Partial Response Continuous Phase Modulation Schemes Research Articles

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.

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.

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 integers for AWGN 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.

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>

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.

Probability of error analysis of digital partial response continuous phase modulation with noncoherent detection in mobile radio channels

An analysis is presented of noncoherent detection of constant-envelope digital partial-response continuous-phase modulation (PRCPM) in fast Rayleigh fading that characterizes land mobile radio channels. Closed-form expressions for the probability of error are derived for limiter discriminator detection, and both 1- and 2-bit differential detection. Numerical results are presented for cases of practical interest to researchers and designers of land mobile radio systems. The expressions derived for the probability of error are general and can be used for all PRCPM schemes. >

Performance evaluation of differential and discriminator detection of continuous phase modulation

Recently, bandwidth efficient constant-amplitude digital modulation schemes have also been shown to be power efficient when coherent detection is used. Partial-response continuous phase modulation (CPM) schemes are within this class. In some applications noncoherent detection is preferred. The performance of CPM systems is analyzed for differential and discriminator detection. An additive white Gaussian channel is assumed. The detectors make symbol-by-symbol decisions. The considered schemes are M-ary with an arbitrary modulation index and pulse shaping over several symbol intervals. The performance is analyzed by means of error probability expressions. The IF filter for the detectors is optimized within a special class of filters to give good performance. The differential detector is also analyzed on a Rayleigh fading channel. The fading is assumed to be slow. The IF filter is also optimized on this channel. Simulated error probabilities for discriminator detection with a Viterbi detector are also presented both for the Gaussian and the Rayleigh fading channel. The discriminator detector making symbol-by-symbol decisions is simulated on the Rayleigh fading channel. It is shown that partial-response CPM schemes with good performance can also be obtained with noncoherent detectors.