidth reduction. In the demodulation technique of the invention, the long carrier signals  610  are at least 3 times the duration of the matching signals. Demodulation sampling is not constant in this technique. Also in  FIG. 8  sampling patterns are shown  680 - 687  in various states of alignment with the received carrier  600 . The sampling pattern consist of equal duration alternating periods of sampling  632 ,  636 ,  640 ,  644 ,  648 ,  652 ,  656 ,  660 , and waiting/not sampling  634 ,  638 ,  642 ,  646 ,  650 ,  654 ,  658  interspersed. 
   In any given sampling period  632 ,  636 ,  640 ,  644 ,  648 ,  652 ,  656 ,  660 , the received carrier  600  is detected using demodulation techniques common in the art (e.g. correlation). A carrier signal  610  will be successfully demodulated to a valid symbol by at least one of the sampling periods  632 ,  636 ,  640 ,  644 ,  648 ,  652 ,  656 ,  660 . Using the example of received carrier  670 , demodulation occurs in either sampling period  640  and/or  644  in any alignment  680 - 687 . 
   The demodulation results of pairs of sampling periods e.g. ( 640  and  644 ) both or either of which may be valid. In normal operating conditions, the symbol may be determined by the valid sample. Excessive noise may result in no valid signal or contradictory valid signals. In this case the system must acknowledge demodulation error. Where valid symbols are successively demodulated, there could be an uncertainty if these valid symbols corresponded to the same, or successive, signals. Therefore demodulated symbols are, ideally, considered in relation to the second previous demodulated symbol e.g. sample  648  may be considered relative to  640  for differential signaling. This, in effect, results in two interleaved channels. One of these channels, if clock drift may be ignored, is likely preferable. Lastly, in order to determine which channel is preferable, the carrier  600  may include a preamble of several datums. Comparison of the decoded and expected preamble identifies the preferable channel. 
   A method of demodulation compatible with the aforementioned example is as follows: The incoming signals are sampled in predetermined periods. The samples are partially cross-correlated to detect data signals. A history of the correlations is used to generate data, and synchronization. Synchronization is used to control future sampling. 
   Although the present invention has been described by way of particular embodiments and examples thereof, it should be noted that it will be apparent to persons skilled in the art that modifications may be applied to the present particular embodiment without departing from the scope of the present invention.