CONTINUOUS PHASE MODULATION, CPM, WAVEFORMS

FIELD OF THE INVENTION

[0001] The present invention relates to modulator apparatus and methods to simplify the generation of M-ary Continuous Phase Modulation (CPM) signals.

BACKGROUND OF THE INVENTION

[0002] Continuous Phase Modulation (CPM) is a bandwidth, energy and battery efficient digital modulation technique, exhibiting smooth transitions in its phase, which conveys the information content. Smooth phase transitions enable bandwidth efficiency gains by virtue of concentrating the signal's power in a compact spectral band, allowing adjacent waveforms to be packed closer together in the frequency domain. The constant envelope property of CPM leads to significant savings in DC (direct current) power, which translates into battery efficiency for mobile digital communication terminals, such as handsets or satellites.

[0003] To achieve the phase smoothness, most CPM techniques employ phase smoothing pulses such as raised cosine (RC) or rectangular (REC) pulses, whose length (L) may be several integer multiples of symbol duration (T), and acts as the modulation memory. This boils down to intentionally introducing intersymbol interference, as multiple pulses occupy one symbol interval. Besides the phase smoothing pulse, the two other free parameters managing the characteristics of a CPM signal are the modulation index h, and the alphabet size, M. The modulation index h is described as the ratio of the frequency deviation to the frequency of the modulating wave, and defined to be h = k/p such that k and p are two mutually prime integers. As h gets smaller, the distance among the CPM symbols is decreased, which results in an even more compact spectra at the expense of reduced resilience to error. M on the other hand determines the variety of information messages to be transmitted. As M gets higher, transmission signals are selected from a richer set, offering greater error resilience.

A CPM signal can be expressed as

where t denotes time, and T denotes the symbol duration, both measured in seconds. _n £ {±1, ±3, . . . , ±( — 1)} is the M-ary message symbol, and a stands for the history of message symbols such that a = [« _η , « _η _ _ΐΓ . .]. g(.) is the phase smoothing response of a CPM waveform, and it is related to the underlying frequency pulse, /(.) with the following relation:

[0004] Various CPM decomposition techniques have been proposed in the scientific literature, among which the work of Laurent [1] , and that of Mengali and Morelli [2] are the most prominent techniques from a complexity-reduction standpoint. Laurent's decomposition expresses a CPM waveform as a superposition of Pulse Amplitude Modulated (PAM) components for M = 2, i.e. , binary CPM. Laurent's seminal work for binary CPM is generalized to an arbitrary CPM alphabet size by Mengali and Morelli [2] . According to Laurent, Mengali and Morelli's method, a CPM waveform can be approximated as

F-1

z(t, «) ~∑∑ a _n g _k (t - nT) (3) Q A ₂ L- i _; p _log2 , F = Q ^P (M - 1) (4) where F is the number of PAM components in the decomposition, <¾ _n denote CPM pseu- dosymbols, and (¾(.) denote the Laurent pulses. The sign = denotes the mathematical definition of a parameter, and the operation .] denotes the ceiling operation, which rounds its argument to the nearest integer above its current value. Generation of CPM pseudosym- bols, with respect to the actual message symbols, _n , and the calculation of the Laurent pulses, Qk(t) are presented in detail in the papers [1] for binary CPM, and in [2] for M-ary CPM.

[0005] An important observation related to (¾(.) is that, the main pulse go(t) , carries a significant portion of the signal energy in a binary CPM realization. This observation leads to various simplifications of CPM waveforms by simply truncating the PAM decomposition to a single pulse representation for binary CPM, where only the main pulse, go (t) is retained in the decomposition, and the rest of the pulses are discarded [3, 4] . Similarly, for M-ary CPM, the first 2 ^P - 1 pulses convey most of the signal energy. Following from this, for M-ary CPM, a principal pulses approximation is developed in [5-9] , retaining the first 2 ^P — 1 pulses in the Laurent-Mengali-Morelli decomposition and dismissing the rest of the pulses.

[0006] Although reduced complexity CPM demodulator development has received a significant attention in the literature so far, design of simplified CPM modulators has received little attention. In [3] , a method is proposed to express a binary CPM (i.e., M = 2) waveform as a concatenation of a differential encoder and a transmitter filter. For higher-order CPM waveforms (i.e. , M > 2) , however, CPM modulators require complicated circuitry since higher-order arithmetic operations are required using binary circuitry.

