Continuous Phase Modulation Schemes Research Articles

Multiple-symbol noncoherent decoding of uncoded and convolutionally coded continuous phase modulation

Recently, a method for combined noncoherent detection and decoding of trellis-codes (noncoherent coded modulation) has been proposed, which can practically approach the performance of coherent detection. Here, we successfully apply the technique to the detection of Continuous Phase Modulation (CPM), coded or uncoded. Both full and partial response CPM schemes with arbitrary modulation index are considered. This method is based on multiple-symbol observations, such that the observations are time-overlapped. The results show that most CPM schemes require short observations to achieve almost the same power efficiency as optimally detected coherent CPM. Compared to the previously proposed methods for noncoherent detection that can approach the coherent performance, the required observation length is much shorter and also the decoding complexity is much lower. A new trellis diagram for noncoherent CPM is suggested for simplifying the analysis and the decoder structure. The error performance for uncoded CPM is evaluated by using the union bound technique applied on the symbol-difference trellis diagram. For the coded case a pair-state trellis is required. Very efficient sub-optimal decoding algorithms with very small degradation may implement the noncoherent decoder. The performance achieved with these algorithms is demonstrated by simulations.

Coded and uncoded CPM schemes over rings of integersforAWGN and Rayleigh fading channels.

Coded and uncoded modulation schemes based on continuous phase modulation (CPM) over rings of integers are investigated. A baseband modulator utilising a decomposed model of CPM is used at the transmitter and a Viterbi soft-decision decoder is employed at the receiver. The performances of a number of partial-response CPM schemes are investigated when operating over an additive white Gaussian noise (AWGN) channel and Rayleigh flat fading (RFF) channel. The simulation results obtained are shown to compare favourably with theoretical bounds.

MLSE and soft-output equalization for trellis-coded continuous phase modulation

This paper presents two equalizer structures for trellis-coded continuous phase modulation (TC-CPM) on multipath fading intersymbol interference (ISI) channels. An equivalent discrete-time (DT) model is developed by combining the tapped-delay-line (TDL) model of the frequency-selective channel and by oversampling at the receiver. The (noninterleaved) fractionally spaced maximum-likelihood sequence estimation (MLSE) equalizer performs continuous phase modulation (CPM) demodulation, trellis-coded modulation (TCM) decoding, and channel equalization by exploiting the finite state nature of the ISI-corrupted TC-CPM signal. Both simulation and analytical results show diversity-like improvement when performing joint MLSE decoding and equalization. For the interleaved soft-output equalizer, the soft symbol metric is delivered to the TCM decoder by using a forward and backward recursion algorithm. Three variants of the soft-output equalizer are examined. We conclude that the backward recursion is essential to partial response CPM schemes, and with moderate complexity, the soft-output equalizer can have a substantial advantage over a noninterleaved MLSE equalizer.

Performance of binary CPM schemes in frequency selective fading channels with pilot symbol assisted detection

Signals transmitted over a land mobile radio channel are very often subjected to frequency selective fading. A detection technique is proposed for continuous phase modulation (CPM) operating in such an environment. The technique uses embedded pilot symbols for channel impulse response estimation. The estimated channel response is updated from symbol to symbol and is used during the sequence detection of the CPM signal. Unlike pilot symbol assisted linear modulation, the pilot symbols in this CPM system are divided into two groups. The first group of pilot symbols is data-dependent and is used to force the modulator to return periodically to a known system state. The second group is not data-dependent and is used to specify a known waveform emanating from the periodic known state, for the purpose of channel estimation. The proper pilot symbol encoding rules, as well as the structure of the companion channel estimator, are presented. It is shown that CPM schemes employing this detection technique exhibit no irreducible error floor even in the presence of fast fading and large delay spread. The modem actually performs better in a heavily frequency selective fading environment, due to the implicit diversity effect provided by the channel. The difference in energy efficiency between frequency selective and flat fading can be as large as 5 dB at a 10-3 bit error rate and 8 dB at a 10-4 error rate. These results suggest that the proposed technique is very suitable for use in a system which employs diversity.

