Binary Continuous Phase Research Articles

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.

An Improved Data-Aided Linear Estimator of Modulation Index for Binary CPM Signals

This letter considers the estimation of modulation index for binary continuous phase modulated (CPM) partial response signals. The actual value of modulation index in low-cost implementations turns out to be different than the nominal value used at the transmitter, leading to severe performance degradation. One possible solution is the deployment of an estimation algorithm at the receiver. The proposed data-aided best linear unbiased estimator (BLUE) is based upon a linear model approximation of the differential phase of pre-averaged CPM signal. Theoretical analysis of the variance of the estimator is presented to establish its improved performance. Simulation results also corroborate significant improvement of the proposed estimator at lower signal-to-noise ratio (SNR) values as compared to existing estimators, while retaining the linear bound performance at high SNRs. We show that the bit error rate (BER) performance at low SNRs is also improved when the modified BLUE estimator is deployed at the receiver.

Reconstruction of Finite-Alphabet Block-Sparse Signals From MAP Support Detection

This paper addresses finite-alphabet block-sparse signal recovery by considering support detection and data estimation separately. To this aim, we propose a maximum a posteriori (MAP) support detection criterion that takes into account the finite alphabet of the signal as a constraint. We then incorporate the MAP criterion in a compressed sensing detector based on a greedy algorithm for support estimation. We also propose to consider the finite-alphabet property of the signal in the bound-constrained least-squares optimization algorithm for data estimation. The MAP support detection criterion is investigated in two different contexts: independent linear modulation symbols and dependent binary continuous phase modulation (CPM) symbols. The simulations are carried out in the context of sporadic multiuser communications and show the efficiency of proposed algorithms compared to selected state-of-the-art algorithms both in terms of support detection and data estimation.

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.

Noncoherent Multiple-Symbol Detector of Binary CPFSK in Physical-Layer Network Coding

It is well known that the binary continuous phase frequency shift keying (CPFSK) signal is power efficient with constant envelope, because it allows transmission with inexpensive and energy efficient nonlinear amplifiers. Recently, physical-layer network coding (PNC) using the binary CPFSK is considered as a potentially attractive solution to the dual needs of high throughput and high power efficiency in two-way relay wireless network. However, most recent studies on PNC have assumed that the carrier phases of the two transmitted signals arriving at the relay are ideally aligned. In fact, the carrier phase offset between the two node-signals always exists in practice. In this letter, a noncoherent multiple-symbol detector of binary CPFSK signals with unknown carrier phase offset in physical-layer network coding is proposed, which is based on the log-likelihood ratio test. It is shown by simulation that the algorithm with five symbol observation interval achieves 6.7 dB performance gain, compared with only one symbol observation interval.

Low-Complexity Detection of Binary CPM With Small Modulation Index

Binary continuous phase modulation (CPM) with modulation index $h = 0.5$ can be approximated by a linear modulation, which leads to a low-complexity serial receiver. By reconstructing CPM signals generated with a small modulation index into equivalent CPM signals with modulation index $h = 0.5$ , a low-complexity detector (LCD) for binary CPM with small modulation index is proposed. The complexity of the resulting detector is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. In addition, the detector can generate appropriate metrics for the soft decision decoding, which is desirable in a coded CPM system.

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.

Robust Detection of Binary CPMs With Unknown Modulation Index

We consider soft-output detection of a binary continuous phase modulation (CPM) generated through a low-cost transmitter, thus characterized by a significant modulation index uncertainty, and sent over a channel affected by phase noise. The proposed detector is designed by adopting a simplified representation of a binary CPM signal with the principal component of its Laurent decomposition and is obtained by using the framework based on factor graphs and the sum-product algorithm. It does not require an explicit estimation of the modulation index nor of the channel phase and is very robust to large uncertainties of the nominal value of the modulation index. Being soft-output in nature, this detector can be employed for iterative detection/decoding of practical coded schemes based on a serial concatenation, possibly through a pseudo-random interleaver, of an outer encoder and a CPM modulation format.

