Abstract:
A method and apparatus for improving the bandwidth efficiency of a constant envelope continuous phase modulation waveform and transmitting data in a bandwidth efficient manner is disclosed. The method and apparatus utilizes a non-constant envelope continuous phase modulation signal which possesses many of the advantages of a multiple modulation index continuous phase modulation signal. One such advantage is the natural trellis structure of a multiple modulation index continuous phase modulation signal. In comparison to a constant envelope continuous phase modulation waveform, the non-constant envelope continuous phase modulation signal possesses a reduced transmit signal spectra and may also be demodulated by a standard maximum likelihood demodulator without any loss of performance.

Description:
BACKGROUND  
       [0001]     This application is related to the field of digital communications and more specifically to communications systems that require waveforms which occupy a fixed bandwidth channel.  
         [0002]     For digital transmission over band limited channels, the demand for bandwidth efficient signaling schemes has increased. A system often used for band limited channels is multi-bit per symbol phase shift keying (M-ary PSK) which has the drawback that for M equal to 2 or 4, the signal possesses a wide band because of discontinuous phase. Thus, radio frequency filtering has to be performed before transmission causing decreased receiver sensitivity. Other systems such as minimum shift keying (MSK) and fast frequency shift keying (FFSK) possess an error probability performance similar to 2- or 4-ary PSK but with a narrower spectrum for large frequencies. Choosing an M larger than 4 (e.g., M=8 or M=16) in the MPSK system makes the main lobe of the spectrum narrower, but increases the system&#39;s sensitivity to noise.  
         [0003]     Continuous phase modulation (CPM) signals, as discussed in  Digital Phase Modulation  by Anderson, J., Aulin, T. and Sundberg, C. E., the entirety of which is herein incorporated by reference, have many advantages over phase shift keying (PSK) signals. PSK signals must be filtered and transmitted through linear amplifiers. After filtering, PSK signals have an amplitude variance that must be accounted for to prevent signal distortion and transmit power amplifier over-current. CPM signals do not possess this problem and may be transmitted at the maximum power level allowed by a radio power amplifier. To transmit at the same amount of power of the CPM signal, a PSK signal would require a power increase at the amplifier generally on the order of 4-5 dB. On the contrary, a non-constant envelope (NCE) CPM signal would require a power amplifier that only provided 1.2 dB more power. Any loss in bit error rate (BER) of the NCE-CPM signal with respect to the PSK signal may be compensated by the trade-off in power amplifier transmitted power.  
         [0004]     Further improvements may be realized with NCE-CPM signals. For example, these signals may possess multiple modulation indices, h, which relate the size of the baseband pulse of a signal to the phase variation. A multi-h signal has a natural trellis structure that may be used to improve the modem BER performance without additional, redundant parity bits. Multi-h codes are phase codes in which the modulation index varies in a cyclic pattern from interval to interval. When this feature is added to an existing trellis encoder, a concatenated code results, in which trellis paths remain apart longer and minimum distance improves. This changes the modulation index of each symbol thereby delaying the point at which phase trajectories with different starting symbols remerge. This increases the minimum Euclidean distance (constraint length) and reduces the probability of symbol error. The cost for obtaining better detection efficiency through the use of a multi-h scheme is an increase in receiver complexity as compared to the single-h case. The optimum decoder for a trellis code in Gaussian noise is the Viterbi algorithm which traverses every path in the trellis structure to find the optimum path. An NCE-CPM waveform has both a reduced transmit signal spectra in comparison to a CPM waveform and the inherent CPM multi-h trellis structure which makes the NCE-CPM signal a better overall waveform for band limited channel communications. Furthermore, the NCE-CPM signal may be demodulated by a standard CPM maximum likelihood demodulator without any loss of performance. This allows an NCE-CPM signal a degree of interoperability with existing CPM demodulation capable receivers.  
         [0005]     A performance summary of PSK, CPM and NCE-CPM waveforms is shown below in Table 1:  
                                               Power (Peak to               Modulation   Average)   Bandwidth   BER Performance                   PSK   +4 dB to 5 dB   Base   10-5 at 9.5 dB       CPM   unity   −25%   10-5 at 8.5 dB       NCE-CPM   +1.2 dB   Same bandwidth as   10-5 at 12 dB               PSK                  
 