Multichannel Coherent Subcarrier Multiplexed Lightwave Systems Employing Continuous Phase Modulation Schemes

Multichannel coherent subcarrier multiplexed lightwave systems are considered in this paper. The continuous phase modulation schemes are employed at the microwave level over multioctave subcarrier frequency bands, and analyses are presented for M-ary continuous phase frequency shift keying and multi-h codes. A complete description of the system performance in terms of the carrier-to-noise ratio, intermodulation distortion and receiver sensitivity is given for each of the M-ary cases (M = 2, 4, 8 and 16). It is demonstrated that significant improvement in system performance can be achieved by increasing the signal alphabet size M from 2 to 4.

Error probability of coherent detection for trellis-coded partial response CPM on Rician fading channels

Trellis-coded continuous phase modulation (TC-CPM) schemes are attractive for bandwidth and power limited communication systems such as mobile satellite communications and land mobile radio communications. A coherent receiver for interleaved partial response TC-CPM is derived. A true upper bound on the bit error probability for flat fading channels is derived by showing that TC-CPM is equivalent to a trellis-coded modulation scheme. The upper bound is evaluated by defining an error-state diagram along with a set of characteristic distances and then applying transfer function bounding techniques. Comparison with simulation results shows the upper bound tight to within 1.5-2 dB.

Pilot symbol-assisted detection of CPM schemes operating in fast fading channels

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes.

Coded continuous phase modulation using ring convolutional codes

Rate 1/2 convolutional codes over the ring of integers modulo M are combined with M-ary continuous phase modulation (CPM) schemes whose modulation indices are of the form h=1/M. An M-ary CPM scheme with h=1/M can be modeled by a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers modulo M. The fact that the convolutional code and the CPE are over the same algebra allows the state of the CPE to be fed back and used by the convolutional encoder. A modified Euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes. Numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity.

Catastrophic continuous phase modulation schemes and their noncatastrophic equivalents

Continuous phase modulation (CPM) schemes are bandwidth and energy efficient constant-envelope modulation schemes that can be viewed as a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is of convolutional type. It is observed that CPM schemes can be catastrophic in the sense that pairs of input sequences that differ in an infinite number of positions can be mapped into pairs of signals with finite Euclidean distance. This can happen in spite of the fact that the CPE is never catastrophic when considered as a stand alone convolutional encoder. The necessary and sufficient condition for a general CPM scheme to be catastrophic is given. Each member of the two major families of CPM schemes, namely the LREC and the LRC, has been classified as a catastrophic or noncatastrophic scheme. For the catastrophic schemes, the probability that a catastrophic event occurs is determined. A canonical precoder which transforms each scheme of both families into an equivalent noncatastrophic scheme is derived. The equivalent noncatastrophic scheme has the same number of states as the original one. Moreover, it has the property that if two input sequences differ in the ith position, the corresponding output signals have nonzero Euclidean distance in the ith interval. >

Closed-form of the power spectral density for full response M-ary CPFSK modulation

In recent years, continuous phase modulation (CPM) scheme has gained increasing attention due to its attractive spectra properties. The continuous-phase frequency shift keying (CPFSK) modulation scheme has previously been studied and much effort has been spent to find simple analytical and numerical methods for computing the spectrum of CPFSK signals [1–16]. Some authors have derived formulas for the autocorrelation and power spectral density (PSD) functions of CPFSK signals, but the calculations are extremely laborious requiring numerical integration in two dimensions involving truncation errors. This paper presents a special method of analyzing the spectral properties of M-ary CPFSK for full response signaling. The autocorrelation function is presented in closed-form thereby avoiding truncation. The Fourier transform is used to find the power spectral density function, which is also expressed in closed-form. The effect of the system parameters, i.e. the size of the alphabet, the modulation index, and others on the system bandwidth and PSD are analyzed. The conditions under which the spectrum contains discrete lines are outlined. The continuous part of PSD is expressed in exponential form, and a large number of PSDs have been computed and plotted in a relatively short time and samples are presented in the paper. Finally, it is shown that systems with normalized modulation indices Δ = 1/ M offer superior performance in terms of bandwidth and power efficiency for different schemes.