A system-theory approach to decompose CPM signals into PAM waveforms

In 1986, Laurent showed that binary continuous phase modulated (CPM) signals can be decomposed into pulse amplitude modulated (PAM) waveforms. This result, later extended to multilevel CPM signals by Mengali and Morelli, has attracted much attention, especially for the design of simplified receivers. The paper proceeds from the premise that the decomposition into PAM waveforms is not unique, and follows a systemtheory approach that leads to a natural formulation. First, the CPM modulator is represented by a nonlinear part (encoder) followed by a linear part (bank of PAM modulators).The two parts are then rearranged with the aim of obtaining real-valued continuous PAM waveforms and to reduce their number. Several classes of decompositions arise with this approach, each of which admits an infinite number of different decompositions of the same CPM signal, among which the Laurent and MengaliMorelli results appear as special cases. Throughout the paper, a systematic use is made of the Kronecker product, which appears to be the natural tool for dealing with CPM decompositions and for expressing results in a very simple form.

Phase structures impact the rheological properties of rennet-casein-based imitation cheese containing starch

The dynamic rheological and microstructural properties of rennet-casein-based imitation cheeses containing various concentrations of potato starch were investigated using a stress-controlled rheometer and confocal laser scanning microscopy. The influence of added starch on the size of the oil droplets in the imitation cheeses was also examined. Imitation cheeses with 0–15% protein replaced by starch were processed in a Rapid Visco Analyser (RVA) at 90 °C for 10 min at a shear rate of 800 rev/min and were then evaluated using oscillatory shear measurement and a temperature sweep (20–90 °C). The storage modulus ( G′) of the rennet casein imitation cheeses increased abruptly at added starch concentrations >4%. In the temperature range 20–90 °C, tan δ of the imitation cheeses decreased with increasing starch concentration and was <1 at added starch concentrations >4%. A binary continuous phase consisting of a protein phase and a starch phase was observed in systems containing >4% starch, whereas the starch was dispersed in the protein matrix as small particles of irregular shapes at added starch concentrations ≤4%. As the dispersed phase, the size of the oil droplets increased with starch addition in the imitation cheeses. The marked increase in G′ and the reduction in tan δ may be attributed to the formation of a binary continuous separated phase structure in imitation cheeses containing added starch that is driven by thermodynamic incompatibility between rennet casein and starch.

Simplified receiver design for STBC binary continuous phase modulation

Existing space-time codes have focused on multiple- antenna systems with linear modulation schemes such as phase- shift keying and quadrature amplitude modulation. Continuous phase modulation (CPM) is an attractive scheme for digital transmission because of its constant envelope which is needed for power efficient transmitters. Recent research has shown that space-time coded CPM can achieve transmit diversity to improve performance while maintaining the compact spectrum of CPM signals. However, these efforts mainly combine space- time coding (STC) with CPM to achieve spatial diversity at the cost of a high decoding complexity. In this paper, we design space-time block codes (STBC) for binary CPM with modulation index h = 1/2 and derive low-complexity receivers for these systems. The proposed scheme has a much lower decoding complexity than STC CPM with the Viterbi decoder and still achieves near-optimum error performances.

A New Finite Series Expansion of Continuous Phase Modulated Waveforms

The Laurent Decomposition expresses any binary single-h continuous phase modulated (CPM) signal as the summation of a finite number of pulse amplitude modulated (PAM) waveforms, and the resulting signal space is so constructed that the waveform can usually be synthesized with a reasonable degree of accuracy by using only the ldquomainrdquo component pulse. This derivation has been very useful for reduced complexity demodulation of binary CPM signals. Subsequent to Laurent's work, it was shown that commensurate expressions could be obtained for multilevel and multi-h CPM, but with an exponential increase in the total number of PAM component pulses in the signal representation. In this paper, we show that by expressing a CPM signal in its equivalent binary multi- form, we can derive a generalization of Laurent's result for the general class of such waveforms that use noninteger modulation indices. In this new signal representation, there is a clearly identifiable data-dependent ldquomainrdquo expansion pulse during each symbol interval which carries most of the signal energy. As in the Laurent Decomposition, the number of terms in this decomposition is only dependent on the CPM signal memory.