         [0006]     It is therefore an object of the disclosure to present a method for improving the bandwidth efficiency of a CPM signal comprised of plural symbols. The method includes the steps of coding the data stream, modulating the data stream with a constant envelope CPM waveform and converting the constant envelope CPM waveform into an NCE-CPM waveform.  
         [0007]     It is another object of the disclosure to present a method for improving the bandwidth efficiency of a constant envelope CPM waveform signal encoded with data symbols comprising the steps of varying a complex amplitude of a signal between successive constellation points prior to transmission and controlling the complex amplitude of the signal to follow a path between constellation points.  
         [0008]     It is a further object of the disclosure to present a method of transmitting data as an NCE-CPM signal comprised of a plurality of symbols in a constellation. The method includes the steps of coding the plurality of symbols and transecting each symbol by direct path during modulation of the coded plurality of symbols.  
         [0009]     It is still another object of the disclosure to present a method for modulating an input data stream comprised of a plurality of symbols represented as constellation positions in a complex plane. The method includes the steps of generating a CPM waveform modulated with the plurality of symbols and modifying the complex amplitude between the successive constellation positions to traverse the complex plane in a straight path from constellation position to constellation position.  
         [0010]     It is an additional object of the disclosure to present a system for improving the bandwidth efficiency of a CPM waveform communication system. The system includes a transmitter for transmitting data as CPM symbols, a receiver with a constant envelope CPM demodulator, and a conversion means for converting a constant envelope CPM waveform to an NCE-CPM waveform prior to transmission such that the complex amplitude of the signal between successive constellation points is less than the complex amplitude at each of the constellation points.  
         [0011]     It is an object of the disclosure to present a method for transmitting an input data stream as phase locations in a complex plane in a CPM waveform wherein the CPM waveform modulated with the input data stream transects the complex plan between successive phase locations in a substantially straight path.  
         [0012]     It is also an object of the disclosure to present a method for communicating data wherein the data is transmitted as a plurality of symbols with a complex plane as a CPM waveform wherein the magnitude of the waveform in the complex plane varies between symbols.  
         [0013]     These and many other objects and advantages of the present disclosure will be readily apparent to one skilled in the art to which the disclosure pertains from a perusal of the claims, the appended drawings, and the following detailed description of the preferred embodiments. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]     The subject matter of the disclosure will be described with reference to the following drawings:  
         [0015]      FIG. 1   a  illustrates a block diagram of a transmission system according to an embodiment of the disclosed subject matter used for transmitting data.  
         [0016]      FIG. 1   b  illustrates a block diagram of a prior art receiver capable of receiving a signal transmitted according to an embodiment of the disclosed subject matter.  
         [0017]      FIG. 2   a  is a representative constellation plot over a three symbol period of a prior art constant envelope continuous phase modulation (CPM) signal  
         [0018]      FIG. 2   b  is a representative constellation plot over the three symbol period of a non-constant envelope (NCE) CPM signal according to an embodiment of the disclosed subject matter.  
         [0019]      FIG. 2   c  is a illustration of a transected path between two successive constellation point according to an embodiment of the disclosed subject matter.  
         [0020]      FIG. 3  is a representative bandwidth comparison chart of an NCE-CPM signal according to an embodiment of the disclosed subject matter, a standard h=4/16, 5/16 1REC CPM signal and a QPSK signal.  
         [0021]      FIG. 4  is a representative comparison chart of the bit error rate (BER) performance of an NCE-CPM signal according to an embodiment of the disclosed subject matter, a standard h=4/16, 5/16 1REC CPM signal and a PSK signal.  
         [0022]     It is to be understood that these drawings are solely for the purposes of illustrating the concepts of the invention and are not intended as a definition of the limits of the invention. The embodiments shown in  FIGS. 1   a,    2   b  and  2   c  and described in the accompanying detailed description are to be used as illustrative embodiments and should not be construed as the only manner of practicing the invention. Also, the same reference numeral, possibly supplemented with reference characters where appropriate, have been used to identify similar elements. 
     
