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Showing papers on "Continuous phase modulation published in 1992"


Journal ArticleDOI
Johannes B. Huber, W. Liu1
TL;DR: Novel methods for the joint and nonjoint estimation of carrier-phase and symbol-timing for general coherent CPM (continuous phase modulation) receivers are proposed, and results show that synchronizers using such estimation structures exhibit an excellent steady-state behavior.
Abstract: By means of a signal representation in a signal space spanned by a few time-limited exponential basis-functions, and data-aided maximum-likelihood techniques, novel methods for the joint and nonjoint estimation of carrier-phase and symbol-timing for general coherent CPM (continuous phase modulation) receivers are proposed. The estimators are quite simple, especially in obtaining symbol-timing. Simulation results show that synchronizers using such estimation structures exhibit an excellent steady-state behavior. Whereas a fast acquisition of the carrier-phase is always possible, joint synchronizer loops tend to hang up for CPM-schemes with partial response signaling. Several ways to overcome the hang-up problem are discussed. >

96 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived expressions relating the out-of-band spectra to the misalignments in the quadrature modulator feeding a nonlinear high power amplifier and derived the complex coefficients of the power series describing the amplifier.
Abstract: Misalignments in the quadrature modulator feeding a nonlinear high power amplifier can produce distortion products that lead to spectrum leakage into adjacent channels. Expressions are derived relating the out-of-band spectra to these misalignments and to the complex coefficients of the power series describing the amplifier. For most applications the adjacent channel leakage is proportional to the square of the misalignment error (carrier leak, differential gain, differential phase and level error) except in the case of some higher order products of continuous phase modulations (CPM). A technique for estimating the spectrum for the above situations is described. It involves summing the weighted spectrum of each distortion product. The weighting coefficients can be varied to account for amplifier characteristics, backoff, and misalignment error. The analysis is applicable to linear or continuous phase modulations with or without predistortion. The spectrum estimate is particularly good for continuous phase modulated signals where the error is normally much less than 1 dB. >

72 citations


Proceedings ArticleDOI
11 Oct 1992
TL;DR: In this article, a modulation model is formed by estimating the instantaneous frequency and bandwidth using autoregressive spectrum analysis, which performed extremely well for input carrier-to-noise ratios as low as 15 dB.
Abstract: A modulation model representation of a signal is used to provide a convenient form for subsequent analysis. The modulation model is formed by estimating the instantaneous frequency and bandwidth using autoregressive spectrum analysis. In particular, the instantaneous bandwidth and derivative of the instantaneous frequency prove to be valuable parameters in estimating modulation type. This method performed extremely well for input carrier-to-noise ratios as low as 15 dB. Additionally, since the autoregressive fit to the frequency spectrum is second order, the autoregressive polynomials coefficients and corresponding roots can be computed with closed-form expressions. Thus, the method is computationally efficient. >

58 citations


Journal ArticleDOI
TL;DR: The authors propose feedforward neural networks (NNs) as receivers for partial-response continuous-phase-modulation (CPM) systems by replacing the entire receiver structure with a neural net unit whose inputs are time samples of the incoming baseband signals, and whose outputs are the decoded symbols.
Abstract: The authors propose feedforward neural networks (NNs) as receivers for partial-response continuous-phase-modulation (CPM) systems. Their approach is to replace the entire receiver structure, excluding timing recovery, with a neural net unit whose inputs are time samples of the incoming baseband signals, and whose outputs are the decoded symbols. Simulation results for coherent and incoherent NN-based receivers are presented, and their performance is compared with that of the optimum maximum-likelihood receiver. The performance of NN-based receivers at large SNR is analyzed. >

41 citations


Journal ArticleDOI
TL;DR: A range of space-invariant and space-variant holographic optical interconnections are demonstrated with the aid of a nematic liquid-crystal panel that is capable of nearly continuous phase modulation.
Abstract: A range of space-invariant and space-variant holographic optical interconnections are demonstrated with the aid of a nematic liquid-crystal panel that is capable of nearly continuous phase modulation. Results on fan-out, nearest-neighbor/next-nearest-neighbor interconnects, and 8-bit perfect shuffle are presented. The diffraction efficiencies are close to 15% of incident light in all cases.

