Continuous Phase Modulation Schemes Research Articles

Performance vs. Spectral Properties for Single-Sideband Continuous Phase Modulation

This study revokes the performance of continuous phase modulation (CPM) able to generate a single-sideband (SSB) spectrum directly. This signal is analyzed in terms of modulation indices, pulse lengths, and pulse widths, all of which affect error probability, bandwidth, SSB property, and receiver complexity. The error probability performance is based on an approximation of the minimum Euclidean distance. A numerical power spectral density calculation for this particular SSB modulation in terms of the modulation index is presented. Reasonable tradeoffs in designing modulation schemes have been proposed using multi-objective optimization to ensure sizable improvements in bit error rate (BER), spectral efficiencies, and complexity without losing the property of being a SSB signal. Performance comparisons are made with known CPM schemes, e.g., Gaussian Minimum Shift Keying (GMSK) and Raised Cosine based CPM (RC).

Low-Complexity LMMSE–SIC Turbo Receiver for Continuous Phase Modulation, Based on a Multiaccess–Multipath Analogy

Low-complexity iterative reception of Continuous Phase Modulation (CPM) is addressed using Linear Minimum Mean-Square Error (LMMSE) filtering empowered by Soft Interference Cancellation (SIC). The transmitter emits a convolutionally encoded, true CPM signal with a constant envelope. The receiver exploits Laurent–Mengali–Morelli’s (LMM) decomposition to reduce the detection complexity, where the transmitted true CPM signal is approximated as a superposition of a small number of parallel Pulse Amplitude Modulated (PAM) and phase–encoded terms. Pulses and phase–encoded pseudo-symbols arising from the LMM decomposition are treated, respectively, as parallel Inter–Symbol Interference (ISI) channels and Multiple Access Interference (MAI) components. Hence the transmitted signal is regarded to inherently contain controlled ISI and MAI, which are equalized for at the receiver front-end using LMMSE–SIC filters. The receiver back-end comprises a serially concatenated turbo scheme encompassing a Soft Input–Soft Output (SISO) CPM detector and a SISO channel decoder. Simulations conducted on various CPM schemes show that the proposed receiver provides significant complexity reduction for a small performance penalty. Consequently, CPM waveforms with long pulses, which have traditionally been deemed infeasible due to the prohibitive complexity, can now be implemented employing the proposed receiver. Hence substantial spectral side-lobe compaction offered by long CPM pulses can be harnessed.

Spatially coupled turbo-coded continuous phase modulation: asymptotic analysis and optimization

For serially or parallel concatenated communication systems, spatial coupling techniques enable to improve the threshold of these systems under iterative decoding using belief propagation (BP). For the case of low-density parity-check (LDPC) codes, it has been shown that, under some asymptotic assumptions, spatially coupled ensembles have BP thresholds that approach the bitwise maximum a posteriori (MAP) threshold of the related uncoupled ensemble. This phenomenon is often referred to as threshold saturation, and it has sometimes very important consequences. For example, in the case of regular LDPC code ensembles, spatial coupling enables to achieve asymptotically the capacity for any class of binary memoryless symmetric channels. Since then, this threshold saturation has been conjectured or proved for several other types of concatenations. In this work, we consider a serially concatenated scheme which is the serial concatenation of a simple outer convolutional code and a continuous phase modulator (CPM) separated by an interleaver. Then, we propose a method to do the spatial coupling of several replicas of this serially concatenated scheme, aiming to improve the asymptotic convergence threshold. First, exploiting the specific structure of the proposed system, an original procedure is proposed in order to terminate the spatially coupled turbo-coded CPM scheme. In particular, the proposed procedure aims to ensure the continuity of the transmitted signal among spatially coupled replicas, enabling to keep one of the core characteristics and advantages of coded CPM schemes. Then, based on an asymptotic analysis, we show that the proposed scheme has very competitive thresholds when compared to carefully designed spatially coupled LDPC codes. Furthermore, it is shown how we can accelerate the convergence rate of the designed systems by optimizing the connection distributions in the coupling matrices. Finally, by investigating on different continuous phase modulation schemes, we corroborate the conjecture stating that spatially coupled turbo-coded CPM schemes saturate to a lower bound very close to the threshold given by the extrinsic information transfer (EXIT) area theorem.

