Multi-h Signals Research Articles

Symbol Timing Estimation with Multi-h CPM Signals

A new symbol timing estimation algorithm for Multi-h CPM signals is proposed. It is an extension to an existing non-data aided symbol timing estimator that is only for Single-h CPM signals. A reduced-complexity scheme of proposed algorithm is introduced with negligible performance losses. Performance in AWGN channel is assessed by computer simulation, and the simulation results show that the proposed algorithm is suitable for full response and partial response formats. Meanwhile, it has a good performance and is not sensitive to the carrier frequency

PAM Decomposition of<tex>$M$</tex>-ary Multi-<tex>$h$</tex>CPM

It is known that any multilevel continuous phase-modulated (CPM) signal with a single modulation index can be exactly represented by a sum of pulse-amplitude modulated (PAM) waveforms. In this paper, we show how multi-h CPM signals can also be represented in this manner. The decomposition is presented in general terms as a function of the alphabet size, modulation indexes, and phase pulse of the CPM scheme. The number of pulses required to exactly construct the signal is shown to increase over that previously given for single-h schemes; this increase is in proportion to the number of modulation indexes. We propose an approximation which significantly reduces the number of signal pulses and which minimizes the mean-squared error for an arbitrary set of modulation indexes. We show that this approximation can have two objectives: 1) to reduce the number of pulses in the same manner as has been proposed for single-h schemes; and/or 2) to reduce the number of multi-h pulses; we also show the conditions where this latter objective is most practical. We compare this minimum mean-squared error approximation with another method which was recently proposed for CPM. We also give numerical results on detection performance which demonstrate the practicality of the proposed approximation.

Hybrid multi-h/multi-T continuous phase frequency shift keying

A class of hybrid multi-h/multi-T CPFSK signals is obtained by combining multi-h and multi-T signalling techniques. Hybrid signals are constructed by varying both the modulation index and the symbol duration simultaneously. Numerical results show that hybrid multi-h/multi-T signals perform significantly better than ordinary multi-h and multi-T signals.

Nonlinear multi-h phase codes for CPFSK signaling

Two novel trellis-coding techniques, called nonlinear multi-h signaling and nonlinear asymmetrical multi-h signaling, which achieve higher constraint length than ordinary multi-h signals, are introduced with CPFSK signals. In contrast to ordinary multi-h signaling where the modulation index is changed at the end of every symbol interval, nonlinear multi-h signals are constructed by changing the modulation index based on the previous symbol, and the current symbol interval. A class of nonlinear asymmetrical multi-h signals, which change the modulation index based on the current symbol too, is then constructed by extending nonlinear multi-h signals and combining them with asymmetrical multi-h signals. Binary full-response nonlinear multi-h and nonlinear asymmetrical multi-h CPFSK signals are constructed and analyzed. Minimum Euclidean distances and spectral properties of these signals are calculated at different phase states and various selected modulation index patterns. Numerical results indicate that nonlinear multi-h and nonlinear asymmetrical multi-h signals achieve significantly higher distance than other existing multi-h formats reported in the literature. >

Correlatively encoded multi-h signals

A correlatively encoded multi-h CPFSK signaling technique which performs significantly better than partial response multi-h signaling is introduced. Numerical results presented for binary 2-h signaling indicate that correlatively encoded 2-h signals can achieve significant gains over both constant h signals and partial response 2-h signals.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multi-T signalling with coded CPFSK modulation

The multi-T realisation of combined trellis coded/multi-h, and combined correlatively encoded/multi-h signals is considered. Numerical results indicate that the multi-T signals produce minimum distances similar to, and generally higher than, those of multi-h signals.

Combined coded/multi-h CPFSK signaling

A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi-h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Practical Receiver Structure for Multi-h CPM Signals

Multi- h schemes are bandwidth-efficient CPM signaling formats which offer means of coding without explicit redundancy. However, the required (optimal) receiver structures tend to be very complex [1], [4], [8] requiring a large number of filters of correlators. Here a reduced complexity receiver for the joint estimation of M -ary data, carrier phase, and symbol timing is realized through the use of an approximate representation of the likelihood function. Evaluation of receiver performance indicates a fraction of a decibel degradation in coding gain and almost no loss in synchronization performance.

Easy calculation of power spectra for multi-h phase-coded signals

The letter presents an easy method which allows a fast calculation of the spectra of M-ary multi-h phase-coded signals under very general conditions for the shape of the modulating pulse.

Erratum: Easy calculation of power spectra for multi-h phase-coded signals

Erratum: Easy calculation of power spectra for multi-h phase-coded signals