35 citations


Journal ArticleDOI
G.K. Kaleh1
TL;DR: In this article, a differential detection strategy which compensates for the inherent intersymbol interference (ISI) and avoids noise enhancement is presented, and a phase estimate that takes into account the presence of the inherent ISI is derived.
Abstract: The differentially coherent reception of two families of constant-envelope signals, the linear offset quaternary phase shift keying and the binary partial response continuous phase modulation with index 0.5, is addressed. When the conventional (PSK-type) differentially coherent detector is used, a large performance degradation, compared with that of coherent receiver, is observed. The reason for this is the presence of an inherent intersymbol interference (ISI) in the signal and also noise enhancement and correlation introduced by the receiver filter. A differential detection strategy which compensates for ISI and avoids noise enhancement is presented. A phase estimate that takes into account the presence of the inherent ISI is derived. This phase estimate is then used in the decision metric of a coherent receiver. The resulting decision rule can be implemented using the Viterbi algorithm. Simple Viterbi receivers with good performance are obtained. Simulation results are given. >

29 citations


Journal ArticleDOI
TL;DR: The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth.
Abstract: Differential phase shift keying (DPSK) in the presence of both additive white Gaussian noise and a phase impairment, modeled by a Brownian motion is considered. A time-diversity scheme is used for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. An upper bound on the bit error probability, relying on a bivariate moment-generating function admitted by certain real functionals of the phase sample-path, is derived. The approach taken yields a trackable analysis, which rigorously adheres the phase noise effects. The impact of an incomplete statistical characterization on the tightness of the resultant bound is addressed. The theory, which is applicable to assess the design and performance of general heterodyned lightwave systems using (delay) differential demodulation (as DPSK and CP-FSK, or continuous phase frequency-shift keying), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth. >

25 citations


Patent
19 Mar 1992
TL;DR: In this article, a computer having one or more wave tables stored therein is used to synthesize sounds represented by a series of digital samples produced at a sample rate by specifying parameters including a carrier frequency, a modulating frequency and an index of modulation.
Abstract: A computer having one or more wave tables stored therein is used to synthesize sounds represented by a series of digital samples produced at a sample rate by specifying parameters including a carrier frequency, a modulating frequency and an index of modulation. At each sample time, a modulation value determined during an immediately preceding sample time is scaled to produce a digital control signal. Also at each sample time the modulation value to be used during an immediately succeeding sample time is read from a location of a wave table determined by the modulating frequency, and a carrier value used to produce the digital samples is read from a location of a wave table determined by the carrier frequency and the digital control signal. Modulation effects are therefore delayed by one sample in order to speed execution of the method using the computer. Phase accumulation is performed using a multiplier making it unnecessary to store the sum of all of the previous steps as would be otherwise be required using an additive approach.

18 citations


Journal ArticleDOI
TL;DR: A novel signal generation concept for continuous phase modulations (CPMs) with modulation index 1/2 based on real impulses that can be generated directly in one step instead of the two consecutive steps, namely, the generation of the complex envelopes and the modulation of the carrier by the complex envelope.
Abstract: A novel signal generation concept for continuous phase modulations (CPMs) with modulation index 1/2 based on real impulses is presented. With this concept, bandpass CPM signals can be generated directly in one step instead of the two consecutive steps, namely, the generation of the complex envelope and the modulation of the carrier by the complex envelope, which are necessary in conventional signal generators. Mathematical expressions for both the real impulses and the bandpass CPM signals are derived and a simple modulator structure is discussed. Examples for the real impulses are given. Among these are the well-known CPM schemes of minimum shift keying (MSK), sinusoidal frequency shift keying (SFSK), and Gaussian minimum shift keying (GMSK). As an example, the validity of the novel signal generation concept is shown for the latter CPM scheme. >