Serially concatenated extended CPM scheme based on TDRSS

Tracking and Data Relay Satellite System (TDRSS) can meet the needs of Low EarthOrbit (LEO) satellite real-time transmission, but it also has large Doppler shift, transmission delay and channel fading. Continuous Phase Modulation (CPM), with excellent properties of both bandwidth and energy efficient, are very suitable for nonlinear and/or fading channels such as satellite channel due to the constant envelope nature. In this paper, the CPE in the SCCPM scheme is replaced by the designed ECE to construct a new scheme called SCECPM scheme, in order to enhance the robustness of the signal. Compared with previous SCCPM scheme, the proposed system shows an improvement concerning the convergence threshold and bit-error-rate (BER).

CPM modulation index estimation using LS and BLUE methods

SummaryIn this paper, we propose two methods for blind estimation of modulation index of full‐response binary continuous phase modulation (CPM) scheme. Most of previous works assume that there is a single sample for each symbol; thus, they cannot improve their performance when sampling rate is bigger than symbol rate. In our proposed methods, modulation index is estimated using samples of autocorrelation function of the received signal, which is a nonlinear function of modulation index. We propose Taylor expansion for approximating this nonlinear function by a linear function. Then, by choosing some samples of the autocorrelation function, we estimate the modulation index with the least square (LS) estimator. For decreasing estimation errors, in the second proposed method, we apply the statistical properties of the autocorrelation function estimation errors, to design the best linear unbiased estimation (BLUE) estimator. The numerical performance analysis in terms of mean‐squared error (MSE) and bit error rate (BER) shows that the proposed methods outperform the reference methods in accurate estimation of the modulation index.

Achievable Rate With 1-Bit Quantization and Oversampling Using Continuous Phase Modulation-Based Sequences

Analog-to-digital conversion with high resolution in amplitude has a relatively high energy consumption in communication systems. A promising alternative to reduce the energy consumption is 1-bit quantization. Considering such a receiver, we design and analyze continuous phase modulation (CPM) schemes, which are favorable because of their bandwidth efficiency and their constant envelope. In this context, oversampling with respect to the symbol duration is promising because CPM signals are not strictly bandlimited and because it reduces the loss in achievable rate caused by the quantization. The additional degrees of freedom brought by oversampling can be exploited by higher order modulation schemes. A lower bound on the achievable rate is computed based on an auxiliary channel law. In a further step, we optimize the input distribution with an optimization strategy based on a Markov source model. For a specific example, we give upper bounds on the achievable rate and present a state-machine representation for sequences which are reconstructible at the receiver. Finally, the proposed approach has the advantage of a constant envelope enabling an energy efficient transmitter design while achieving only a slightly lower 90% power containment bandwidth efficiency than existing methods with 1-bit quantization and oversampling.

On the Estimation of Modulation Index for Binary Full Response CPM Signals

This letter considers a full response binary continuous phase modulation (CPM) scheme with a single modulation index. Two estimators are proposed for estimating the modulation index of the underlying CPM scheme. The first estimator is based on the method of moments (MoM) that makes use of the auto-correlation function of the received signal whereas the second estimator is the best linear unbiased estimator (BLUE), which is based on an approximate linear model. A closed-form expression of the modified Cramer-Rao bound (MCRB) is also derived. The MoM estimator is developed only for the rectangular phase shaping functions, while the MCRB expression and the BLUE estimator are applicable to signals with arbitrary phase shaping functions. Numerical performance analysis in terms of mean-squared error and bit-error rate shows that the method of moments estimator performs better at low signal-to-noise ratio (SNR), whereas the performance of the BLUE is close to MCRB at high SNR.

Demodulation Method for Continuous Phase Modulation Signals Based on Least-Squares Method

Continuous phase modulation (CPM) schemes are attractive for telecommunication systems, which are limited in terms of the bandwidth and signal power due to their high spectral efficiency. In this paper we present a method for the demodulation of continuous phase modulation signals based on least-squares method (LSM). This method (CPM-LSM) is based on the optimal linear estimation of information symbols from the phase of the received signal by solving the overdetermined system of equations using the least squares method. Mathematical substantiation for the application of the proposed CPM-LSM method is presented. Preliminary experimental results of modeling using Geo-Mobile Radio (GMR-2) signals indicate that the method is robust with respect to carrier phase errors. Another feature of CPM-LSM method is that it does not use unique words (symbol patterns for amplitude/phase alignment). The latter fact is very important since unique words usually occupy up to twenty percent of transmitted packet size. The absence of unique words can substantially increase the information throughput.