[0007] What is needed in the art is a method and apparatus to simplify the coherent CPM modulator design for all CPM configurations and arbitrary values of h, M, and L, so that efficient and computationally inexpensive signal generation algorithms and hardware may be designed building on binary circuitry.

SUMMARY OF THE INVENTION

[0008] It is an object of this invention to provide low complexity alternative to apparatus and methods for coherent modulation of constant or quasi-constant envelope, binary (i.e., M equals 2) or higher order (i.e., M greater than 2) CPM signals, or corresponding programs or corresponding methods to produce configurations for processors for carrying out such methods.

[0009] It is yet another object of this invention to provide a simplification in the generation of constant or quasi-constant envelope, binary (M equals 2) or higher order (i.e., M greater than 2) CPM signals.

[0010] In accordance with one aspect of the invention, is a method and apparatus for transmitting a CPM signal using Laurent's and Mengali-Morelli's CPM decompositions. In this method, an information message sequence is inputted to a bank of P parallel Binary Time Invariant Phase Encoders (BTIPE). The sequence outputted by BTIPE units are first mapped onto CPM subsymbols by an element-wise memoryless mapper. CPM subsymbols are inputted into a product generator, generating CPM pseudosymbols. CPM pseudosymbols are modulated onto an -ary PAM waveform, that is the superposition of PAM component pulses in each symbol duration such that the pulses are derived by full decomposition of Laurent-Mengali-Morelli.

[0011] The number of PAM component pulses within the modulator can be K = F = Q ^P (M— 1) if the full Laurent-Mengali-Morelli decomposition is invoked. Alternatively, the number of PAM component pulses can be reduced to K = 2 ^P — 1 principal pulses. As yet another alternative, the K = 2 ^P — 1 principal pulses can be further optimized with respect to the mean square error criteria as presented in Laurent's [1] and Mengali-Morelli's work

[2] ·

[0012] The invention accordingly comprises the several steps and the relation of one or more of such steps with respect to each of the others, and the apparatus embodying features of construction, combinations of elements and arrangement of parts that are adapted to affect such steps, all is exemplified in the following detailed disclosure, and the scope of the invention will be indicated in the claims.

[0013] Any of the additional elements can be combined together and combined with any of the aspects. Numerous variations and modifications can be made without departing from the claims of the present invention. Therefore, it should be clearly understood that the form of the present invention is illustrative only, and is not intended to limit the scope of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other aspects, features and advantages will become apparent in the following Detailed Description of the Preferred Embodiments, when read in conjunction with the appended drawings, in which:

[0014] Fig. 1 is a block diagram of an example of a typical transmit and receive chain of a digital communication system, showing different modulators and demodulators, interleavers and deinterleavers, and forward error correction (FEC) encoders and decoders.

[0015] Fig. 2 is a block diagram of an example for generation mechanism of a CPM signal within the present invention, which concerns the digital modulator in a typical communication system of Fig. 1.

[0016] Fig. 3 is a block diagram for realization of a Binary Time Invariant Phase Encoder within present invention.

[0017] Fig. 4 is an example of a trellis diagram showing state transitions for a Binary Time Invariant Phase Encoder within present invention.

[0018] Fig. 5, Fig. 6, Fig. 7 and Fig. 8 depict example baseband transmit signals for M = 2, h = 1/4, 3RC CPM, M = 2, h = 1/4, 4RC CPM, M = 4, h = 1/4, 3RC CPM, and M = 4, h = 1/4, 4RC CPM, respectively, to illustrate performance of modulator section of invention. Signals obtained by invention are presented in comparison with original CPM signals.

[0019] LIST OF THE ELEMENTS INDICATED IN DRAWINGS

• 10 Transmitter. 100 Source. 101 Channel Encoder. 102 Interleaves 103 Encoded Data.

104 (Digital) Modulator. 105 Baseband Transmit (Tx) Waveform. 106 Up Converter and Amplifier. 107 Channel. 11 Receiver. 108 Down Converter and Amplifier. 109 Baseband Received (Rx) Waveform. 110 (Digital) Demodulator. Ill Deinter leaver. 112 Channel Decoder.113 Sink.200 Base 2 Converter, or Demultiplexer.