18 citations


Journal ArticleDOI
S. Fleisher1, S. Qu
TL;DR: A new modulation scheme that produces a constant envelope continuous phase signal set with a compact power spectrum and power efficiency better than that of MSK is proposed, which lends itself to a variety of applications, one of them being the digital satellite link.
Abstract: A new modulation scheme that produces a constant envelope continuous phase signal set with a compact power spectrum and power efficiency better than that of MSK is proposed. The scheme can be implemented by quadrature-carrier multiplexing of two frequency/phase modulated signals of the type NFSK/2PSK, both with the same frequency in each transmission interval, and with sinusoidal symbol shapes. The generated signal can be viewed in each transmission interval as an MSK signal at one of the N frequencies and is referred to as multifrequency minimum shift keying (MF MSK). Modulation, demodulation, and synchronization circuits are described, and the spectral properties and power efficiency on the AWGN channel are analyzed. Combining a number of attractive attributes such as constant envelope, excellent spectral properties, high power efficiency, and self-synchronization capability, the proposed modulation format lends itself to a variety of applications, one of them being the digital satellite link. >

16 citations


Patent
31 Aug 1992
TL;DR: In this article, a coherent demodulating device is characterized by a demodulation circuit and a carrier recovering circuit produced entirely in digital form, where the analog signals are digitized by sampling at symbol reception frequency into incoming digital signals.
Abstract: A coherent demodulating device is characterized by a demodulating circuit and a carrier recovering circuit produced entirely in digital form. Two quadrature demodulation carrier waves produced by a local oscillator are mixed with a demodulation carrier signal modulated by symbols to produce analog signals. The analog signals are digitized by sampling at symbol reception frequency into incoming digital signals. A digital phase shifter phase shifts the incoming signals by a demodulation phase derived by a phase loop digital processing circuit as from error signal pulses supplied by a comparing circuit receiving outgoing digital signals from the phase shifter. The compensation for the phase and frequency differences between the demodulation and modulation carrier waves is carried out a posteriori in digital form by phase shifting the incoming signals.

Journal ArticleDOI
Shalini Periyalwar1, S. Fleisher1
TL;DR: The authors explore the trellis coding of continuous-phase quadrature frequency/phase modulated (CPQFPM) signal sets and continuous- phase FPM (CPFPM), which are embodiments of the quadratures biorthogonal modulation (QBOM) technique.
Abstract: The authors explore the trellis coding of continuous-phase quadrature frequency/phase modulated (CPQFPM) signal sets and continuous-phase FPM (CPFPM) signal sets, which are embodiments of the quadrature biorthogonal modulation (QBOM) technique. Conventional TCM and multiple TCM schemes with these modulation formats are examined using both the AWGN channel and the Rician fading channel design. Asymptotic coding gains in d/sup 2/(free) are tabulated for trellis-coded rate 3/4, 5/6, and 6/7 QFPM schemes, in comparison with uncoded modulations (8AMPM, 32AMPM) and other trellis-coded modulations (TCM (2FSK/4PSK 16QAM, 64QAM), MTCM (2FSK/8PSK)) of equivalent throughput rate. Performance gains on the Rician fading channel are demonstrated by increased values of the design parameters for this channel, namely symbol diversity L/sub min/ and branch distance product P. >

Proceedings ArticleDOI
14 Jun 1992
TL;DR: The authors address a technique for achieving carrier synchronization for all four of these PSK schemes in a single modem by using quadrature channel carrier recovery processing and a version of the maximum a posteriori (MAP) estimation phase detector algorithm.
Abstract: It is economical for a single modem to receive multiple modulation formats. The use of binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), 8PSK, and 16PSK modulation is considered. The authors address a technique for achieving carrier synchronization for all four of these PSK schemes in a single modem. This is accomplished by using quadrature channel carrier recovery processing and a version of the maximum a posteriori (MAP) estimation phase detector algorithm. A model for the simulation of this tracking process is derived, and results are presented to confirm its functionality. >

Journal ArticleDOI
TL;DR: Several nonlinear trellis modulation codes based on multi-level continuous-phase frequency-shift keying (M-CPFSK) are presented, which achieve higher minimum Euclidean distances and memory lengths than conventional CPFSK signals.
Abstract: Several nonlinear trellis modulation codes based on multi-level continuous-phase frequency-shift keying (M-CPFSK) are presented. On additive white Gaussian noise channels these digital FM schemes achieve higher minimum Euclidean distances and memory lengths than conventional CPFSK signals.