From quantum physics to digital communication: Single sideband continuous phase modulation

Abstract In the present paper, we propose a new frequency-shift keying continuous phase modulation (FSK–CPM) scheme having, by essence, the interesting feature of single-sideband (SSB) spectrum providing a very compact frequency occupation. First, the original principle, inspired from quantum physics (levitons), is presented. Besides, we address the problem of low-complexity coherent detection of this new waveform, based on orthonormal wave functions used to perform matched filtering for efficient demodulation. Consequently, this shows that the proposed modulation can operate using existing digital communication technology, since only well-known operations are performed (e.g., filtering, integration). This SSB property can be exploited to allow large bit rates transmissions at low carrier frequency without caring about image frequency degradation effects typical of ordinary double-sideband signals.

Estimation of Modulation Index for Partial Response CPM Signal

Continuous phase modulation (CPM) is a power and bandwidth efficient modulation scheme used in cellular, personal, and satellite communications among other applications. If the modulation index of the CPM waveform used by the transmitter is unavailable at the receiver, serious performance degradation may occur. This paper investigates the problem of modulation index estimation for partial response continuous phase modulation schemes. Specifically, we propose two novel estimators for the CPM signal observed in an additive white Gaussian noise channel. A non-data aided method of moments (MoM) estimator based upon the fourth-order cumulants and a data-aided best linear unbiased estimator (BLUE) based upon an approximate linear phase model of the received CPM signal have been proposed. Modified Cramer-Rao lower bound is derived for the partial response CPM schemes to assess the performance of the estimators. We also perform numerical simulations to compare the mean-squared error (MSE) performance of the proposed MoM and BLUE estimators with previously proposed estimators in the literature. It is shown that the MoM estimator exhibits good MSE performance at low signal-to-noise ratio (SNR) while the BLUE estimator performs very well at high SNRs. Moreover, the proposed estimators have lower complexity than existing methods and are based upon non-iterative algorithms.

Exploiting the Fast Spectral Roll-Off of CPM Sidelobes to Improve Bandwidth Efficiency in Satellite Communications

Simple and efficient carrier-overlapping and interference-reduction techniques are addressed for frequency-division multiplexing–continuous phase modulation (FDM–CPM) schemes. CPM carriers are densely multiplexed (packed) in the frequency-domain, without leaving any guard bands, thus allowing frequency content in adjacent bands to overlap, so as to enhance the bandwidth efficiency. The intentional adjacent channel interference, introduced by carrier-overlapping during transmission, is combated at the receiver front-end using simple interference-reduction filters that are designed to exploit the fast roll-off of CPM spectral sidelobes. The receiver back-end is governed by a serially concatenated CPM iterative demodulation/decoding detector. Numerically optimal carrier-packing ratios are determined with respect to information-theoretic bounds. The presented method does not require cooperation among users, and is extended to QAM and PSK schemes as well. Bit error rate analyses show that the proposed non-cooperative receiver design facilitates bandwidth and energy-efficient communication for both the nonlinear and linear satellite channels, without resorting to multiuser detectors, and becomes an attractive solution when cooperation may not be feasible among users that are geographically spread-out.

Binary Continuous Phase Modulations Robust to a Modulation Index Mismatch

We consider binary continuous phase modulation (CPM) signals used in some recent low-cost and low-power consumption telecommunications standard. When these signals are generated through a low-cost transmitter, the real modulation index can end up being quite different from the nominal value employed at the receiver and a significant performance degradation is observed, unless proper techniques for the estimation and compensation are employed. For this reason, we design new binary schemes with a much higher robustness. They are based on the concatenation of a suitable precoder with binary input and a ternary CPM format. The result is a family of CPM formats whose phase state is constrained to follow a specific evolution. Two of these precoders are considered. We will discuss many aspects related to these schemes, such as the power spectral density, the spectral efficiency, simplified detection, the minimum distance, and the uncoded performance. The adopted precoders do not change the recursive nature of CPM schemes. So these schemes are still suited for serial concatenation, through a pseudo-random interleaver, with an outer channel encoder.