Limiter-discriminator detection of continuous phase modulation (CPM) Tomlinson filtering

Limiter-discriminator detection of continuous phase modulation (CPM) partial response signals is of special importance in systems in which phase coherence is very difficult to establish and/or maintain (e.g., mobile communications systems). The authors propose a Tomlinson-based approach which copes with the intersymbol interference (ISI) introduced by the baseband partial response frequency modulating pulses of the CPM schemes, (e.g., GTFM, GMSK, raised cosine (RC)). In this approach, the ISI equalization is divided between the transmitter and the receiver. The authors investigate, through simulation, the detectability performance and spectral properties of a number of CPM signals and receiver structures with special emphasis on the Tomlinson approach. It is shown that this novel application of the Tomlinson configuration allows the use of relatively simple receivers which exhibit almost the same performance as more complex Viterbi structured receivers. It is shown that a bandwidth-efficient narrow-band quaternary CPM-2RC modulation with either a Viterbi, a DFE or a Tomlinson receiver structure outperforms classical binary FSK (discriminator-integrate and dump detection) by approximately one db. It is pointed out in the paper that in general it is also possible to achieve detectability results similar to that of classical discriminator (integrate and dump) detection of binary CPFSK, for a number of bandwidth-efficient binary CPM schemes (e.g., GMSK) using the aforementioned receiver structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multiple differential detection of continuous phase modulation signals

A sequence estimation algorithm for the differential detection of the continuous phase modulation (CPM) signals, yielding significant gains in BER performance and with considerable resistivity to fading, is introduced. These advantages, along with the reduced hardware complexity, low cost, and fast synchronization which characterize the differential detector, make the proposed receiver useful for land mobile radio and mobile-satellite communications. The new receiver is based on multiple differential detection. The multiple differential detection strategy provides the decoder with more information regarding the transmitted data and applies a noise decorrelation process on the received signal, useful to the sequence estimation. The algorithm is derived in a general form, and can be applied on any CPM scheme, with any degree of complexity. The authors have evaluated the receiver for two of the most popular CPM schemes, the tamed frequency modulation (TFM) and Gaussian minimum-shift keying (GMSK) (with B/sub 1/T=0.25), in the presence of additive white Gaussian noise (AWGN) and Rician fading. The BER performance evaluation results indicated significant gains and considerable reduction of error floors. In AWGN improvements close to 9 dB have been verified.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Error-control properties of minimum shift keying

A phase representation of minimum shift keying (MSK), which is a general framework suitable for use with other continuous phase modulation (CPM) schemes, is discussed. The representation is used to show that MSK can be viewed as a coded-modulation scheme with an expanded signal set using Ungerboeck's set partitioning concept (see IEEE Trans. Inf. Theory, vol.IT-28, no.1, p.55-67, 1982). The properties which follow from this view of MSK are explored. The uniqueness of the representation of MSK as a coded-modulation scheme and the structural relationships between different versions of MSK are described.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Better rate 1/2 coded continuous phase modulation schemes and the M-algorithm

Continuous phase modulation (CPM) signals may be precoded by a convolutional code followed by a mapping rule. Better codes may, however, be obtained by a more general code formed by a finite state machine. We provide improved codes for one such finite state machine. A new description of codes and design rules are presented. Better results are demonstrated for the partial response CPM schemes and previous optimum results are matched for the full response case. Tests of an M-algorithm decoder achieve near maximum-likelihood performance with only a fraction of the complexity of the Viterbi algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Erratum: Differential detection of correlative encoded continuous phase modulation schemes using decision feedback

Erratum: Differential detection of correlative encoded continuous phase modulation schemes using decision feedback

Reduced state sequence detection of partial response continuous phase modulation

A reduced state sequence detector (RSSD) which combines decision feedback with Viterbi decoding is proposed for partial response continuous phase modulation (CPM). This detector can successfully be used for both binary and high-level partial response CPM schemes. This detector is analysed by means of minimum Euclidean distance and by simulations of the symbol error probability. It is shown that the phase states in the receiver trellis of the maximum likelihood detector for partial response CPM can be exchanged by decision feedback in the metric calculations. This can be achieved without sacrificing minimum Euclidean distance of the first error event or symbol error probability. This RSSD is most attractive for narrow-band CPM schemes and at most about 2 dB in increased energy efficiency as compared with MSK is possible. Further reductions in number of states is possible, especially for high-level CPM schemes, by reducing the number of correlative states. For the most frequently used CPM schemes this can be done with a very small degradation in error performance. In this class of schemes, a complexity reduction of at least a factor five to ten is possible.