Proceedings ArticleDOI
11 Oct 1992
TL;DR: The authors address the problem of constructing continuous phase modulation classifiers by the likelihood approach by starting from the likelihood functions of CPM signals in additive white Gaussian noise, and based on a small signal-to-noise ratio approximate LF, they derive easily implementable classifiers.
Abstract: The authors address the problem of constructing continuous phase modulation (CPM) classifiers by the likelihood approach. They start from the likelihood functions (LFs) of CPM signals in additive white Gaussian noise, and, based on a small signal-to-noise ratio (SNR) approximate LF, they derive easily implementable classifiers. Two log-LF-based classifiers are proposed. One of them, e(h/sub 1/, h/sub 2/), is equivalent to an energy comparator; the other, c(h/sub 1/, h/sub 2/), has a novel form. It is shown that the c(h/sub 1/, h/sub 2/) rule performs much better than the e(h/sub 1/,h/sub 2/) rule for short observation time., However, the e(h/sub 1/, h/sub 2/) rule may outperform the c(h/sub 1/,h/sub 2/) rule for adequately long observation time, since a performance upper bound exists for the c(h/sub 1/,h/sub 2/) rule, while the performance of the e(h/sub 1/, h/sub 2/) rule can be improved by increasing observation time without limits. >

Proceedings ArticleDOI
11 Oct 1992
TL;DR: A class of spread-spectrum multiple-access systems with continuous phase modulation is defined, which is unique in that the information bits and spreading chips affect the phase separately.
Abstract: A class of spread-spectrum multiple-access systems with continuous phase modulation is defined. The signals are unique in that the information bits and spreading chips affect the phase separately. The signal allows shaping of the lower spectral density, via the spreading phase, with little impact on receiver complexity. Receiver complexity is driven by the information phase modulation method. A specific subclass that uses a serial MSK receiver is examined. >

Patent
03 Jun 1992
TL;DR: In this paper, variable shift keying (VSK) was used for the transmission of data, and a modem for use in such a system, in which a data signal is modulated to form a continuous phase signal in which successive symbols are represented by successive signal segments of constant phase angle, typically 180° or one half cycle, different symbols being distinguished by the segments being of different duration.
Abstract: A system for the transmission of data, and a modem for use in such a system, utilize variable shift keying (VSK), in which a data signal is modulated to form a continuous phase signal in which successive symbols are represented by successive signal segments of constant phase angle, typically 180° or one half cycle, different symbols being distinguished by the segments being of different duration, i.e. at different frequencies. The ratios of the frequencies may be chosen to facilitate signal modulation and demodulation, and to control the frequency spectrum of the transmitted signal. Each symbol may represent one or more bits of the data signal. The lengths of half cycles used to represent different symbols may be adjusted by introducing flat peaks into the half cycles whilst maintaining uniform the profile of their flanks so as to facilitate generation and reduce zero crossing detection jitter during reception.

Proceedings ArticleDOI
TL;DR: In this article, an acousto-optic processor capable of analyzing signals consisting of a high frequency carrier modulated by an envelope signal is described, where space-integrating spectral analysis is used to channelize signals by carrier frequency.
Abstract: An acousto-optic processor capable of analyzing signals consisting of a high frequency carrier modulated by an envelope signal is described. Space-integrating spectral analysis is used to channelize signals by carrier frequency. Time-integrating spectral analysis is used to characterize the envelope signal that modulates each carrier frequency. The output is a two- dimensional display with carrier frequency along one axis and envelope frequency along the orthogonal axis. Several advantages of the processor are explained and proof-of-concept experimental results are presented. One possible application of the processor is to the automatic separation and determination of the carrier frequencies and pulse repetition frequencies of multiple received radar signals.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: A criterion for the phase function that ensures noncoherent orthogonality of the modulated signal over one symbol interval is introduced and a new family of phase modulated signals is presented.
Abstract: This work considers noncoherently orthogonal signaling with full response digital phase modulation and focuses on the phase function shaping problem. A criterion for the phase function that ensures noncoherent orthogonality of the modulated signal over one symbol interval is introduced. Furthermore, a new family of phase modulated signals is presented. This new orthogonal modulation format lacks the well-known spectral lines of noncoherently orthogonal FSK and hence uses the power efficiently to convey information. >