Performance improvement techniques for the DVB‐RCS2 return link air interface

SummaryThis paper presents performance improvement techniques for the second‐generation digital video broadcast return channel via satellite air interface, which can be used for supporting future demands for Tbit/s traffic requirements. In particular, we have investigated minimum‐shift keying (MSK) type of continuous phase modulation (CPM) waveforms by considering both single‐carrier and multi‐carrier transmission and single‐amplitude and multi‐amplitude signals, which improve the spectral efficiency. In addition, we consider frame timing and synchronization techniques, which make synchronization more accurate and robust. Our research has shown that the MSK single‐carrier frequency‐division multiple access (SC‐FDMA) outperforms the quadrature phase‐shift keying SC‐FDMA in terms of resilience to distortion with the performance gap increasing when the amplifier shows a milder distortion. The performance of a multi‐amplitude CPM scheme, based upon the superposition of two single‐amplitude MSK signals at the radio frequencies level, is also investigated. In comparison with other equivalent linear modulation schemes, performance evaluation results have been shown that the proposed multi‐amplitude CPM scheme significantly improves the spectral efficiency in the presence of adjacent channel interference. Finally, we have proposed a viable and efficient methodology, which enables reliable and accurate timing and frequency synchronization for the SC‐FDMA satellite return link. This involves a combination of global positioning system (GPS)‐based pre‐compensation of differential timing between user terminals, preamble detection in an integrated random access channel, and user channel frequency estimation based on repetitive symbols in the time domain. Copyright © 2015 John Wiley & Sons, Ltd.

Non-orthogonal Amplify and Forward Relay Selection Systems with Distributed Space–Time Trellis Coded Continuous Phase Modulation

Most of the works on cooperative systems with or without relay selection have focused on linear modulations such as phase shift keying and quadrature amplitude modulation. Whereas, continuous phase modulation (CPM) is a good alternative to these modulations due to its constant envelope property which enables us to use inexpensive and energy-efficient non-linear power amplifiers. In the literature, a few works are based on relaying systems with CPM. To the best of our knowledge, none exists with relay selection. In this paper, we propose single and multiple relay selection CPM schemes based on a new generalized relay selection criterion for non-orthogonal amplify and forward (AF) systems operating with various time sharing protocols. In particular, using the proposed criterion, the best relay or the best two relays over a set of four available relays is/are selected. Error performances of the non-orthogonal AF relay selection systems and their counterparts are compared over frequency non-selective quasi-static Rayleigh fading channels using Viterbi algorithm at the destination terminal. Our numerical results present superiority of the proposed non-orthogonal relay selection systems.

Receiver structure and estimation of the modulation index for tamed frequency modulated (TFM) signals

Tamed frequency modulation (TFM) is a spectrally efficient constant amplitude continuous phase modulation (CPM) scheme which can be simply realized by using a frequency modulator (FM). In the implementation the modulation index of TFM is calibrated to have a nominal value of 0.5, but due to temperature variations it can drift causing time varying phase jitter. In this paper we present novel algorithms and performance results to measure and control the modulation index in a coherent receiver based on the joint reduced state sequence detector (RSSD) and per-survivor processing (PSP) carrier phase estimation. The modulation index estimator measures phase transitions in the receiver and derives estimates by comparing the result to the coding rule of the TFM signal. The estimator has acquisition and tracking ability, and the current estimate can be used to replace the nominal index value. Our simulation results show that the proposed coherent receiver with the novel modulation index estimator has less than 1 dB performance degradation compared to around 4.5 dB exploiting only the PSP carrier phase estimation.

A Timing False Lock Detector for M-ary Partial-Response CPM

We consider a timing false lock detector for continuous phase modulation (CPM), which is needed for M-ary partial-response CPM schemes. Our approach maintains a running count of successive, simple, short-term false lock decisions, rather than conducting a single, long-term decision. Using a Markov chain model, we show that our scheme can provide accurate and rapid synchronization for capacity-approaching CPMs that operate at very low signal-to-noise ratios.