Performance evaluation of a composite microscopic plus macroscopic diversity system

Closed-form analytical solutions are obtained for the performance of M-branch maximal-ratio and selection microscopic diversity systems with a class of continuous phase and constant amplitude modulation schemes for Rayleigh and log-normal fading. The results indicate that diversity improvement is related to the standard deviation of the log-normal component and the improvement decreases as the standard deviation increases. Since microscopic diversity only mitigates the effect of fast (Rayleigh) fading, other means are needed to mitigate the effect of the slow (log-normal) component. Further development of the theory indicates that a composite microscopic plus macroscopic diversity system can substantially improve the performance by counteracting the two fading components simultaneously. Analytical results are produced for two-branch microscopic selection or maximal-ratio plus N-branch macroscopic selection diversity systems.

Symbol timing tracking for continuous phase modulation over fast flat-fading channels

The symbol timing tracking problem for a class of continuous phase modulation (CPM) schemes transmitted over unfaded and fast flat-fading channels is studied. The specific family of CPM considered is that of M-ary continuous-phase modulation with a modulation index of h=1/M. A particular symbol synchronizer structure that constructs a tone at the symbol frequency by passing the received signal through an Mth power law nonlinearity and multiband filter followed by a squared-envelope nonlinearity and narrowband filter is proposed. The operation and parameters of this symbol synchronizer are discussed as well as the performance of the synchronizer. Simulation results giving the root-mean-square timing jitter of this system for several binary, quaternary and 8-ary instances of modulation using rectangular, raised-cosine, truncated Nyquist III, and truncated tamed FM pulse shapes are presented to illustrate the synchronizer performance. >

Differential detection of correlative encoded continuous phase modulation schemes using decision feedback

We generalise a differential detection technique, introduced elsewhere for a Gaussian minimum shift keying (GMSK) scheme, to include any correlative encoded continuous phase modulated (CECPM) signalling format. The proposed symbol-by-symbol receivers employ decision feedback to partially remove the effects of the destructive intersymbol interference (ISI) which corrupts the differentially detected CECPM signal. After achieving wider eye opening with the decision feedback, the outputs of the two or more differential detectors are jointly utilised to further improve the performance. As a typical example of the CECPM family of signals and because of its excellent spectral characteristics, the new receiver configurations employing up to 3-bit differential detectors have been applied to a tamed frequency modulation (TEM) signal. Bit error rate (BER) performance evaluation results have indicated that performance improvements of more than 5 dB (at BER = 10-4) over a conventionally differential detected TFM scheme are possible. As compared with a limiter/discriminator receiver employing maximum likelihood sequence estimation (MLSE), the proposed receivers offer gains of more than 2 dB(at BER = 10 -4).

Signal modelling and coding for linearly detectable CPM

The equivalence between continuous phase modulation (CPM) and offset quadrature amplitude-shift keying (OQPSK) which can be detected using linear receivers is considered, and a hierarchy of such schemes developed based on the degree to which the CPM schemes can be described with a coded offset quadrature amplitude-shift keyed modulation. The nature of the coding required to make the two schemes equivalent (exactly for some forms and approximately in general) is discussed, and the nature of the optimum linear receivers is developed showing that with an appropriate phase offset of carriers, the optimum linear receiver will be an inphase-quadrature receiver. The problem of designing trellis codes for these CPM schemes is considered and it is shown how optimum codes basedon Hamming distance can be transformed into codes for application to these CPM schemes. The results show that it is possible to apply a trellis code with a constraint length of v+ 1 as described by a Mealy model with 2 v states and yet decode the signal using a Viterbi decoder involving only 2 v- 1 states.