Proceedings ArticleDOI
16 Nov 1992
TL;DR: The authors examine the actual BER improvement of the sequence estimation scheme for a few IF filter types for static AWGN channels using computer simulation.
Abstract: For a communication scheme using binary continuous phase FSK with limiter-discriminator and integrate and dump filter detection the improvement of bit error rate at the receiver side has been carried out through the bandwidth optimization of the IF filter or the decision feedback equalization using multilevel decision method. This channel is inherently the intersymbol interference channel due to the narrow band IF filter, so sequence estimation techniques using the Viterbi algorithm can also be used, although the channel is not purely additive white Gaussian. The authors examine the actual BER improvement of the sequence estimation scheme for a few IF filter types for static AWGN channels using computer simulation. Very large estimation gains are obtained for the modulation index h >

Journal ArticleDOI
TL;DR: In this paper, the transmission characteristics of a CPFSK differential detection system with LD direct modulation were studied by computer simulation and it was shown that the optimum wavelength for LD-Direct Modulation (LD-DM) transmission shifts to a wavelength longer than zero dispersion wavelength because of the phase difference between the intensity and frequency modulation components.
Abstract: Transmission characteristics of a CPFSK differential detection system with LD direct modulation are studied by computer simulation. Simulation results show that the optimum wavelength for LD direct modulation CPFSK transmission shifts to a wavelength longer than zero dispersion wavelength because of the phase difference between the intensity and frequency modulation components. A precise investigation of the dependence of optimum total dispersion on several parameters reveals the essential role of the phase difference between intensity and frequency modulation induced by LD direct modulation. The transmission distance allowing a 1-dB power penalty at 10 Gb/s is 117 km for a wavelength 30 nm shorter than the zero dispersion wavelength, while the distance is 183 km for a wavelength 30 nm longer. This indicates that the zero dispersion wavelength shift is 11 nm for 100-km transmission. >

Journal ArticleDOI
TL;DR: A novel algorithm for the determination of these impulses in simulation and experiment by the excitation of certain modulator responses shall be illustrated, allowing further insight in the nature of binary CPM.
Abstract: Laurent's representation of binary continuous phase modulations (CPMs) based on real impulses of finite duration is advantageous for the signal generation in the transmitter as well as the signal processing in the detector. In the present paper, a novel algorithm for the determination of these impulses in simulation and experiment by the excitation of certain modulator responses shall be illustrated. The algorithm is an interesting alternative to conventional signal processing applying phase detection, thus allowing further insight in the nature of binary CPM.

Proceedings ArticleDOI
10 May 1992
TL;DR: The improved probability of error of a narrowband continuous phase M-ary frequency shift keying system of B b/s/Hz (B>2) with a limiter-discriminator-integrator detector when compensating for the effect of the bandlimiting filter using a nonlinear postprocessor following the FM discriminator is determined.
Abstract: The improved probability of error of a narrowband continuous phase M-ary frequency shift keying (CPMFSK) system of B b/s/Hz (B>2) with a limiter-discriminator-integrator detector when compensating for the effect of the bandlimiting filter using a nonlinear postprocessor following the FM discriminator is determined. This postprocessor uses an adaptive decision scheme to combat the severe intersymbol interference caused by the bandlimiting filter. Error probability results are presented for the receiver, both with and without a postprocessor, as a function of various system parameters for M=2, 4, 8, and 16 symbols to support the superiority of this algorithm. >

Journal ArticleDOI
TL;DR: The best multi-h phase codes which produce the highest minimum Euclidean distance are reported at preselected numbers of states.
Abstract: The best multi-h phase codes which produce the highest minimum Euclidean distance are reported at preselected numbers of states. 2-h, 3-h and 4-h signals are considered in the code search. Numerical results are presented separately for binary full-response and partial-response signals, with a rectangular and a raised cosine baseband pulse.

Journal ArticleDOI
TL;DR: In this paper, it was shown that a simple assumption due to Fornery leads to a simplified finite-state representation and also easily shows that CPM has q phase states, where the modulation index h = p/q.
Abstract: In most of the literature it is claimed that the number of phase states in CPM is equal to q if p is even, and 2q if p is odd, where the modulation index h = p/q. In the Letter it is shown that a simple assumption due to Fornery leads to a simplified finite-state representation and also easily shows that CPM has q phase states.