The Cramer-Rao Bound for Training Sequence Design for Burst-Mode CPM

In this paper, we study the Cramer-Rao bound (CRB) for continuous phase modulation (CPM) signals where frequency offset, carrier phase, and symbol timing are jointly estimated when transmitted over an additive white Gaussian noise (AWGN) channel. We consider a data-aided (DA) estimation scenario in which the estimator takes advantage of a known training sequence at the start of each burst. Thus, we first derive the joint CRBs as functions of a known training sequence and CPM parameters. By analyzing the CRB expressions, we propose the optimum training sequence for which the CRB is minimized. We show that the same training sequence is optimum for all three estimation parameters. Additionally, we compare the performance of the optimum training sequence with a random one by providing a closed-form expression for the unconditional CRB (UCRB) for symbol timing estimation of CPM signals. Comparing the UCRB and the CRB for the optimum training sequence reveals that a DA estimator with the optimum training sequence leads to significant gains in terms of the mean-square error of the estimation parameter when the underlying CPM scheme is non-binary and/or partial response.

Continuous Phase Modulation (CPM) Revisited: Using Time-Limited Phase Shaping Pulses

Conventional CPM signals employ information sequence with time-unlimited phase shaping pulse (PSP) to achieve power and bandwidth efficient transmission. On the contrary, information sequence using time-limited PSP was believed to produce power-wasting data-independent discrete spectral lines in CPM spectra, and was suggested to be avoided. In this paper, we revisit this problem and adopt the time-limited PSP to replace the one with time-unlimited, it turns out to have an alternative solution to the CPM scheme. We first modify the spectral computing formula for the CPM with time-limited PSP (or CPM-TL) from conventional CPM formula and show that the discrete spectral lines appeared in the power density spectrum of CPM-TL signals can be diminished or become negligible by appropriately choosing PSP. We also show that this class of CPM can use any real number modulation index (h) and the resultant trellis structure of CPM guarantees the maximum constraint length allowed by the number of states in the MLSD receiver. Finally, the energy-bandwidth performance of CPM using time-limited PSP is investigated and compared with conventional CPM with time-unlimited PSP. From numerical results we show that, under the same number of states in the MLSD receiver and bandwidth occupancy, this subclass of CPM could outperform the conventional CPM up to 6 dB coding gain, for h < 1, in many cases. key words: continuous phase modulation, time-limited phase shaping pulse, power spectrum, euclidean distance, constraint length, continuous phase encoder

The Study of Coded CPM Schemes

Continuous Phase Modulation (CPM) schemes belong to a class of constant-envelope digital modulation schemes, the constant-envelope nature of the CPM signals makes them robust for the nonlinear and fading channels, and very useful for the satellite and/or the mobile radio channels. Comparing to PSK modulation, CPM modulation can not only provide spectral economy, but also exhibit a “coding gain”. CPM can be decomposed into a Continuous Phase Encoder (CPE) followed by a Memoryless Modulator (MM), this allows many new coded modulation schemes of combination of convolutional encoder and CPM modulator to be possible, such as serially-concatenated CPM (SC-CPM), SC-CPM with Convolutional Codes over Rings, pragmatic CPM (P-CPM), Concatenation of convolutional endocder and extended CE（CCEC）, etc. Some simulations show that these new CPM schemes can offer superior performance.

Linear Diophantine Constrained Intra-Fix for Frequency Domain Equalization of Multi-h CPM

This paper considers the problem of constructing a symbol block to generate a cyclic multi-h continuous phase modulated (CPM) signal so as to permit frequency domain equalization (FDE) at the receiver. Like single-h CPM, the memory inherent in a multi-h CPM waveform requires the use of an additional segment, called an intra-fix, in each transmitted block. The intra-fix forces the transmitter state machine to regress to the state it had at the start of the block. The constraints on the symbols of the intra-fix, which ensure above condition, are shown to be a set of Linear Diophantine Equations (LDEs). Three different methods are proposed for finding the symbols of the intra-fix, such that the length of the intra-fix is minimized. The last two methods connect the problem of intra-fix insertion to the problem of trellis termination of the tilted phase. This connection enables us to state and justify that existing bounds established on the length of the terminating sequence are effective for the length of the intra-fix. We observe that multi-h CPM schemes typically require a shorter intra-fix, as compared to single-h CPM schemes having similar modulation parameters. We apply the proposed procedure to a dual-h CPM scheme.