• 201 Binary Symbols (Bits).

— 201a Bit in the (O)'th parallel arm, i.e., 7^' '.

— 201b Bit in the (l)'st parallel arm, i.e., 7^'.

— 201c Bit in the (P— l)'th parallel arm, i.e., 7^ ^'.

• 202 Phase Encoder.

— 202a Binary Time Invariant Phase Encoder (BTIPE) in the (O)'th parallel branch.

— 202b BTIPE in the (l)'st parallel branch.

— 202c BTIPE in the (P - l)'th parallel branch.

• 203 Phase Encoder Output Vectors.

— 203a Binary Time Invariant Phase Encoder Output Vector for the (O)'th parallel branch, n K - 203b Binary Time Invariant Phase Encoder Output Vector for the (l)'st parallel branch, n K

- Invariant Phase Encoder Output Vector for the (P— l)'th parallel

• 204 Decimal Converter.

• 205 Decimal Correspondents of BTIPE Outputs.

- 205a Decimal Correspondent of BTIPE Output x„ for (O)'th parallel branch.

- 205b Decimal Correspondent of BTIPE Output x„ for (l)'st parallel branch.

- 205c Decimal Correspondent of BTIPE Output for (P - l)'th parallel branch.

• 206 Element-Wise Memoryless Mapper.

• 207 CPM subsymbols.

- 207a CPM subsymbol b^, for the (O)'th parallel branch.

- 207b CPM subsymbol b^ _n , for the (l)'st parallel branch.

- 207c CPM subsymbol for the (P - l)'th parallel branch.

• 208 Pseudosymbol Generator.

• 209 CPM Pseudosymbols.

- 209a CPM Pseudosymbol ao, _n> for the (O)'th parallel branch.

- 209b CPM Pseudosymbol αχ _;η , for the (O)'st parallel branch.

- 209c CPM Pseudosymbol ακ-ι,η, f° ^r the (K— l)'th parallel branch.

• 210 CPM Pulses.

- 210a CPM Pulse g ₀ (t), for the (O)'th parallel branch.

- 210b CPM Pulse t/i(i), for the (l)'st parallel branch.

- 210c CPM Pulse j iK-i(t), for the (K - l)'th parallel branch.

• 211 Decimal summer.

• 30 A Binary Symbol (Bit).

- For I = 0, 30=201a, for I = 1, 30=201b, ..., for I = P - 1, 30=201c.

• 31 A Binary Adder. 32 A Unit Delay Element. 33 A Binary Multiplier.

• 34 An Element of A Binary BTIPE Output Vector.

- 34a (O)'th element of a Binary BTIPE Output Vector.

- 34b (l)'st element of a Binary BTIPE Output Vector.

- 34c (V - l)'th element of a Binary BTIPE Output Vector.

• 400 A Node in A Trellis. 401 A Parallel Branch in A Trellis. 402 A Diagonal Branch in A Trellis. A BRIEF DESCRIPTION OF A COMMUNICATION SYSTEM IN WHICH THE INVENTION IS USED

[0020] The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments are shown. This invention may however be embodied in many different forms, and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0021] For purposes of description, a typical digital communication system used for transmitting and receiving digital data is shown in Fig. 1. As shown in Fig. 1, a source 100 emits digital data, typically composed of binary digits of "0"s and "l"s. The channel encoder 101 encodes data to accomplish forward error correction (FEC), and applies a FEC algorithm to data, which are passed onto an interleaver 102. The encoded and interleaved data 103 are modulated by a digital modulation scheme 104. The present invention uses coherent constant or quasi-constant envelope Continuous Phase Modulation in the modulator 104. The baseband transmit waveform obtained at the modulator output 105 is up-converted to bandpass, and amplified 106 and transmitted to a channel 107. Said channel 107 can be a high frequency (HF), very high frequency (VHF), ultra high frequency (UHF), super high frequency (SHF), extremely high frequency (EHF), or tremendously high frequency (THF) channel.