    
     DETAILED DESCRIPTION  
       [0023]     A system and method for increasing bandwidth efficiency in a band limited channel is disclosed. A continuous phase modulated (CPM) signal may be represented as  
         s   ⁡     (     t   ,   α     )       =           2   ⁢   E     T       ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   0     ⁢   t     +     ϕ   ⁡     (     t   ,   α     )       +     ϕ   o       )             
 
 where the information carrying phase may be defined as  
           ϕ   ⁡     (     t   ,   α     )       =     2   ⁢   π   ⁢           ⁢   h   ⁢       ∫     -   ∞     t     ⁢       ∑     i   =     -   ∞       ∞     ⁢           ⁢       α   i     ⁢     g   ⁡     (     τ   -   iT     )       ⁢           ⁢     ⅆ   τ               ;       -   ∞     &lt;   t   &lt;   ∞         
 
 where α= . . . α −2  α −1  α 0  α 1  . . . 
 
         [0024]     is an infinitely long sequence of uncorrelated M-ary data symbols each taking one of the values α i =±1, ±3, . . . , ±(M−1); i=0, ±1, ±2, . . . with equal probability of 1/M. (M is assumed even).  
         [0025]     E is the symbol energy, T is the symbol time, f 0  is the carrier frequency, and ø o  is an arbitrary constant phase shift which, without loss of generality, may be set to zero in the case of coherent transmission. “h” is referred to as the modulation index which relates the size of the baseband pulse g(τ) to the size of the phase variation ø(t, α). The amplitude of g(τ) may be chosen to give a maximum phase change απh radians over each symbol interval when all the data symbols in a sequence take the same value α. The subject matter of the present disclosure is directed to a continuous phase frequency shift keying (CPFSK), notated 1REC, where the frequency pulse g(τ) is of rectangular length T.  
         [0026]     The information carrying phase function in CPM signals is continuous at all times for all combinations of data symbols. In M-ary continuous phase frequency shift keying (CPFSK) schemes, the phase change is proportional to the slope of the continuous and piecewise linear phase, i.e., the modulation index h. In multi-h CPM and non-constant envelope (NCE) CPM schemes, the modulation index may be cyclically changed for successive symbol intervals. The cyclic use of properly chosen modulation indices essentially provides delayed merging of neighboring phase trellis paths which leads to an increase of minimum Euclidean distance (constraint length) and provides coding gain for multi-h phase coded modulation schemes.  
         [0027]      FIGS. 1   a  and  1   b  illustrate a novel transmitter  100  and a known CPM receiver  101 , respectively. In such a communication system, an input signal  102  is applied to an encoder  104 , which applies an error correcting code to the input signal  102 . Further, the encoder  104  applies trellis coding to the input signal  102 . The encoded signal is then applied to interleaver  106  to impose time-diversity into the encoded bit-stream. The encoded, interleaved signal is then applied to modulator  108 , which organizes individual bits into symbols based on the communication system characteristics and generated waveform. The transmission symbols are then applied to a linear or non-linear filter  110 , which removes signal components that may be induced by switching instantaneously from one symbol to the next symbol. The symbols are applied to a Digital Up-Converter  112  to up-convert the symbols to a conventional carrier frequency, which is then band-limited by a transmit filter  114 . The resulting CPM signal is then modified into a NCE-CPM signal, by an interpolator  115  which transects the unit circle between successive constellation points. The interpolator varies the complex amplitude of the signal between the constellation positions through amplification or attenuation or both. The interpolator can be implemented with hardware or software, such as a processor. The interpolator can also contain a look up table for driving the attenuator or amplifier. The up-converted NCE-CPM signal  116  is then transmitted over a wireless communication network or channel. The transmission of the NCE-CPM signal is independent of the frequency band used in the communication system and therefore is not limited to any particular frequency band. Additionally the NCE-CPM can be transmitted over an air interface in a wireless communication system or through a wired communication system.  