Space-time trellis code design with binary CPM

Binary continuous phase modulation (CPM) is considered with space-time trellis codes (STTCs) for multiple-input multiple-output systems. Single-h CPM with rectangular, raised cosine and half cycle sinusoid is considered. The upper bound on the minimum product distance of this signalling scheme is determined over a quasi-static Rayleigh fading channel. Based on the rank and determinant criterion, best STTC/CPM combinations are identified for two transmit and an arbitrary number of receive antennas.

Supplementary Proof for “Exact and Approximate Construction of Digital Phase Modulations by Superposition of AMP” by P. A. Laurent

In this letter, we supplement the derivation in Laurent's paper by mathematically proving that combining binary continuous phase modulation (CPM) signals in different bit durations results in the decomposed CPM expression consisting of a set of continuous amplitude-modulated pulse functions.

Blind self-noise-free frequency detectors for a subclass of MSK-type signals

Frequency offset due to Doppler shift and/or oscillator instabilities degrade the receiver performance. A family of frequency detectors for frequency offset estimation and compensation in digital receivers is introduced. The proposed detectors are best suited for frequency offset compensation of a subclass of binary continuous phase modulation with h=1/2 that includes modulation schemes with nonnegative frequency pulses. For the considered modulation schemes, the modulation-induced self-noise term is absent from the variance of the frequency estimate. The estimator is nondata- and nontiming-aided and its estimation range is either half or a quarter of the bit rate (R). With larger frequency offsets, the estimators that have a /spl plusmn/R/2 estimation range introduce a frequency ambiguity of R that is of no relevance to the performance of a differential detection based receiver.

A decision-feedback phase-tracking receiver for continuous phase modulation

In this letter, a new recursive structure of a decision-feedback (DF) phase-tracking receiver for continuous phase modulation (CPM) is derived. This receiver uses the previously detected symbols to continuously estimate the initial phase in the current symbol and thus makes optimum coherent detection. The theoretical and simulation analyses of the error performance are given. It is shown that the BER performance of binary continuous phase frequency-shift keying (2CPFSK) and raised cosine (2RC) with a small modulation index is very close to the ideal bound, and the BER performance of GMSK is better than any previously known noncoherent detection.

Reduced-state trellis and its decoding for full-response CPM

A new reduced-state trellis and Viterbi decoding for binary full-response continuous phase modulation (FRCPM) are derived. The theoretical and simulated error-rate performance of the reduced-state trellis decoding is presented. It is shown that the reduced-state trellis decoding of FRCPM with small modulation index can provide almost the same error-rate performance as the original-state trellis decoding at high signal-to-noise ratio.

The noncoherent least squares phase difference sequence estimator for continuous phase modulation

The noncoherent least squares phase difference sequence estimator (LSPDSE) is presented for continuous phase modulation in an additive white Gaussian noise (AWGN) channel. The applications to Gaussian minimum shift keying (GMSK) and binary continuous phase frequency shift keying (2CPFSK) are considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Laurent's representation of binary digital continuous phase modulated signals with modulation index 1/2 revisited

In order to simplify modulator and demodulator structures, the composition of binary continuous phase modulations (CPMs) by the linear superposition of impulses as developed by Laurent (1986) is advantageous. Based on differential encoding of the binary data sequence, a novel CPM modulator concept for modulation index 1/2 is presented. >

On the availability of trellis decoding schemes for continuous phase FSK signals employing limiter discriminator detection

AbstractAlthough a trellis‐coded modulation scheme has been applied to multilevel PSK or QAM signals, its application for the continuous‐phase FSK (CPFSK) with the limiter‐discriminator detection has not been investigated well and the coding gain associated with it has not been obvious yet. In this paper, using a linear approximation, we have designed modulation parameters of this scheme. We have also executed the exact computer simulation and made clear the problem to obtain the actual coding gain as well as to increase them. Furthermore, utilizing the intersymbol interference caused by the IF filter, which greatly deteriorates the bit error rate (BER) performance in this scheme, we have proposed a sequence estimation scheme using the Viterbi algorithm. In this scheme, the sending signals are those of the binary continuous phase FSK. Through computer simulations, we have made clear that large improvements of BER really exist. The sequence estimation scheme is considered to work better than the trellis encoded scheme when considering the BER performance and the complexity of transmitter and receiver.