At a receiver section, bandpass received signal is amplified by a low noise amplifier and down-converted to baseband 108. Baseband received waveform 109 is demodulated 110, which is followed by deinterleaving 111. A channel decoder 112 decodes data and passes data estimates to a sink 113.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] A communication transmitter 10 comprises a modulator 104, and according to an embodiment it can further comprise a channel encoder 101, and/or an interleaver 102. A communication receiver 11 comprises a demodulator 110, and according to an embodiment it can further comprise a channel decoder 112, and/or a deinterleaver 11, and/or a joint demodulator and decoder 110, 111, 112, comprising at least one interleaver and one deinterleaver.

DETAILED DESCRIPTION OF THE MODULATOR (104)

[0023] The modulator within the invention comprises a base 2 converter (alternatively a demultiplexer) 200, which outputs binary symbols (bits) 201, a total of P parallel Binary Time Invariant Phase Encoders 202, having output vectors 203, a decimal converter 204 with decimal correspondents of BTIPE outputs 205, an element-wise memoryless mapper 206 outputting CPM subsymbols 207, a CPM pseudosymbol generator 208 outputting CPM pseudosymbols 209, which are fed into a bank of CPM pulses 210 and a decimal summer 211. Fig. 2 shows a preferred embodiment pertaining to modulator section of invention where a simple method for constructing CPM waveforms is depicted. As shown in Fig. 2, in a preferred embodiment of invention, if the are first encoded by a channel encoder, M-ary encoded symbols 200 are obtained at the encoder output, which are then converted into binary symbols (bits) 201, (i.e., 201a: ^', 201b: 7< ¹⁾ ',. . ., 201c: ^ ^K -^'). If data symbols 200 are already in binary form, they are demultiplexed into parallel binary streams. If a channel encoder is not used at all, then the -ary symbols 200 are data symbols.

[0024] Binary symbols 201a, 201b,. . . ,201c are fed into Binary Time Invariant Phase Encoders 202. There are a total of P Binary Time Invariant Phase Encoders in parallel arms (i.e., 202a, 202b, 202c) . Binary Time Invariant Phase Encoders 202 are fully recursive encoder structures, each having a code rate of 1/V, where V = | ^~ log ₂ p] is defined (i.e., V is the nearest integer above the value of log ₂ p) . Hence at BTIPE outputs, binary vectors 203 (i.e. )) are formed, where each such vector is V dime the /'th BTIPE is composed of V bits, arranged . . , V - 1.

[0025] Binary BTIPE output vectors 203 are

204, and transformed into decimal form 205 (i.e.

In this conversion, s '° is the most significant bit, while s^'^ ^{- 1} is the least significant bit. Decimal correspondents of BTIPE outputs 205a, 205b,. . . ,205c are obtained from the binary vectors in following way:

I = 0, 1, . . . , P - 1 (5)

[0026] An element-wise memoryless mapper 206 maps decimal values for BTIPE outputs onto CPM subsymbols 207 (i.e. , 207a: 207b: . . ., 207c: 6^ ^_1) ), element-wise.

This mapping is ruled as

bill = ^ex [j ^h(l) ( ^2x n - n) ] , I = 0, 1, . . . , P - 1 (6) = 2 ^l h, l = 0, l, . . . , P - l (7) where n is the discrete time index.

[0027] A pseudosymbol generator 208 generates CPM pseudosymbols 209 (i.e. , 209a: ao,n _? 209b: . . ,209c: ακ-ι, _η ) , which are obtained based on CPM subsymbols 207a,

207b,. . .,207c. For particularly important CPM classes, for example, for binary CPM (M = 2) , one obtains a ₀ ,n = ^o _? ^as there is only one CPM pseudosymbol and one subsymbol, i.e., P = [log ₂ M = 1 , K = 2 ^P - 1 = I .

[0028] Higher order (M greater than 2) CPM pseudosymbols can be obtained using systematic presented in [2] .

[0029] CPM pulses 210 (i.e., 210a: g ₀ (t) , 210b: g^t),. . .,210c: g _K -i (t)) can be obtained simply by maintaining the first K = 2 ^P — 1 pulses (i.e., principal pulses) out of a total of F = Q ^P (M—1) pulses, and dismissing the rest of F—K (non-principal) pulses. Alternatively, K pulses can be chosen in an optimum fashion with respect to the mean squared error criteria. In particular, optimum pulse weighting coefficients can be found as the minimizer of the mean squared difference between the original CPM signal and the approximate CPM signal as presented in [1] , [2] .