         [0028]     The transmitted NCE-CPM signal  116 , when received by the known CPM receiving system  101 , is applied to a linear or non-linear receiver filter  118 , which bandwidth matches the received signal bandwidth to the bandwidth of the transmitted signal. The received signal is applied to a Digital Down-Converter  120  and a receive filter  122 . The down-converted signal is then demodulated by a demodulator  124 , de-interleaved by a deinterleaver  126  and decoded by a decoder  128 , in well known processes that demodulate, deinterleave and decode the received signal. Because the signal may be represented in a finite state trellis, a Viterbi algorithm or decoder may be used for recovering the modulated data. Key functions in the demodulator  124  may include but are not limited to filtering, sampling, tracking and accumulating frequency errors of a phase offset of received symbols, storing, updating subsequently transmitted symbols based on the frequency error of previously transmitted symbols, metric calculation for calculating the optimum path metrics for a received symbol or sequence of symbols, data recovery, and synchronization. The decoded output signal  130  represents an estimate of the input signal  102 . In an alternative embodiment, a receiver may utilize a fixed bank of filters matched to a set of signals corresponding to an h value averaged over a finite set of modulation indices. The use of a fixed bank of filters also avoids the need to cycle banks of matched filters in synchronism with the transmitter h values. A reduced complexity receiver for the joint estimation of transmitted data, carrier phase and symbol timing may also be realized through the use of an approximate representation of the maximum likelihood function. However, a Viterbi decoder still requires knowledge of the signal deviation in use to assign the correct sequence of allowable phase transitions.  
         [0029]     As illustrated in  FIG. 2   a,  the transmit phase spectrum  200  of a three symbol duration prior art constant-envelope CPM signal  210  occupies the unit circle of a signal constellation. The M-ary (eight) constellation is shown with constellation points  201 - 208 . The transmitted signal, in the example shown, moves from constellation point  201  to constellation point  202  along the unit circle  210  through arc  211 . The signal then moves along the unit circle  210  to constellation point  206  through arc  212  and then moves to constellation point  203  along arc  213 . The signal&#39;s complex amplitude is constant throughout the rotation to each constellation point of the signal and is represented in  FIG. 2   a  as R 1 , where R 1  equals k. The CPM transmit signal  210  has a constant envelope as the waveform rotates from symbol to symbol around the unit circle resulting from the constant radius R 1 .  
         [0030]     The NCE-CPM transmitted signal according to an embodiment of the present disclosure is shown in  FIG. 2   b  for the same signal as shown above. The NCE-CPM signal  220  transects each constellation phase position through a direct path, such as a chord of the unit circle, rather than following the path described by the unit circle. The NCE-CPM transmit signal  220  transitions as the waveform shifts from symbol to symbol along a direct path which typically will have a non-constant radius as the signal travels between constellation points. This alteration in the envelope of a CPM signal occurs prior to transmission by changing, linearly or non-linearly, the amplification or attenuation of the amplifier or attenuator respectively. These variable envelope transitions may be created, for example, with selective attenuation during the shift from one constellation point to another constellation point, or by selective amplification of the signal approaching or departing from the constellation points, or both attenuation and amplification can be used during the shift. As stated previously, the application of the subject matter to communication systems is independent of frequency and can be employed in frequency hopping communication systems. The NCE-CPM signal is generated by transecting the unit circle from the present phase position to the next phase position.  
         [0031]     In  FIG. 2   b,  the signal transitions from constellation point  201  to successive constellation point  202  over direct path  221 . The complex amplitude of the signal along direct path  221  is represented by R which is a function of θ and the position of constellation points  201  and  202 . The signal then transitions to constellation point  206  along path  222  and then constellation point  203  along path  223 . The interpolator  115  may determine the path using a metric based on the successive constellation points and rotation angle θ. For example, the positions of constellation points  201  and  202  are expressed in polar coordinates as R∠θ 201 , R∠θ 202  specifically k∠0°, k∠−45°. Using geometric properties and identities, the magnitude R between constellation points  201  and  202  can be interpolated according to:  
       R   =       k   ⁡     (       sin   ⁢           ⁢   γ       sin   ⁢           ⁢   α       )       =       k   ⁢       sin   ⁡     (       90   ⁢   °     -       (       θ   202     -     θ   201       )     2       )         sin   ⁡     (       90   ⁢   °     -   θ   +       (       θ   202     -     θ   201       )     2       )           =     k   ⁢         f   ⁡     (       θ   202     ,     θ   201       )         f   ⁡     (       θ   202     ,     θ   201     ,   θ     )         .               
 