Proceedings ArticleDOI
09 Jun 1992
TL;DR: In this article, the authors proposed a continuous phase modulation (CPM) scheme for coherent optical communications systems, which not only meets their performance objectives but also can be implemented with direct laser modulation and relatively simple differential detection techniques.
Abstract: A variety of modulation schemes have been studied previously for coherent optical communications systems. DPSK and MSK are theoretically 3 dB more sensitive than binary FSK, but are also more susceptible to laser linewidth degradation. Our goal is to attain the sensitivity of DPSK but with better linewidth tolerance. When the linewidth-to-data-rate ratio is small, but not negligible, it becomes feasible to consider the continuous-phase modulation (CPM) family. We report on CPM schemes which not only meet our performance objectives but also can be implemented with direct laser modulation and relatively simple differential detection techniques.

Proceedings ArticleDOI
19 Oct 1992
TL;DR: This paper compares the performance of binary phase shift Keying (BPSK) and minimum frequency shift keying (MSK) in a spread spectrum code division multiple access setting and finds the MSK system has the advantage of being more power efficient.
Abstract: Battery power efficiency of the portable unit is a major issue in the design of indoor radio telecommunication systems. The efficiency of the portables depends on the modulation method employed. Digital modulation methods with constant envelope signals are more battery efficient than those with modulated envelope signals since the latter require inefficient linear radio frequency amplifiers. The improvement in efficiency is very significant when the constant envelope modulation method is minimum shift keying and a directly modulated power radio frequency oscillator is used to generate the modulated signal. This paper compares the performance of binary phase shift keying (BPSK) and minimum frequency shift keying (MSK) in a spread spectrum code division multiple access setting. The BPSK system can support about 8 percent plus 0.5 more simultaneous users for a given carrier to interference ratio but the MSK system has the advantage of being more power efficient. >

Proceedings ArticleDOI
14 Jun 1992
TL;DR: In this article, a symbol-by-symbol (SBS) receiver was proposed for the discriminator detection of continuous phase modulation (CPM) schemes having a modulation index of 0.5.
Abstract: The authors propose a new symbol-by-symbol receiver for the discriminator detection of continuous phase modulation (CPM) schemes having a modulation index of 0.5. The new receivers are based upon the use of multiple signal combining and decision feedback. Theoretical analysis has shown that the proposed receivers result in increased SNR as compared to conventional symbol-by-symbol receivers. Performance evaluation results obtained by means of computer simulation for MSK and duobinary MSK signals have resulted in gains of up to 2.2 dB in an additive white Gaussian noise channel. >

Book ChapterDOI
01 Jan 1992
TL;DR: Digital implementation of power and bandwidth efficient quadrature carrier modulation techniques are identified, evaluated and compared with computer simulation results, which show results in terms of BER performances, statistical properties of the synchronization procedures and computational loads.
Abstract: . Digital implementation of power and bandwidth efficient quadrature carrier modulation techniques are identified, evaluated and compared with computer simulation results. The modulation techniques include QPSK, OQPSK, MSK, π/4-QPSK and Q 2 PSK. Digital algorithms for data-decision, carrier phase offset and timing delay estimation for each of the modems are given. Results in terms of BER performances, statistical properties of the synchronization procedures are shown for AWGN channels. Computational loads of the different modem systems evaluated are also given.

Proceedings ArticleDOI
14 Jun 1992
TL;DR: The proposed technique provides improved BER performances for narrowband digital FM by utilizing a limiter-discriminator-integrator followed by a nonlinear postprocessor to combat the intersymbol interference caused by a bandlimiting filter.
Abstract: A technique for the detection of narrowband multilevel continuous phase frequency shift keyed signals (CPFSK signals) is introduced. This technique is a noncoherent demodulation which utilizes a limiter-discriminator-integrator (LDI) followed by a nonlinear postprocessor to combat the intersymbol interference caused by a bandlimiting filter. The error rate performance is computed for this receiver and compared with that of the LDI receiver. The proposed system was simulated and the bit error rate (BER) performances of 2, 4, and 8-ary CPFSK schemes were obtained. The proposed technique provides improved BER performances for narrowband digital FM. Simulation results have verified the superiority of this method. >