[0030] 211 is a decimal adder, which sums the outputs of CPM pulses, and results in approximate CPM baseband transmit waveform 105 in light of Laurent, Mengali-Morelli decomposition.

[0031] Internal structure of Binary Time Invariant Phase Encoders 202a, 202b,. . . ,202c, which are central to the above preferred embodiment, are shown in Fig. 3. 30 is a binary value (a bit), which is inputted to Z'th BTIPE, / = 0, . . . , P— 1. 31 is a modulo-2 adder (i.e., binary adder), performing Boolean addition, which can be implemented on hardware with an XOR gate. 32 is a unit delay block, which can be implemented on hardware with a shift register. 33 is a modulo-2 multiplier (i.e., binary multiplier), performing Boolean multiplication, and can be implemented on hardware using an AND gate. The binary adder, binary multiplier and delay blocks are interconnected to form a BTIPE as shown in Fig. 3. Binary BTIPE outputs 34 (i.e., 34a: °'°, 34b: °' . .,34c: ^{form a} BTIPE binary output vector according to the rule given in eq. (5).

[0032] The trellis structure, which is common to all Binary Time Invariant Phase Encoders, is depicted in Fig. 4. Trellis nodes 400 represent states of Binary Time Invariant Phase Encoders. Each 0 input bit as 401 causes a lateral transition in trellis. Each 1 input bit as 402 causes a diagonal transition in trellis. Trellis has a total of p states.

POTENTIAL IMPLEMENTATIONS FOR MODULATOR AND DEMODULATOR STRUCTURES WITHIN INVENTION

[0033] In a preferred embodiment, components 100—113 can be partially or fully implemented on Field Programmable Logic Array (FPGA) platforms.

[0034] In another preferred embodiment, components 100—113 can be partially or fully implemented on Application Specific Integrated Circuits (ASIC).

[0035] Yet in another preferred embodiment, components 100—113 can be partially or fully implemented on Digital Signal Processing (DSP) platforms.

[0036] Yet in another preferred embodiment, components 100—113 can be partially or fully implemented on software.

[0037] Yet in another preferred embodiment, various combinations of FPGAs, ASIC and DSP and software can be used to implement transmit 100—113 components can be partially or fully.

EXEMPLAR PERFORMANCE OF THE INVENTION

[0038] Fig. 5 and Fig. 6 exemplify baseband transmit signal generated by invention with comparison to original CPM signal in a binary setting, for two example configurations, M = 2, h = 1/4, 3RC, and M = 2, h = 1/4, 4RC, respectively. The upper panels and the lower panels in the graphs show the real component of the baseband transmit signal, Re{z(t, a)}, and the imaginary component, Im{z(t, a)}, respectively. The x-axis for both upper and lower panel graphs denotes the time, normalized with symbol duration, t/T. As seen in both Fig. 5 and Fig. 6, baseband transmit signal generated by invention follows original CPM signal very closely. In particular, the mean square distance between transmit signal obtained by invention and the original CPM signal is 9.2 x 10 ^~4 for Fig. 5, and 1.68 x 1(T ² for Fig. 6.

[0039] Fig. 7 and Fig. 8 illustrate similarly, baseband transmit signal generated by invention with comparison to original CPM signal in a quaternary setting, for two other example configurations, M = 4, h = 1/4, 3RC, and M = 4, h = 1/4, 4RC, respectively. As seen in both Fig. 7 and Fig. 8, baseband transmit signal generated by invention and original CPM signal still track one another very closely. In particular, the mean square distance between transmit signal obtained by invention and the original CPM signal is 2.42 x 10 ^~3 for Fig. 7, and 2.93 x 1(T ² for Fig. 8. [0040] Although described in the context of particular embodiments, it will be apparent to those skilled in the art that a number of modifications and various changes to these changes may occur. Thus, while the invention has been particularly shown and described with respect to one or more preferred embodiments thereof, it will be understood by those skilled in the art that certain modifications or changes may be made therein without departing from the scope and spirit of the invention as set forth above, or from the scope of the ensuing claims.

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