         [0032]     As shown in  FIG. 2   c,  k is the radius of the unit circle  210  which is a function of transmitter power, θ is the rotation of the signal, and γ and α are angles of the triangle formed by tracking the path  221 . The chords and thus paths between successive constellation points are a function of the constellation and may be predetermined for each combination of successive constellation points. The interpolation shown is linear, however non-linear interpolation is equally envisioned. By reducing the magnitude of the signal between the successive constellation points, the non-constant-envelope continuous waveform is generated.  
         [0033]     Another method of interpolation converts the location of the constellation points  201  and  202  into rectilinear coordinates such that: 
 
( x,y ) 201 =( k  cos θ 201   , k  sin θ 201 ) 
 
( x,y ) 202 =( k  cos θ 202   , k  sin θ 202 ) 
 
         [0034]     Then the number of increments N is selected, the number of increments in arbitrary and dictates the resolution of the path between the constellation positions. For Illustration only the number of increments used set at N=10. The value of the increment is determined by: 
 
 x (increment)=( x   202 - x   201 )/ N =.(707 k− 1.0 k )/10=0.0293 
 
 y (increment)=( y   202 - y   201 )/ N =(−0.707−0.0)/10=−0.0707 
 
         [0035]     The path proceeds from increment to increment to the next constellation point by: 
 
 x (new)= x   201   +x (increment) 
 
 y (new)= y   201   +y (increment) 
 
 and 
 
 x (new)= x (new)+ x (increment) 
 
 y (new)= y (new)+ y (increment) 
 
 where the Radius or complex magnitude is given as simply the square root,: 
 
 R (new)={square root}{square root over (( x (new) 2   +y (new) 2 ).)}
 
         [0036]     Several other method of interpolation using know geometric tools is equally envisioned but are not discussed herein as there are readily determined by one skilled in the art  
         [0037]     A comparison of the frequency spectrum  300  generated by the NCE-CPM signal  320  to an h=4/16, 5/16 1REC CPM transmit signal  310  and QPSK transmit signal  330  is shown in  FIG. 3 . The NCE-CPM signal  320  requires significantly less bandwidth than the QPSK signal  330  and the h=4/16, 5/16 1REC CPM transmit signal  310 . This allows more channels to be packed into a fixed bandwidth allocation. Further improvements for the NCE-CPM spectrum may be made by increasing the length of the frequency pulse g(τ) which results in further decreasing the side-lobes of the NCE-CPM signal  320 . Further, by changing the modulation index h, the spectra may also be altered. As shown, the resulting NCE-CPM spectrum  320  is reduced by twenty five percent over the standard h=4/16, 5/16 1REC CPM spectrum  310 .  
         [0038]     Bit error rate (BER) performance results  400  for a theoretical PSK signal  410 , an NCE-CPM signal  420  according to an embodiment of the disclosed subject matter and a standard h=4/16, 5/16 1REC CPM signal  430  are shown in  FIG. 4 . The NCE-CPM signal  420  represents a better case in terms of gaining bandwidth efficiency as shown in  FIG. 3  while giving up as little energy per bit (E b N o ) performance as possible as illustrated in  FIG. 4 .  
         [0039]     While preferred embodiments of the present invention have been described, it is to be understood that the embodiments described are illustrative only and that the scope of the invention is to be defined solely by the appended claims when accorded a full range of equivalence, many variations and modifications naturally occurring to those of skill in the art from a perusal thereof.